Construction of buildings on expansive soils 9781000108200, 1000108201, 9781000130935, 1000130932, 9781000151350, 1000151352, 9781003078937, 1003078931

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CONSTRUCTION OF BUILDINGS ON EXPANSIVE SOILS

GEOTECHNIKA 5

Selected translations of Russian geotechnicalliterature

CONSTRUCTION OF BUILDINGS ON EXPANSIVE SOILS

E.A. SOROCHAN

AA. BALKEMA/ROTTERDAM/BROOKFIELD/1991

Translation of: Stroitel' stvo sooruzhenii na nabukhausbchikh gruntakh, Stroiizdat, Moscow, 1989

© 1991 Copyright reserved

Translator

Dr. A. Jaganrnohan

Technical Editor

Dr. G. Venkatachalam

General Editor

Ms. Margaret Majithia

ISBN 90 6191 115 X

Distributed in USA & Canada by: AA. Balkema Publishers, Old Post Road, Brookfield, VT 05036, USA

Preface Amongst the main thrust areas envisaged for the economic and social de­ velopment of the USSR during 1986-1990 and the subsequent period up to the year 2000, considerable emphasis has been given to large-scale building con­ struction including renovation of existing buildings and structures. For this, the immediate task is that of improving the efficiency and quality of construction, which can only be achieved by accelerating the pace of scientific and techno­ logical achievements. All these issues have to be considered for construction of buildings on expansive soils. The accumulated experience in building con­ struction over the past several years has shown that the specified standards (particularly SNip* 2.02.01-83) provide adeq~ate reliability for maintenance of buildings and structures. However, these have several shortcomings for the work of laying foundations on expansive soils, necessitating the expenditure of addi­ tional resources to ensure that the buildings constructed on such soils are stable and suited to normal maintenance. Hence, investigations have been carried out during the past few years which have enabled more precise expressions for the process of expansion and contraction of soil, development of methods to study the properties of expansive soils, to identify the relationships governing the in­ teraction between such soils and the foundations laid on them, to suggest more accurate methods of predicting deformations and to determine the optimal load to be transmitted to the foundations. The second edition of this book provides results of recent investigations, examples illustrating the design of foundations of buildings constructed on expansive soils as well as the operational experience of such buildings. In particular, special attention has been given to the behaviour of pile groups in expansive soils, behaviour of piles subjected to lateral load, nature of pressure distribution on retaining walls etc. The author is grateful to Prof. Z.G. Ter-Martirosyan for his valuable critical review of the manuscript.

* SNip--Construction norms and regulations.

Contents

Page Preface

V

1 Laws Governing Expansion and Contraction of Argillaceous

Soils

1

1. Relationship between Expansion and Swelling Moisture Content and

Composition and State of the Soil 1

2. Relationship between Expansion and Pressure. Structural Cohesion

of Soil during Swelling 13

3. Lateral Pressure during Soil Swelling 31

4. Swelling of Soil Wetted by Various Kinds of Fluids 36

40

5. Contraction of Expansive Soils

2 Principles Governing Deformation of Soil Mass and Foundations

during Soil Expansion 1. Deformation of Soil Mass during Artificial Wetting

2. Deformation of Soil Underlying Foundations during its Wetting 3. Zones and Phases of Deformation during Swelling

4. Lateral Deformations and Pressures acting on Protective Structures

43

43

51

56

during Soil Swelling 62

5. Change in Volume of Soil Mass due to Climatic Factors 69

6. Computation of Soil Heave due to Climatic Factors 75

7. Computation of Displacements of Flexible and Elastic Foundations

and Redistribution of Contact Pressure during Soil Swelling 100

3 Engineering Geological Investigations of Regions with Extensive

Occurrence of Expansive Soils 1. Engineering Geological Properties of Expansive Soils

2. Laboratory and Field Investigations on Expansive Soils 4 Design of Structures on Expansive Soils 1. Basic Principles of Design

2. Deformation of Structures Built on Expansive Soils 3. Computaticm of'Heave of Soil Mass and Footings during Soil

Swelling

108

108

123

133

133

137

159

viii 5 File Foundations on Expansive Soils

1. Special Features of Piles on Expansive Soils 2. Investigation of Deformation and Bearing Capacity of Pile Groups

on Expansive Soils 3. Experimental Investigation of Single Piles and Pile Foundations

under Lateral Loading 4. Design of Pile Foundations 5. Installation of Pile Foundations 6 Methods of Construction on Expansive Soils

1. Preparation of Soil Base on Expansive Soils 2. ConstrUctional and Water-protection Measures 3. Techno-Economic Comparison of Alternative Methods of

Construction 4. Maintenance of Buildings Constructed on Expansive Soils and

Methods of Rehabilitation of Deformed Structures REFERENCES

177

177

217

237

254

266

273

273

286

290

291

297

1

Laws Governing Expansion and

Contraction of Argillaceous Soils

1. Relationship between Expansion and Swelling Moisture Content and Composition and State of the Soil

One of the characteristic properties of argillaceous soils is their multiphase state. The specific features of each phase in isolation and its physico-chemical and mechanical properties determine the overall properties of the soil which in­ clude expansion (increase of volume with addition of moisture) and contraction (decrease of volume with reduction of moisture). The solid phase is formed both during the process of evolution of the argillaceous soil and during the subsequent period of its historical-geological existence. It forms the principal constituent of argillaceous soil and exclusively determines its properties. Argillaceous soils consist of a mixture of various elementary particles of different sizes, shapes and surface characteristics. The term elementary particles implies primary and sec­ ondary particles in the form of separate minerals or their fragments, monocrystals and amorphous compounds. Argillaceous soil particles consist of-various miner­ als such as feldspar, mica, montmorillonite, illite, kaolinite, halloysite etc. The crystallo-chemical structure, chemical composition and other features of miner­ als are responsible for determining such specific features of argillaceous soils as peptisation, adsorption etc. The proportion of minerals or the preponderance of one or the other mineral groups exerts a decisive influence on the physico-chemical properties of soils. The most important properties of minerals, in particular those which determine the nature and degree of interaction of the soil with water, are their crystal lattice structure and their ion exchange capabilities. The lattice structures of argillaceous minerals include two elements-alumina and silica. Depending upon tbe combination of the individual layers, two types of minerals are formed: one in which the lattice consists of a single layer of silica and the other in which the lattice consists of one layer of alumina and two layers of silica. The first type is characteristic of the clay mineral kaolinite which is capable of so a binding

2 assemblages of minerals (elementary particles) that the exchange cations and polarised molecules are unable to penetrate into the inner plane of the crystal. In contrast to kaolinite, montmorillonite has a lattice consisting of two outer layers of silica and a single layer of alurnina. Thus assembl~ges of montmoril­ lonite particles are not well bound. Charged molecules of water are able to pene­ trate between such assemblages, forming a water film whose thickness increases with a decrease in the binding strength between them. Hence the characteris­ tic feature of this mineral is intracrystalline swelling which may lead to a total disintegration of such groups. Besides these minerals there. are others of interme­ diate structure, such as illite, for which penetration and accumulation of water molecules between assemblages of particles is negligible. Let us consider several specific features of minerals which exert an influence on the process of swelling during their interaction with water: (a) a large number of uncompensated free electric charges appearing as a result of displacement of one of the atoms in the lattice by another, are present on the outer surface of an assemblage of minerals; (b) depending on the type of mineral, the assemblage may have different cations possessing a positive or negative degree of hydration, which might be exchangeable, difficult to exchange, partially exchangeable, or even totally non-exchangeable; (c) the crystal lattice may differ in bond strength between assemblages of particles, e.g., strongly btf¥ed, weakly bonded or mod­ erately bonded; (d) the surface layer of the crystaltfue lattice may have structural groups OH which are capable of combining with. water molecules through the hydrogen bond. The clay fraction plays an essential role during the interaction between soil and water. A combinati0n of individual particles and aggregates leads to the formation of a structural system. A solid phase structural system implies ·an order or arrangement of simple particles and aggregates in loose soil despite the influence of gaseous or liquid phases formed during sedimentation, diagenetic and post-diagenetic processes. Investigations have shown that structure exerts a significant influence on the mechanical properties of the soil, particularly its strength. With an increase in temperature, the properties of water may not only change but may appear in a new form during interaction with the materials dissolved in it or during its contact with insoluble bodies, i.e.; the solid phase. These features result from the physical and chemical properties of the water itself. Thus; water molecules have a ·l!!rg~ interdipole electrostatic effect, even reaching 80% of the Van-der-Waal f~e. On: the other hand, absence of electrostatic neutrality leads to a condition"whereby water molecUles (dipoles) may be drawn towards ions which have an inherent uncompensated electrical charge, forming hydrate films. The force resulting from hydration isthat due to the attraction of polar molecules of water caused by the action of electrostatic forces which, in turn, leads to· mutual polarisation and advent of induction and dissociation effects. The properties of water determine the osmotic phenomenon occ~ing in soils. The

3 special properties of water molecules which cause them to be bound to soils are: their ability to form a hydrogen bond, absence of electrical neutrality leading to hydration of ions and the presence of osmotic phenomenon. The gaseous phase may occupy up to 50% of the entire volume of the soil. The quantity depends on the type of soil and reduces with an increase in clay content. Investigations of the gaseous component of soils have established the influence of free gases on the volume change of a soil and consequently on the change in its properties. The oyerall amount of gases contained in the soil depends on the mineralogical composition, moisture content and dispersion of soils as well as the type of exchangeable cations. Because of their high polarity, the molecules of water vapour and water are strongly attracted towards the surface of the soil, where they displace the adsorbed molecules of other gases. During interaction of an argillaceous soil with water (or any other fluid) the latter swells, i.e., its volume increases. This may be explained by the following. Because of the special structure of a clay mineral its free surface carries a con­ centration of uncompensated charges, resulting in attraction of water molecules. Adsorption takes place due to the action of intermolecular forces (electrostatic, dispersive and inductive) at the surface of the solid portion of the soil and the liquid leading to a reduction in the free energy surface. Under the action of the forces described above a hydrate layer is formed at the surface of the particles. Water molecules are not only bonded to the ions of the crystalline lattice but also to the exchangeable cations located at the outer surface of the particles. The first layers of water molecules are oriented towards the surface of the particles and establish their own force field which together with the molecular surface layers draw the water molecules towards the hydrated layer. The process of multilayer sorption continues until all these combined forces are balanced by the forces of dissociating water molecules. The hydrate layers that form tend to displace the soil particles. Separation of particles is governed by the emergence of a 'wedge effect' of thin films at the point of contact between· soil particles. Thus, the swelling of a soil is associated with the formation of a hydrate film around its particles. The separation of particles and consequent soil swelling is a result of the interaction between the two phases-solid and liquid. Separation of particles occurs due to the wedge pressure developed during the formation of a liquid layer at the surface of the particles. The hydrate layer formed is not only due to the action of free ions of the clay mineral, but also the exchangeable cations distributed over the surface layer. Swelling caused by the formation of water layers around particles or aggregates is termed 'interparticle swelling'. Another phenomenon caused by swelling of the soil is that of increase in the space between assemblages of minerals. This is caused by the bonding of water molecules in the interspace between assemblages of minerals and is designated as 'intracrystal swelling'. Thus, according to the data of Gorfman and Bilke, who used the X-ray diffraction method in their studies, when minerals come

4 into contact with water the distance between groups of particles successively increases with increase in moisture content: Moisture content,% Spacing between groups of particles, A

10

13.9

19.5

24.2

29.5

36.3

41.8

59.0

11.2

12.1

13.4

14.6

15.1

15.6

15.7

17.8

. When soils are moistened by pore water, the osmotic phenomenon may /occur, which leads to the attraction of water molecules towards the dissolved · materials. Increase in the volume of water in the void spaces is accompanied by a simultaneous displacement of particles and, in such case, one observes an increase in volume, i.e., swelling. The particles lying at the surface and the exchangeable cations participate in the processes occurring at the dividing line between the two phases and dic­ tate the extent of attraction of water molecules. The type of exchange cations determines the strength of 'cross-linkage' between the mineral lattice and the elementary particles. Substitution of the sodium ion for other exchangeable ions weakens the bond between these particles, i.e., leads to peptisation of the soil. Because of this, water is easily adsorbed over the entire surface of the parti­ cles, pushing them further apart and thereby causing the soil to swell. Thus V.V. Okhotin observes that the difference in the extent of swelling of soils satu­ rated with sodium and calcium is explained by the difference in the structure of the soil under investigation. In the first case the individual particles are separated from each other while in the second they appear in the form of fairly well-knit aggregates. Another reason for the different degrees of swelling of soils with dissimilar· exchangeable groups is the ability of ions to enter a state of dissociation. The separated univalent cations leave the surface of the particles and because of this additional adsorption centres become available to link the water molecules. In ad­ dition, the released cations are themselves capable of attracting water molecules and forming a hydrate film around themselves. During the swelling process a unique system consisting of water films and rings develops in the soil, leading to the formation of menisci. The presence of menisci is governed by the capillary phenomena which affect the progress of the swelling process. The presence of capillary water within closed pores leads to the appearance of additional forces which essentially tend to reduce the accumulation of moisture. Thus expansion of soil occurs during its interaction with water (or other fluids) and is governed by primary and secondary phenomena. Primary Phenomena: These comprise (a) the process of penetration and bonding of water in the void space between groups of particles in the crystalline lattice of the mineral. The occurrence of such a phenomenon is entirely governed

5

by the crystal chemical structure of the lattice and is characteristic for specific types of clay minerals. (b) The process of bonding of water flowing at the line of demarcation between the solid and liquid phases. This is a surface phenomenon occurring at the external surface of all clay minerals during their interaction with water. (c) Processes occurring in the pore fluid in the soil. This is an osmotic phenomenon observed at high concentrations of the pore fluid where a significant concentration gradient may develop when the soil is wetted with water. Secondary Phenomena: These accompany the primary phenomena and con­ sist of (a) hydration of exchangeable cations which dissociate during the forma­ tion of an adsorbed layer at the surface of a particle; and (b) capillary effects which appear due to molecular surface phenomena at the interface between the solid and liquid phases. The attraction of water molecules towards the surface or the free adsorption centres leads to an internal wedging pressure governed by the separation of soil particles. Accumulation of water in a soil does not predetermine the process of swelling. It is necessary that there be a pressure build-up which is capable of increasing the space between phase boundaries and overcoming the resistance to such displacement. Consequently, swelling is the process of increase in volume of the soil that occurs during its interaction with a fluid. It is governed by an increase in moisture content and development of pressure in the water films present at the contact points between particles and aggregates (or within groups of particles). The composition and state of the soil differently influence the magnitude and nature of the swelling process, i.e., the laws governing soil swelling. While studying the laws of swelling one must be aware of the influence of the method of experimentation as well as instrumentation on the experimental data. In­ vestigations have shown that the value of relative swelling E8 w obtained from the Vasil'ev apparatus are 1.5 to 1.8 times greater than those obtained from a consolidation apparatus and 2 to 2.3 times greater than those from the triaxial compression apparatus M-2. The height of the specimen also has an effect on the magnitude of Esw· Thus tests conducted on specimens of disturbed structure of Sarmatsk clays showed that when the specimen height was increased 2.5 times, the magnitude of swelling Esw decreased nearly 1.5 to 1.7 times. Tests conducted on disturbed structure specimens in the Vasil 'ev apparatus showed no change in the magnitude of relative swelling when wetted from either the bottom or the top. These studies on the laws governing swelling of soils were carried out using data obtained under identical conditions. The influence of the particle fraction less than 0.005 mm in size on pastes prepared from Sarmatsk and Kirnmeriisk clay was investigated with an initial moisture content of 0.32 and density of 1.32 g/cm3 when-transferring a load of p = 0.05 MPa to the ground. Tests were also conducted on specimens prepared from naturally occurring Khvalynsk clay (Fig. 1.1). These tests showed that (a) with an increase in the clay fraction an increase in the magnitude and rate

6

of swelling occurred; and (b) the influence of the fraction less than 0.005 mm in size on swelling was governed by the type of soil.

Fig. 1.1. Variation of swelling

Esw

as a function of the fraction of less than 0.005 mm in size for clays.

1-Khvalynsk; 2-Sarmatsk; 3-Kimrneriisk.

The exchangeable groups (quantity and composition of the exchangeable cations) determine the appearance of the primary and secondary phenomena during the interactioq,of soil with water and distinctly influence the magnitude and intensity of swelling. Type of cation Swelling,%

Na Mg 29 26

Ca K Fe 23 21 18

H

15

The difference in the amount of swelling of Na-clays and Ca-clays is ex­ plained by the specific features of hydration of these cations as an integral part of the surface layer of the crystal lattice of these minerals. Firstly, depending upon the type of exchangeable cations the bond strength between groups of particles in the lattice varies, decreasing with univalent cations. Secondly, the possibility of dissociation of cations is strongly dependent upon their valency. In the presence of potassium and hydrogen ions the swelling of soil is less than in the case of divalent anions. This is because potassium and hydrogen ions cannot hydrate and since they are located at places where isomorphic substitution takes place, they do not attract water molecules. Furthermore, potassium ions penetrate the void space between groups of particles, strengthening the lattice and thereby reducing the penetration of water into the interspace between groups of mineral particles. The adsorptive capacity of a soil affects its swelling (Table 1.1). Increase of the adsorptive capacity leads to an increase in the amount of bonded water · (when substitution takes place on a large scale the number of uncompensated valencies increases).

7 Table 1.1. Swelling of clays as a function of adsorptive capacity Swelling, %, for adsorptive capacity, in mg equivalent per 100 g of dry soil

Type of clay

Maikopsk Sarmatsk Kimmeriisk

10 -

12.

-

-

3.5

4.0

-

18 5

22

-

30 8.5

28 7.0

5.5

The concentration of salts in the pore fluid affects swelling. The gradient arising out of the difference in the concentration of salts in the pore fluid and the wetting agent leads to an osmotic accumulation of water in the interspace between particles. The extent to which this phenomenon affects the magnitude of swelling was evaluated on pastes of Sarmatsk clays, which were washed with distilled water until the dissolved salts were completely eliminated and were then wetted with solutions of various concentrations (Table 1.2). Further, the specimens were prepared with NaCl solutions with concentrations of 1.5, 10, 20 and 30 g/l which were then wetted with distilled water. The initial moisture content of the specimens was 32% and the initial density was 1.32 g/cm3 . The specimens were tested at a pressure of 0.1 MPa. Table 1.2. Swelling of soil as a function of concentration of pore fluid or wetting solution Concentration ofNaCl, g/1 in pore fluid

Relative swelling of soil when wetted with distilled water, %

Concentration of wetting solution, g/litre

Relative swelling of specimen washed with distilled water and wetted with NaCl solution, %

0 1 5 10 20 30

4.8 4.9 5.1 5.4 5.7 6.2

0 1 5 10 20 30

5.7 5.6 5.4 5.1 5.0 4.9

An analysis of these results reveals the influence of the osmotic phenomenon on swelling of soil. An increase in salt concentration in the pore fluid to 30 g/l led to an increase in the magnitude of swelling. When the soil was wetted with a highly concentrated solution, swelling reduced to some extent since, in this case, the motion of water·molecules was ·apposed. The dependence of swelling on density of specimens of disturbed and undis­ turbed structures is shown in Fig. 1.2. Specimens of disturbed structures were tested in the Vasil'ev apparatus while the undisturbed ones were tested in the

8 consolidation apparatus. The initial moisture content was the same for specimens of different densities. Thus, the specimens of disturbed structure from Sarmatsk clays had a moisture content of 0.35 while for those of undisturbed structure this was nearly 0.30. Correspondingly, for the specimens from Khvalynsk clays the moisture content was 0.08 and 0.27. It is evident from the Figure that the rela­ tionship between these quantities is linear for specimens of different structures and type of wetting agent. When the density of the soil was increased, swelling increased due to increase in the number of solid particles and consequently the total surface of the solid phase. It was ascertained that there exists an 'initial den­ sity of swelling' at which swelling does not occur. For the Sarmatsk clays this corresponded to 0.95 g/cm3 for disturbed structures and 1.05 g/cm3 for undis­ turbed structures. For the Khvalynsk clays the corresponding values were 0.85 and 1.0 g/cm 3 . The lower limit of density which characterises the initiation of swelling is not constant but depends on the structure (disturbed or natural), type of wetting agent (in particular, on the dielectric constant), the initial moisture content and the percentage of clay fraction.

Fig. 1.2. Swelling of soil as a function

of its density Pd·

1-Khvalynsk clay of disturbed structure; 2-Khvalynsk cll;ly wetted with acetone; 3-Khv.alynsk clay in undisturbed condition; 4-Sarmatsk clay of disturbed structure; 5-Sarmatsk clay of undis­ turbed structure. : I

The magnitude of swelling is inversely ,Proportional to the initial moisture content of the soil (Fig. 1.3). With an inqfease in initial moisture content w in the specimen, swelling decreases rapidly. Thus for the Khvalynsk clays an increase in the moisture content from 0.05 to 0.1led to a decrease in the relative swelling by only 0.03. However, when the initial moisture content was large, this decrease was quite significant. For instance, for w = 0.15 swelling was 13% while for w = 0.40 the specimens did not swell when wetted. Consequently, the initial moisture content is one of the basic factors governing the magnitude

9

of swelling of soils. In such cases there exists a limiting moisture content, the 'swelling moisture content', at which swelling does not occur.

Fig. 1.3. Swelling of clays as a function of their moisture content. !-Aswan clay; 2-Khvalynsk clay of undisturbed structure; 3-Khvalynsk clay of disturbed structure.

Thus the initial state of the soil significantly influences the overall magnitude of swelling. Evaluating the combined effect· of these factors, it was established that the effect of density on swelling is practically independent of the initial moisture content. However, a tendency towards large variations in swelling with increase in density was observed. On the other hand, when the soil density was high the initial moisture content in a specimen had a greater effect on swelling than in the case of low density specimens. Consequently, one may select such a soil composition for which its swelling lies within desired limits (Fig. 1.4) or is completely absent since such a state may be achieved by varying both these factors. Density and moisture content influence the nature of deformation with time due to swelling. This is illustrated by the swelling of a soil with disturbed structure in Fig. 1.5 (Table 1.3). Table 1.3. Characteristics of specimens before and after wetting Expt.

No. 7 12 60 62

w,%

Pd• g/cm3

Sr

Esw

Wsw•%

Before test 8.4 8.4 3.0 2.9

1.17 1.45 1.12 1.45

Pd· g/cm3

Sr

Wsw -w,%

0.97 1.00 0.92 0.95

47.6 41.0 23.0 9.3.

After test 0.17 0.26 0.57 0.88

0.10 0.23 0.08 0.09

56.0 49.4 53.0 38.2

1.07 1.17 1.04 1.32

10

Fig,

L4.

Swelling of soil as a function of density and moisture content

Fig. 1.5. Swelling of soil as a function of time. Experiment nos. 7, 12, 60 and 62.

Tests indicated that while the initial state of the soil (moisture content and density) influenced the fmal magnitude of swelling, the nature of its variation with time was influenced by the extent to which the pores were inundated with water (degree of saturation) Sr. Thus for specimens with Sr varying from 0.17 to 0.57 the swelling process proceeded rapidly while for specimens with Sr = 0.88 this process considerably slowed down. An experimental correlation was

11

established for the intensity of swelling J = ( Esw, tfc.sw), which is the ratio of swelling after t hours of wetting to its total magnitude, as a function of the degree of saturation Sr of the soiL Thus for a specimen with Sr = 0.2, swelling after 24 hours of its wetting was found to be 90% of the total while for specimens with Sr = 0.8 the swelling was only 60%. In the case of a specimen with sr < 0.6, swelling stabilised 3 days after its initial wetting; in specimens with a greater degree of saturation stabilisation did not occur. The slow rate of swelling and the. prolonged duration of this process in specimens of a high moisture content was c.hJe to the substantial thickness of the hydrate film around the particles, resulting in weaker force of attraction between water molecules. With a smaller moisture content in the soil, i.e., when the pores are not completely saturated, the particles are covered with a thin film. Moreover, there are many voids through which free water may migrate. In such a case better conditions prevail for wetting of soil particles. As a consequence the process of attraction of water into a given volume accelerates, leading to an increase in the rate of swelling. All the aforesaid holds true within certain specific limits of density since with its increase the number of contact points become greater and consequently there may be some deviations from the established correlations. The rate of swelling is likewise governed by the structure of the soil. For specimens of undisturbed. structure in which water-resistantbonds exist, this pro­ cess may proceed extremely slowly compared to specimens of disturbed. struc­ tures. Thus, specimens of natural Khvalynsk clays swelled far more slowly than those with a disturbed structure. For instance, in the case of specimens with a degree of saturation Sr = 0.7 (moisture content 0.21), swelling of specimens of undisturbed structure was 45% of their total volume while swelling of identical specimens of disturbed structure was as much as 70%. A well-defined relationship between soil swelling and moisture content at the liquid limit wL and the plastic limit wp is not yet available. However, for all the swelling soils that were studied, a tendency towards an increase in the magnitude of swelling was observed with an increase in these limits. (Table 1.4). Table 1.4. Relative swelling of soil at different values of .., p .and .., L Type of clay Khvalynsk

wp

-

E:sw

0.50 0.60

0.12 0.17 0.06 0.17

0.40 0.75

0.03 0.06 0.02 0.06

0.25 0.32

Sarmatsk

WL

0.25 0.40

Note: The value of E:sw was obtained at p = 0.05 MPa.

12 It was established that with an increase in soil density the swelling moisture content decreases. This is due to the fact that the number of contact points between particles increases with an increase in density, with the thickness of the water film at these contact points being smaller than that at the free surface of the particles. The quantity of water bound in the soil is greatest when the soil particles do not touch each other. In such a case the thickness of the water film surrounding the particles becomes uniform. Wherever there is contact between particles the film thickness reduces, which means that the total water bound in the clay decreases. As the number of contact points increases the available free surface of particles decreases, leading to reduced amount of bound water. Consequently, with an increase in density the amount of water bound in the soil reduces, i.e., the denser the soil the lesser the swelling moisture content. With an increase 'in initial moisture content of a specimen, its swelling moisture content decreases. The relationship between swelling moisture content of clays and pressure (Fig. 1.6) is close to E8 w = f (p) in nature, i.e., with an increase in pressure the swelling moisture content decreases. The maximum decrement in moisture is observed in the pressure range of 0-0.1 MPa. Thereafter swelling moisture decreases less rapidly and at a pressure of 0.3 MPa it practically remains con­ stant. A comparison of the relationships E8 w = f(p) and w 8 w = f(p) shows that the maximum soil expansion is caused by the action of the peripheral weakly bonded water layers.

Fig. 1.6. Variation of swelling moisture content as a function of pressure for clays: 1-Maikopsk; 2-Khvalynsk.

The slow variation of swelling moisture may be explained by the fact that with an increase in load the thickness of the water film decreases only at the

13 contact points, whereas at the free surface of the particles, i.e., the surfaces constituting the pore space, it remains constant and is independent of the load applied on the specimen. The water trapped in the pore space forms the major part in the total water balance. Table 1.5. Characteristic moisture content ratios of clays Type of clay Khyalynsk Sarmatsk Kimmeriisk Maikopsk Aral'sk Quaternary

B

A

in Vasil'ev apparatus 1.48 1.30 1.50 1.25 1.58 1.57

Note: A= W 8 w/WP and B =

0.71 0.75 0.88 0.76 0.70 0.67

B

A

in consolidation apparatus 1.34 1.10 1.12 1.10 1.45 1.47

0.65 0.67 0.76 0.66 0.65 0.62

B

A

Field tests 1.37 1.10 1.10 1.07 1.30 1.28

0.61 0.63 0.64 0.66 0.58 0.58

Wsw/WL

It should be emphasised that increase in moisture content is observed when the soil does not expand, i.e., when E8 w = 0 the moisture content of soil after it is wetted will be greater than that under natural conditions. Consequently, swelling moisture content is a quantity which defmes the quantity of moisture which is attracted by the soil and held within it by internal forces, i.e., it is a specific amount of bound water held by the expansive soil. The relationship between swelling moisture determined by various test apparatuses as well as field tests and that at the plastic and liquid limits for various clays is given in Table 1.5. These data show that with an increase in the plasticity index the magnitude of B decreases. Further, it was observed that an extremely stable relationship exists between W 8 w and wL.

2. Relationship between Expansion and Pressure. Structural Cohesion of Soil during _Swelling Investigations conducted on argillaceous soils have shown that when soils are wetted, two types of deformations may occur when various external loads are applied, namely swelling or subsidence. Depending upon the magnitude of these deformations all argillaceous soils may be classified as expansive subsi­ dent, expansive-subsident and normal. Argillaceous soils for which the relative expansion with no load exceeds 0.04 may be classified as swelling soils. Tests were conducted in a consolidation apparatus and a triaxial compres­ sion apparatus M-2 to obtain a quantitative relationship between swelling and pressure. The soil was wetted after its subsidence due to load had stabilised and the resultant expansion was measured. Tests were conducted for pressures rang­

14

ing from 0.05 to 0.7 MPa. Some of the specimens were wetted without applying any external load. These results were utilised to obtain a relationship between swelling and pressure (Fig. 1.7).

Fig. 1.7. Relationship between swelling of clays of undisturbed structure and pressure. 1-for Maikopsk clay; 2-for Sarmatsk clay; 3-for Khvalynsk clay.

It can be seen from Fig.1.7 that these relationship are non-linear in nature. With an increase in pressure, swelling decreases. The swelling decrea!.ed sharply in the pressure range of 0 to 0;05 MPa-for Khvalynsk and Sarmatsk clays by 6% and for Maikopsk soil by 9%. If the decrease in swelling is taken to be 100% over the pressure range 0-0.7 MPa for Khvalynsk clays and 0-0.45 MPa for Sarmatsk clays, then the decrease in swelling constitutes 70 and 80% when the pressure is raised from 0-0.1 MPa. Consequently, the major portion of swelling occurs due to the formation of a hydrate film around the soil particles consisting of peripheral layers of weakly bonded water molecules. Small external pressures up to 0.1 MPa exceed the wedging pressure of hydrate films. As the external pressure increases, the decrease in swelling proceeds at much slower rate and at pressures exceeding 0.1-0.15 MPa this relationship becomes almost linear. For these varieties of soils increase of pressure from 0.2 to 0.4 MPa led to only 1-2% decrease in swelling. For the Sarmatsk soils practically no swelling was observed at a pressure of 0.4 MPa. The same was true for the Maikopsk soils atp = 0.6 MPa, i.e., in this case the external pressure was completely balanced by the internal forces. This pressure is taken to be the swelling pressure of soil of a given state. In this case the pressure of the hydrate film does not increase when the soil is wetted. Table 1.6 shows the average values of relative swelling at various external pressures for several genetic types of expansive soils. The relative swelling was determined in a consolidation apparatus on specimens of undisturbed structure.

a

15

The external pressure not only affects the total deformation during swelling but also the nature of this process. In the absence of an external load, swelling proceeds rapidly and stabilisation of swelling commences later than when it is present. Table 1.6. Relative swelling of soils Relative swelling, %, at various pressures, MPa

Type of clay

Kimrneriisk (Kerch') Aral'sk (Egmak) Quaternary Meotiche (Kerch')

0

0.05

0.1

0.2

0.3

10

3.1

2

1.2

0.5

12

4.1 2.3 3.5

2 1.1 2

1.3 0.3 1.3

0.9

6 9

0.4

0.4

0.5

Tests on Khvalynsk soils of undisturbed structure were carried out in an M-2 apparatus. The specimens were set up in such a way that stratification was oriented horizontally. In one group of tests loading was only vertical with loads of different magnitudes with no horizontal pressure (crxy = 0). Fig. 1.8 shows the nature of variation of swelling as a function of time. These curves show that with vertical pressure there is a significant decrease in vertical deformations whereas the decrease in horizontal deformations is far less. When stratification was oriented vertically, horizontal deformations considerably exceeded the ver­ tical deformations. During this the volumetric swelling remained the same as for the specimens with horizontal orientation of stratification. Tests on specimens under multiple stress conditions showed that most of the deformation during swelling occurs in the vertical direction while the horizontal deformation could be practically ignored. Here the vertical deformations remain the same as in the absence of any horizontal pressure (Fig. 1.9). Let us consider the equilibrium conditions for forces during load tests on soils where E8 w = 0. When the soil is wetted the thin films of water at the points of contact between soil particles develop a wedge pressure Pr. Two sys­ tems of opposing forces, i.e., internal and external, counterbalance this pressure. The external forces are due to the pressure transmitted to the soil such as the pressure p from the foundations or Pg due to the soil's own weight. The internal forces are due to the resistances of the internal bonds in the soil, namely the structural bond of the soil during swelling Pie and the capillary forces Pp- The external forces may be variable while the internal forces remain constant for a given type of soil. Thus for equilibrium conditions of a soil when wetted, i.e., at E8 w = 0 one may write P + Pg +Pie +Pp - Pr

= 0.

. . . (1.1)

16

Fig. 1-.8. Variation of relative swelling and moisture content of soil (w, %) as a function of time (d). a-swelling of soil in vertical direction; b--swelling of soil in horizontal direction; c-volumetric expansion of soil; 1 to 5-for vertical loading at pressures of 0, 0.05, 0.1, 0.15 and 0.2 MPa; 6-same, at pressure of 0.05 MPa with vertical orientation of complex structure.

When the thickness of the specimen under consideration is small, it may be assumed that Pg = 0 and further assuming Pp = 0 during wetting of soil we have . . . (1.2) p 0 =p+pg =pr -Pie =Psw· Thus swelling pressure is seen to be the difference between the wedging pressure of the hydrate films of water and structural cohesion of the soil during swelling. It is well known that the initial dispersion of soil due to free expansion leads to a drop in the swelling pressure. This feature has an influence on the working mechanism of various types of buried structures. Thus, when a retaining wall is displaced the horizontal pressure caused by swelling would decrease, improving the working conditions of the wall. An analogous behaviour is observed in laterally loaded piles. Table 1.7 ~bows the experimental data obtained for the effect of degree of dispersion of soil on the decrease of swelling pressure for two different varieties of clays. In order to determine the swelling pressure with different initial degrees of dispersion, soil specimens of undisturbed structure were placed in the consoli­ dation apparatus and were moistened with water. During this the locking device was set in such a way that the press could rise to some specific height equal

17

Fig. 1.9. Variation of relative swelling and soil moisture (w, %) as a function of time (d) under multiple stresses. a-swelling of soil in vertical direction; b-swelling of soil in horizontal direction; c-volumetric expansion of soil; 1-at

C1z

= 0 MPa and

CJr

= 0.01 MPa; 2-at

C1z

= 0.05 MPa and

CJr

=

0.05 MPa; 3-at CJ z = 0.05 MPa and CJ r = 0.1 MPa; 4-at CJ z = 0.1 1\IIPa and CJ r = 0.05 MPa; 5-at C1z:::: 0.15 MPa and CJr = 0.05 MPa; 6-at C1z = 0.1 MPa and CJr = 0.1 MPa.

to 0.02 to 0.08 tinies. the initial height of the specimen, i.e., a controlled free expansion C: 8 w was carried out. After soaking the soil for two weeks the press was loaded in steps of 0.025 MPa. The swelling pressure was taken to be that load at which compressive defo~tions commenc;ed. In this way both the mag­ nitudes of swelling and their corresponding swelling pressures were determined

18 Thble 1.7. Characteristics of experimentally investigated clays I Type of clay

Moisture content,

Density, gm/cm3 Mineral component,

Degree of saturation,

w

Coefficient of porosity, e

Dry Soil component,

Ps

Soil component, p

Khvalynsk soil: disturbed structure

2.76

1.35-1.65

1.28-1.40

0.05-0.20

1.0-1.15

0.12-0.51

Khvalynsk soil: undisturbed structure

2.74

1.8-1.9

1.33-1.45

0.32-0.35

0.89-1.06

0.89-0.99

Blanket layer of disturbed structure

2.70

1.52-1.79

1.38-1.55

0.10-0.15

0.74-0.96

0.3-0.4

Sr

Pd

by the above-described method (Fig. 1.10). The swelling pressure increased with a decrease in initial dispersion of clay particles in the specimen. It was demon­ strated that the swelling pressure, obtained by tests on specimens with initially dispersed states, equals the external pressure at which the magnitude of swelling equals the degree of dispersion. The swelling pressure of soils, both in an undisturbed as well as dispersed state, is governed by its initial density and moisture content. When the initial moisture of soil of one particular density is increased, swelling pressure decreases for the same amount of preliminary swelling. Increasing the initial density of a soil with constant moisture content leads to an increase in. the swelling pressure. Fig. 1.11, a shows the relationship between swelling pressure and the degree of preliminary dispersion of Khvalynsk soils of disturbed structure with an initial moisture content w = 0.10. The most significant decrement in swelling pressure occurred for small preliminary dispersion of soil particles. Thus for specimens of density Pd = 1.38 g/cm3 with an initial dispersion of 3%, the swelling pressure decreased from 75 to 46 kPa, i.e., by 40%. Linear relationships between swelling pressure of a soil and its initial density were obtained for different degrees of initial dispersion of its clay particles. This linearity between swelling pressure and initial density is conserved even for a dispersed state of the soil. However, the slope of this straight line with respect to the absd.ssa decreases with an increase in preliminary dispersion '11· Fig. 1.12 show.s the relationship between the ratio of swelling pressure at various '11 to the pressure developed by the soil in the absence of swelling de­ formation (Piw / p sw) and the ratio of preliminary soil dispersion to its free swell, ('11/Esw)· The nature of this relationship is influenced by the soil struc­ ture. However the initial state of soils of disturbed structure had little effect on this relationship over the range of densities and moisture contents investigated.

19

Fig. 1.10. Relationship between swelling and swelling pressure for initially dispersed Khvalynsk soil with moisture content of 0.1 and density of 1.38 g/cm3 • 1, 2, 3, 4 and 5-correspond to initial soil dispersions of 0.01, 0.025, 0.031, 0.041 and 0.061.

Curve 1 in Fig. 1.12 represents the results of tests on Khvalynsk clays of dis­ turbed structure with different initial densities and moisture contents as shown in Table 1.7. The experimental points lie quite close to one single curve irre­ spective of their corresponding initial densities and moisture contents. It can be seen that the nature of distribution of experimental points is also similar for a soil cover of disturbed structure. The mineralogical composition of the soil has an influence on the above­ described relationship between the swelling pressure ratio and the preliminary dispersion ratio. Thus it is clear from Fig. 1.12 that for surface clay the effect of dispersion on the decrease of swelling pressure is more than that for the Khvalynsk clay. The mineralogical composition of the former consisted of 23% montmorillcmite, 63% illite and 14% kaolinite while the latter contained 72%

20

Fig. 1.11. Relationship between (a) swelling pressure and degree of preliminary dispersion and (b) swelling pressure and initial density of soil.

1, 2 and 3-for Khval}'l!-sk clay of disturbed structure with corresponding densities of 1.38,

1.33 and 1.28 g!cm3 •

Fig. 1.12. Relationship between the ratios (P~w!Psw) and (11/Esw)· 1-for Khvalynsk clay; 2-for surface clay.

21 illite and 28% kaolinite. For soils of natural structure the governing principles differ. Thus the ini­ tial density of the soil shows a significant influence on the relationship be­ tween swelling pressure and preliminary dispersion of soil. Tests on the Khva­ lynsk clays of undisturbed structure with initial densities of Pd = 1.33, 1.45 and 1.56 g/cm3 and moisture content w = 0.28 (curve 3) and w = 0.32--0.35 (curves 1 and 2) showed that soil dispersion had a more pronounced effect on decrease of swelling. pressure in denser soils than in lighter ones. Thus for a soil with a preliminary swelling of 5% of its free swelling volume, the swelling pres­ sUre decreases compared to those in the absence of soil dispersion were as fol­ lows: 70% for clays with Pd = 1.56 g/cm3 ; 20% for clays with Pd = 1.45 g/cm3 and 8% for clays with Pd = 1.33 g/cm3 . Decrease in swelling pressure with preliminary dispersion of the soil may be, explained by the action of adsorptive, capillary and osmotic forces which lead to a thickening of the diffused hydrate films and disjunction and weakening of the molecular forces of cohesion in the soil particles. It is well known that fractional dispersion (expressed as a percentage of the initial density of the soil) increases with greater compaction of the soil. The relative decrement in swelling pressure,' which is a linear function of the initial density of the soil, is manifested in dense soils. During these experiments, the density of soils of disturbed structure was found to lie within such limits that its decrease during swelling compared to initial density was insignificant and hence change in initial density of the soil showed no noticeable influence on decrease in pressure with soil dispersion in the range covered by the experiments. The relationship between swelling pressure ratio and the degree of preliminary dispersion of soils of disturbed and undisturbed structure may be represented in the form of an exponential function. The swelling pressure for soils which might be characterised by preliminary dispersion of soil particles, is determined from the expression 'Tl -(A -Bx- C) Psw e Psw•

. . . (1.3)

where 'T] is the preliminary dispersion; p is the swellirig pressure for constant volume of the specimen ('f) = 0); x is the ratio of preliminary dispersion to free swell of the soil, Eswf A, B and C = A- 1 are parameters determined experimentally. / The parameters in equation (1.3) were selected from a programme devel­ oped for this purpose. The correlation coefficient and the root mean square deviation were determined simultaneously. The data obtained from tests on the Khvalynsk soils of disturbed structure with various densities and moisture con­ tents were utilised to plot a curve described by equation (1.3) with coefficients A = 1.08; B = 2.63 and C = 0.08. The correlation coefficient of this curve with experimental data is seen to be 0.995 while the root mean square deviation does not exceed 0.05. This confirms the fact that density and moisture content of

22

Fig. 1.13. Relationship between increment in moisture content ~w of Khvalynsk clay of 1.28 g/cm3 density and its preliminary dispersion 'll· I, 2, 3 and 4-at initial moisture contents of 0.05, 0.1, 0.16 and 0.18.

soils of disturbed structure do not affect the nature of the relationship between swelling pressure and possible preliminary dispersion of the soil over the range of parameters considered here. The results of tests on surface clay (Table 1.8) were also treated similarly. Table 1.8. Values of coeffidents A., B and C for determining swelling pressure Type of clay Khvalynsk soil of disturbed structure. Surface clay of disturbed structure. Khvalynsk soil of undisturbed structure: Pd 1.33 g/cm3 Pd 1.45 g/cm 3 Pd 1.56 g/cm3

= = =

c

A

B

1.08

2.63

0.08

1.013

4.44

0.013

1.39 1.014 1.001

1.25 4.24 9.80

0.39 0.014 0.001

It may be noted that the exponential index B depends upon the type of soil (for disturbed soils) and density (for soils of undisturbed structure). With increase of soil density the magnitude of coefficient B increases logarithmically. Fig. 1.13 shows the relationship between increment of moisture content of soil and its initial dispersion. These data show that in the case of preliminary dispersion up to 2 to 8%, the increment in moisture remains constant. During this the smallest value of dispersion corresponds to soil with the least density and high moisture content and the greatest value to the much denser soil with negligible moisture content.

23 Tests conducted to study the effect of an addition of highly compressible polymer materials to the soil on its swelling pressure showed that such addi­ tives are helpful in compensating swelling pressure and causing a significant decrease in its magnitude. Foam plastic in the form of chips was utilised as the compensating additive while porolon was used as the bed at the bottom of the consolidation apparatus. The foam plastic chips were added to the soil while it was being packed into the apparatus in the ratio of 2-4% of the volume of the odometer ring. The swelling pressure Psw,m of specimens with additives in the soil and that of the control specimen without additives was determined by measuring the travel of the locking device. Results of these tests are shown in Table 1.9. It is evident from Table 1.9 that the addition of a highly compressible mate­ rial to the soil reduces the swelling pressure by 24-62% and a resilient cushion in the form of a layer of porolon at the bed almost entirely compensates it. These data show that the introduction of compressible additives into the soil may be utilised in practice to reduce swelling pressure for structures buried in the soil. Table 1.9. Swelling pressure of natural soil and soil with additives Type of soil

Percentage of additive with reference to volume of ring of test apparatus

Natural soil: Pd = 1.32 g/cm3 ; w = 0.15 Soil with additives: (i) with addition of foam plastic: p = 0.017 g/cm3

p = 0.0666 (ii) with addition of porolon in the form of a 5.3 mm layer at the bed of the apparatus.

Swelling pressure Psw' kPa

Psw,m

Psw

0

66.0

e e

21.5

Decrease inPsw•%

50.0 42.0

0.758 0.636

24.4 36.4

37.5 25.0

0.568 0.379

43.2 62.1

0.09

91.0

6.0

From the foregoing discussion one may draw the following conclusions: -During preliminary dispersion of soil the swelling pressure decreases due to soil expansion;

24

-The relationship between relative swelling pressure and the degree of preliminary dispersion of soil is described by an exponential function; -The initial density and moisture content in soils of disturbed structure did not affect this relationship over the range of variation of these- quantities in the present experiments. The coefficients appearing in the expression describing the approximating curve are constant for soils of a given mineralogical composition; -For soils of natural structure increase of initial density leads to an ex­ tremely large decrement in the swelling pressure when preliminary dispersion is possible compared to the decrease in pressure in the total absence of soil deformation due to swelling; -Introduction of highly compressible additives into the soil helps to de­ crease the swelling pressure. It was found that a linear relationship exists between swelling pressure and free swell of a soil (Fig. 1.14, a). This was established from tests conducted on ten types of argillaceous soils. It was shown that the coefficient of this relationship k = PswfEsw is a linear function of the moisture content wL at the liquid limit (Fig. 1.14, b). With a knowledge of the free swell of a soil and moisture content at its liquid limit one may obtain the swelling pressure with the help of the following expression Psw =

where

~

~WLEswi

. . . (1.4)

is a coefficient equal to 0.6 kPa.

Fig. 1.14. Relationships between (a) swelling pressure and free swell and (b) the coefficiep.t

k = Psw/Esw and the moisture content at the liquid limit wL.

25 The swelling pressure depends not only on the type and composition of the soil but also on its state, i.e., its moisture content and density (Fig. 1.15). With an increase in initial moisture content, the swelling pressure of a soil decreases. During this the density of the soil has practically no influence on the nature of this relationship. Thus for a moisture content of w = 0.05 the swelling pressure Psw =50 kPa (at Pd = 1.28 g/cm3 ) while for w = 0.19 the pressure Psw = 25 kPa, i.e., it decreases by two times. In contrast to this relationship the swelling pressure increases with an increase in density. Thus at Pd = 1.28 g/cm3 the swelling pressure Psw = 25 kPa (at w = 0.2) while at Pd = 1.38 g/cm3 , Psw = 60 kPa, i.e., it increases by 2.4 times.

Fig. 1.15. Relationship between (a) swelling pressure and moisture content and (b) swelling pressure and density. 1, 2 and 3-at corresponding densities of soil of 1.38 [1.33*] and 1.28 g/cm3 ; 4, 5, 6 and 7-at corresponding moisture contents of 0.05, 0.10, 0,15 and 0.20 respectively.

Let us examine the influence of a disturbed structure of soil on its swelling. It was established that soils of one and the same type having identical material composition, dispersion, initial moisture content and density have different mag­ nitudes of swelling depending upon their structure. For instance, specimens of disturbed structure Khvalynsk clay of 1.3 g/cm3 density swelled about 2.5 times more than those of undisturbed natural structure. Table 1.10 shows the values of free swell for various types of soils of disturbed and undisturbed structure and the ratio between these quantities. The data presented in the table confmn the existence of structural bonds in the soils. The magnitude of structural cohesion may be determined experimentally based on the following assumptions. When the soil structure is disturbed, the internal irreversible bonds in the soil which inhibit its swelling are practically *Omitted in the Russian original-General Editor.

26 Table 1.10. Swelling of soils of disturbed and undisturbed structure

Type of clay Khvalynsk Sarmatsk Aral'sk

Free swell%

Disturbed Undisturbed structure structure 22 18 21.5

12 10 11.5

Esw,b Esw

1.83 1.80 1.86

destroyed. Hence specimens from soils of undisturbed structure swell to a less extent compared to those of disturbed structure. This decrease in swelling is equivalent to the action of pressure which is equal to the structural cohesion of the soil. Utilising the relationship €sw = f(p) obtained from tests on natural soil specimens and knowing the magnitude of free swell of disturbed soil, one may determine Pie· For this purpose let us extend curve 2 (Fig. 1.16) until it intersects the line AB passing through the point B whose ordinate corresponds to the free swell of a specimen of disturbed structure. Thereafter, dropping an ordinate through point A onto the extension of the abscissa, we obtain the intercept which specifies Pie· Thus the magnitude of Pie is equivalent to such an external pressure as should be applied to a disturbed structure specimen so that its observed deformation equals the free swell of a specimen of undisturbed structure (as given by the diagram of Esw - p). Table 1.11 shows the values of Pie and Pis (structural strength) and their ratio for various types of expansive soils.

Fig. 1.16. Method for determining the structural cohesion of soils during swelling. 1-for a specimen of disturbed structure at p = 0; 2-for specimen of undisturbed structure at various values of p; 3-variation of structural cohesion during swelling.

The magnitudes of structural cohesion and structural strength obtained from the compression curve depend upon the state of the soil. The greatest value of

27 Table 1.11. Magnitude of structural cohesion and structural strength Pressure, MPa Type of soil

Pi)P; 8 Pie

P;s

0.07-{).09 0.05-{).07 0.075-{).10 0.05-{).06 0.04-{).05

Khvalynsk Sarmatsk Aral'sk Kimmeriisk Yursk

0.120 0.185 0.130 O.o75 0.130

0.71 0.70 0.67 0.73 0.35

structural cohesion is observed in specimens of natural structure. Specimens of disturbed structure-strata, possess practically no structural cohesion, i.e., internal forces which inhibit swelling· are absent. Consequently, as the volume of the specimen increases during swelling the structural cohesion of the soil decreases. This decrease is caused by the destruction of crystallisation bonds and reduction in molecular attraction. A formula for determining the wedging pressure Pmp during swelling of wetted specimens up to E. 8 w was obtained based on experimental correlations. While deriving this expression the conditions assumed were as follows: at p = Psw• E. 8 w = 0 and at E. 8 w = E. 8 w max• p = 0. During the determination of structural cohesion it was assumed 'that Pie decreases with an increase in E. 8 w and tends to zero as E. 8 w ---+ oo. Then Pr

= Pice-'lj!Esw

+ Psw

[1 -

E.~weaEsw(l-E~w)]

'

. . . (1.5)

where E.~w = E. 8 w/Esw max (here E. 8 w is swelling of soil; E. 8 w maxis the maximum swelling of a specime~ with no load); 't)J and a are coefficients which account for the change in the structural cohesion and swelling pressure. The relationship between swelling and volumetric moisture content of a specimen is given by I Esw

Esw

= =

(

W 08 w-

(wsw-

w)/(1 w)/(1

+ w);

+ w);

. . . (1.6)

where w~w• w and w 8 w are the volumetric moisture contents of a specimen after swelling at no load, specimen of undisturbed structure, and of a soil which swells up to E. 8 w respectively. Utilising expressions (1.6) and (1.5) one may obtain the wedging pressure of specimens of different moisture contents w · ( w~w > w sw > w). The swelling process of a soil in the presence of a constant external load may be described by the model shown in Fig. 1.17 for the conditions assumed earlier. The model consists of a cylinder (1) and a piston (2) which is subjected to a pressure p by an external load and the self-weight of the soil Pg· Tension springs (3) are attached to the bottom of the piston with the help of brittle hinges

28 of different strengths. These springs represent the internal forces which inhibit swelling-structural cohesion during swelling. The lower end of the springs are attached to another piston (4). Cylinder (1) is connected to another cylinder (5) provided with a movable piston (6). A gas for which the relationship between p and ~V is described by equation (1.5) according to which increase of volume leads to decrease of pressure, is trapped between the top of this cylinder and the piston.

Fig. 1.17. Model of the process of soil swelling.

Expansion of the soil occurs due to the action of wedging pressure, which corresponds to the pressure Pr developed by the gas. This pressure is transmitted to piston 2 through water filling the space below the piston. If this is greater than the pressure pb = p + Pg and also the resistance offered by spring 3, i.e., Pr

> Pb +Pie•

. . . (1.7)

then piston 2 would be displaced upwards, i.e., the swelling process commences. As a result the volume occupied by gas increases, leading to a drop in gas pressure in accordance with equation (1.5). Simultaneous with the upward dis­ placement of the piston, the hinge holding spring 3 breaks, i.e., pressure Pie decreases. This process, i.e., rise of piston, fall in gas pressure and decrease of Pie• continues until equilibrium conditions are achieved which correspond to Pr = Pb +Pie·

. . . (1.8)

Expansion of the soil is caused by increase in the thickness of the water film and hence the extent of imbalance of the swelling soil considered as a system may be examined from the point of view of the non-equilibrium condition of the . water film, using thermodynamic principles. It is well known that for thermody­ namic equilibrium the system temperature (T) and the chemical potential f-L must be constant. Considering the swelling process to be isothermal it follows that equilibrium conditions for the system are obtained when the chemical potentials are constant. Applying thermodynamic ~rinciples it is possible to determine, for instance, the structural cohesion of soil during swelling. It is evident from Fig. 1.16 that

29 curve 2 represents the change in the system during transition from one quasi­ equilibrium condition (swelling corresponding to some specific load) to another. Hence the equations of reversible process may be applied to the present case. The thermodynamic equation for a film is given by dU = T dS - p dV + a dJ + ~11i dmi,

. . . (1.9)

where dU is the change in the internal energy of the system; dS is the change in the entropy of the system; dV is the change in the volume of the system; a is the surface tension of the film; dJ is the change in the area of the film; 11i is the chemical potential of the component i and mi is the mass of component i. Let us assume that the thickness of the hydrate film of an undisturbed structure soil during its swelling (state 1) is h 1 while that for a disturbed structure soil (state 2) is h 2 and that the corresponding chemical potentials are 11 1 and 11z· Then when the volume decreases from ~Vsw to ~V the thickness of the film decreases by ~h = h 1 - h 2 while the chemical potential decreases by ~11· The change in chemical potential is equal to d11 =pdVjm.

. . . (1.10)

In the present case

m(111 -112) = Pic(~Vsw- ~V),

(1.11)

l11 -112 = Pic(~Vsw- ~V)jm.

(1.12)

from which Consequently, to restore the thermodynamic equilibrium an additional load has to be applied satisfying the conditions adduced by Gol'dshtein [3]. For this the chemical potential in the present case wholly refers to the liquid phase. It is evident that during tests on soils of undisturbed structure the pressure p 3 may be so selected that the thickness of the hydrate film of the specimen after expansion is less than h 2 by ~h, i.e., ~h = h 2 - h 3 • Then the corresponding change in chemical potential during transition from equilibrium condition 2 to equilibrium condition 3 is equal to 112 - 113 • Applying the equation of change of energy and total energy during an isothermal process we have -md11 =-V dp +Jda.

. . . (1.13)

Assuming equilibrium transition of the system from state 2 to state 3 and considering the expression for change in volume during swelling deduced from experiments for a real process, we have a 1-k -m (l12 -113 ) = 1 _ k +p +J(a2 -cr3)

. . . (1.14)

where a, k are coefficients which describe the functional relationship ~V = and are dependent on the type of soil.

f (p)

"

30 Substituting the value of 1-12 in the above· expression we have Pie= 6V ·

SW

~-6v[-l:kpl-k+l(a2-a3)+m(l-11-l-13)] ....

(1.15)

./Thus the quantities which influence the swelling process of argillaceous soils may be determined with the help of thermodynamic relationships and ex­ perimental correlations. Bondarenko [1] provides an explanation to the thermodynamic approach applied to the swelling process of soils. In particular, specific steps are presented which allow determination of the thermodynamic quantities characterising the swelling process of soils. As stated earlier, when water interacts with the solid phase its molecules are attracted towards the latter, which transit from a free state to a bound state. As a result, a change in free energy takes place which, in turn, leads to swelling of the soil. In particular, during an isothermal process the soil system works to displace water through its pore spaces. The work done in displacement of a small volume of water may be determined from the expression dAm= 0.95 shrinkage was found to be 7%. Shrinkage was observed to decrease with increase in the density of the specimen. Finally, tests were conducted on natural specimens according to the fol­ lowing method. The specimens were gradually loaded until the desired pressure was reached, after which they were wetted until the swelling process stabilised. Thereafter the soil wa.s again dried over a period of 8 hours at a temperature

41 of 105°C and subsequently rewetted. Each successive cycle of drying led to an increase in the relative swelling. This is explained by the fact that the initial moisture content of the specimen at which wetting was commenced decreased with each successive cycle. Similar results were obtained by Zh.E. Rogatkina who conducted tests on specimens of disturbed structure in triaxial apparatus M-2. Results of these tests during cyclic wetting and drying of Khvalynsk soil with an initial moisture content of 25% and density Pd = 1.56 g/m3 showed that the alternating moisture content led to an increase in swelling from one cycle to another. On the other hand, tests conducted on specimens of disturbed structure Sarmatsk clay in a consolidation test apparatus at different loads with alternate drying up to an air-dried state and subsequent wetting showed that swelling decreased from cycle to cycle, with the maximum decrease observed when there was no external load. After the fourth cycle subsequent drying has practically no effect on swelling of the soil (Table 1.16). 1.16 Swelling and swelling moisture content for different number of cycles of wetting and drying Swelling and swelling moisture content, % at No. of cycles of wetting and drying 0

variousloads,~a

0

0.05

19.4 40.0 14.0

18.5 35.0 13.0 -32.0 10.4 ­ 30.0 9.2 28.9 8.9 ­28.9

-

35.0 11.2 2 32.0 10.0 3 31.5 10.1 4 31.5 Note: Magnitude of swelling is given above the dividing indicated below it.

0.1 12.7 32.0 10.0

0.2

0.3

12.0 30.8 9.2

11.0 30.0 8.7

28.5 8.0 27.5 7.0 ­ 27.0 7.0 26.9

28.0 7.4 27.0 6.3 26.0 6.3 26.1

-

­

-

-

29.1 9.1 28.1 8.1 27.5 8.1 27.7

line while swelling moisture content is

A similar behaviour was also observed for change in moisture content of natural specimens of Khvalynsk clays. During cyclic wetting and drying up to degree of saturation of 0.65, the processes of expansion and contraction were practically reversible. Drying to a degree of saturation of less than 0.65 led to a reduction in the swelling moisture content, which was most intense in the first two cycles. After the fourth cycle the swelling moisture content remained almost unaltered. This change in swelling moisture at Sr < 0.65 is explained by the influence of cations of Ca which constituted nearly 80% of the total. For Khvalynsk soils

42 Sr = 0.65 ·Corresponds to a moisture content of 17.5% which slightly exceeds the maximum hygroscopic content. In this case the thickness of the hydrate film is sufficiently large and the 'agglutination' effect of particles due to these cations is negligible. Drying the soil to the air-dried state causes agglutination of particles, i.e., increase in structural cohesion. Hence, on repeated wetting of soil it swells to a lesser extent. It should be noted here that for the upper layers of soil the decrease in moisture content is much smaller because of greater aggregation of the soil and its repeated wetting and drying. On the other hand, tests conducted on specimens of disturbed structure Khvalynsk clay in the PNG test apparatus showed that with alternate drying and wetting the difference between the relative expansion and relative contraction remained constant. In this case the shrinkage moisture decreased, reaching a con­ stant value after the fourth cycle. The durations of the expansion and contraction processes differed. The shrinkage process was about 3 to 4 times longer than the expansion process. The duration of the shrinkage process increased from cycle to cycle, whereas the duration of the swelling process decreased with successive cycles but only up to a limit and after the fourth cycle the duration of these processes did not change.

2

Principles Governing Deformation of

Soil Mass and Foundations during

Soil Expansion

1. Deformation of Soil Mass during Artificial Wetting

The nature and principles governing expansion of soils in large tracts and under foundations of structures do not differ from those considered earlier. Thus, deformation of soil due to swelling in large tracts as well as under foundations increases with greater loosening of the soil particles, smaller moisture content, increasing density etc. However, this case has certain special features associated with the stressed state of .the soil, in particular the varying stress along the depth, due to the weight of the soil itself as well as external load. Hence one must consider the fact that wetting of the soil at the foundation is usually of a localised nature, as a result of which deformation due to swelling occurs in a specific portion of the soil mass whereas the rest of the mass remains in equilibrium. In such a case it may be expected that the portion of the mass which is not wetted will exert an influence on the deformation occurring in the wetted portion of the soil mass. The principles governing deformation of soil mass during its wetting were examined over areas of cohesive soils of various genetic types. These studies helped to establish the general principles for deformation of all types of expan­ sive soils in large tracts as well as in foundations during their expansion and contraction. Consider the deformation of the layers of an expansive soil mass along the depth due to its own weight when it is wetted at the surface and through drainage holes. The nature of these deformations was studied when the soil was wetted in trenches of 1.5-2.5 m depth. Depth gauges were installed in the trenches to register displacement of the soil over a given depth. The markers consisted of reference tubes of 25-40 mm diameter and casing tubes of 89-108 mm dia. The vertical displacement of the surface was observed with the help of surface markers consisting of rods 18-24 mm diameter driven into the bed of a small

44 pit which was later filled with concrete. Vertical displacement of the surface markers and depth gauges was measured by aligning them with the help of a precision level and invar straight edge with respect to two to three reference markers. When the soil was wetted through, boreholes 128-146 mm in diam­ eter were drilled to the requisite depth from the bottom of the trench. The drainage holes as well as the bed of the trench were filled with stone chips or gravel. Fig. 2.1,a shows the movement of Khvalynsk soil layers as a function of time. The soil was wetted from the surface over a period of seven months. After the soil was wetted the bed of the trench began to rise while the marker located at a depth of 0.75 m remained stationary. This indicates that swelling occurred in the layer less than 0.75 m thick. After a lapse of another 16 days this marker also began to rise while the marker at a depth of 1.25 m began to rise 26 days after commencement of wetting. Table 2.1 shows the duration of wetting of the trench and the corresponding depth from the surface of the expansion front at which deformations began as also the rate of displacement of the latter. It can be seen from the Table that the rate of displacement of the expansion front is practically constant in loamy soils. Table 2.1. Depth of wetted zones and rate of displacement of expansion front Type of soil

Sarmatsk

Duration of wetting, months

Distance from surface to expansion front, m

Rate of displacement of expansion front, m/month

1

0.8 1.6 2.4

4

3.1

5

4.0 4.8

0.8 0.8 0.8 0.7 0.9 0.9

1.1 1.9 2.8

1.1 0.8 0.9

2

3

6 Khvalynsk

1 2

3

Surface wetting of Sarmatsk soil several tens of metres thick showed that the displacement of layers is similar to that shown in Fig. 2.1,a. The soil surface continued to rise throughout the period of wetting covering a period of 24 months and was found to be 170 mm. The swelling process stabilised in 4.5 months in the 0-{).5-m thick layer, in 8 months in the 0.5-1-m thick layer and in 13 months in the 1-2-m thick layer after commencement of wetting.

45

Fig. 2.1. Movement of Khvalynsk soil layers when wetted. (a) from the surface and (b) through 3-metre deep boreholes. !-heave of surface; 2, 3, 4, 5 and 6--heave of soil layers at depths of 0.7, 1.25, 1.7, 2.8 and 2.2 m respectively.

The nature of movement of the layers of the soil mass when wetted through boreholes is shown in Fig. 2.1,b. In this case all the layers heaved together, i.e., swelling of the soil occurred at the same time -throughout the depth of the soil mass. The maximum rate of swelling in all the layers was observed in the first month of weiting. The rate of heave of the soil surface during this decreased with time. Table 2.2 shows the rate of heave of the surface for various types of soils depending on the mode of their wetting. It can be seen from Table 2.2 that the rate of heave of the soil surface in the first two months was 1.5 times greater with wetting through boreholes compared to wetting from the surface. However these rates equalised a little later, after

46 Table 2.2. Rate of heave of soil surface

Type of soil Khvalynsk, Sarmatsk

Method of wetting Surface

Duration of wetting, months 1 2 3 4

5 6 7

Quaternary

At depth through

2 3 4

bor~holes

5 6 7

Rate of heave of soil surface, mm/day 1.9; 2.3 0.5; 0.7 0.4; 0.5 0.4; 0.4 0.3; 0.35 0.25; 0.3 0.25; 0.25 0.8 0.4 0.3 0.2 0.15 0.1 0.1

which the situation changed. This is explained by the fact that in the first case the swelling process stabilises almost from the very beginning while during wetting from the surface the underlying soil layers have to absorb moisture and expand due to which the soil surface heaves. The time required to stabilise the heave of the soil surface, as can be seen from Fig. 2.l,b, was nearly 6 months for Khvalynsk soil when wetted at depth through boreholes. When wetting was carried out at the surface, the rise at the bed of the trench during this period was 0.8 times the heave at the surface in the first case. Consequently, the duration of the swelling process of large tracts of Khvalynsk soil with a layer thickness of nearly 3 was nearly 1.5 times greater with wetting from the surface compared to wetting at depth through boreholes. This difference continued to increase with an increment in thickness of the soil layer being soaked. An analysis of experimental data shows that swelling of soil in a large mass occurs over different time periods. The soil in the lower layers swells more rapidly than that in the upper layers, i.e., with an increase in pressure the duration of swelling decreases (Fig. 2.2). It follows from this that heave of the soil surface with time is governed by the duration of swelling of the upper layers, which implies that the time necessary for stabilisation of heave of the soil surface is independent of the thickness of the soil layer subjected to wetting (Table 2.3). It can be seen from Table 2.2 that the duration of swelling of a large mass of Sarmatsk soils of various thicknesses was about 5 to 6 months when wetted at depth through boreholes. During this the dimensions of the wetted tract exerted no influence on the time required for the surface to rise. However, the time re­ quired for the deformation caused by swelling to practically stabilise depended

47

Fig. 2.2. Variation of duration of swelling of Sannatsk soil as a function of pressure.

on the type and structure of the soil. The duration of swelling for various soils was as follows: Sarmatsk-5 to 6 months; Kimmeriisk-3.5 months; Aral'sk-9 to 10 months; Khvalynsk-6 months; Quaternary-17 months. The swelling process at foundations of structures, where wetting of the soil may not occur as inten­ sively as in the above-considered case, may continue over a prolonged period. The rate of swelling of a soil mass depends on the textural features of soils. In a large tract the Kimmeriisk soils swelled more rapidly than others, which is explained by the presence of a large .quantity of sand particles which augments their permeability. As a result the water rapidly percolated through the soil, prpviding favourable conditions for rapid wetting of the clay particles. Further­ more, the tracts of Kimmeriisk soils consisted of alternate layers of clays and silty and sandy materials which facilitate rapid flooding of the soil layers. Owing to this condition, the deformation due to swelling of large tracts of Kimmeriisk soils exceeded 80% of the total during the very first two months. Khvalynsk and Sarmatsk soils swelled substantially faster than the Aral'sk which is like­ wise explained by the variety and textural features of these soils. In the case of Khvalynsk soils, especially in the upper cross-section, there are many layers of sandy materials which help to rapidly wet the soil while Aral' sk soils in terms of texture tend towards a continuous monolithic mass. With increase in depth of wetting an increase in heave of the soil surface occurs. An almost linear relationship between heave of the soil surface and depth of wetted soil was observed when the thickness of the wetted layer was 6-7 m. At large wetted depths this relationship broke down and the heave was smaller. The influence of the area of the tract subjected to wetting on the magnitude of heave of the soil surface was established through experiments (Fig. 2.3). Thus, when the area of wetting was increased, heave of the surface also increased. 'However, this increase was observed up to a specific area of wetting, after which the soil surface rose no further. For a depth of wetting of 3 m the limiting width of the trench for which rise of soil surface was not observed was found to be 6 m while for a 12.5~mdepth of wettmg the limiting trench width was equal to 12 m.

48 These phenomena occur in all types of expansive soils and are independent of their properties. They are governed by their characteristics according to which deformation occurs during swelling of the soil mass as a single unit together with its stressed state and influence of the dry portion of the soil. Table 2.3. Duration of swelling of Sarmatsk soil mass No. of trench

3 11 10 4 34

Dimensions of trench, m 6.5 X 5 6x5 6 X 10 4 X 4.5 6x6

Heave of soil surface,

mm 170 190 150 140 150

Duration of swelling, months,

for different layer thicknesses, m

5

7

-

-

-

-

10

15

5

-

6

6

5.5

5

Fig. 2.3. Relationship between heave of the soil surface and wetted area. 1 and 2-for Aral'sk soils with depth of wetting 12.5 and 6 m; 3 and 5-for Sarmats!c soils with depth of wetting 5 and 3 m; 4-for Khvalynsk soils with h

=4 m.

Drying of the soil in the trenches affected the nature and magnitude of swelling of the soil mass. This was observed during tests conducted on Sarmatsk

49 soils. Thus the rise of the bed of trench No. 1, left open during summer for 60 days, was more than lOO.mm over a period of 5 months. Trench No. 22, of the same dimensions, was wetted for 9 days subsequent to preparation and the heave of its bed was only 65 mm. Rapid swelling was observed in trench No. 1 during its initial period of wetting but later diminished whereas in trench No. 22 the swelling process continued to be uniform. After these trenches were dug the moisture content of the soil decreased, due to which swelling increased, which is explained by the formation of vertical and horizontal fissures that facilitate rapid inundation of the soil mass. When Khvalynsk soil was dried over a period of 14 days, no significant increase in the rise of the trench bed or the test plates placed on it was seen. Thus while the relative swelling of the layer without and with an external load on the test plate with a pressure of 0.012 MPa was 0.042 and 0.032, these for a trench inundated for 14 days after being dug were 0.044 and 0.037 respectively. The reduced data show that the soil in the trenches should not be left exposed for prolonged durations since with subsequent wetting it is prone to increased deformation caused by expansion. The heave of the soil at the bed of the trench was relatively uniform in the central portion of the wetted area whereas it decreased at the banks. The heave of the soil surface was also observed to be smaller beyond the con­ fines of the wetted area. This heave declined with increasing distance from the source of wetting and became zero at some specific distance L. The dis­ tance from the point of zero heave to the edge of the trench being wetted depended on the magnitude of heave at the trench bed. When the soil was wet­ ,ted through boreholes, the markers outside the trench began to uplift almost simultaneous with heave of the surface inside the trench. In this case the dis­ tance L increased proportionate to the increase in heave of the soil surface. With increased wetting of the soil in the trench, the rate at which distance L increased slowed down. The heave outside the trench continued at some specific distance, which was practically constant irrespective of the duration of wetting. In case of wetting from the surface the heave outside the trench occurred later than when the soil was wetted through boreholes. These data show that heave of the soil surface is observed in a restricted zone from the source of wetting and its magnitude primarily depends on the textural features of the soil and the soil properties. Thus, when Khvalynsk soil consisting of layers of sandy material was wetted, heave of the soil surface was observed up to a distance of 15 m, i.e., considerably more than that for Sarmatsk soils devoid of such layers. The magnitude of relative swelling during wetting of soil through boreholes and from the surface is shown in Table 2.4. The relative swelling of soil wetted through boreholes was greater than that for wetting from the surface since in the latter case the swelling process had not yet stabilised.

50 Table 2.4. Magnitude of relative swelling with different methods of wetting Relative swelling of Khvalynsk soils, %, at various depths, m 0.75-1.25 1.25-1.8 1.8-2.8

Methods of wetting 0--0.75 6.7 7.6

Surface Through boreholes

4.0 6.1

4.3 5.5

2.8-3.8 4.3 5.1

2.8 2.9

The method adopted for wetting the soil changes the dynamics of the pro­ cess, which practically has no influence on the overall magnitude of swelling. This was confirmed by tests under laboratory conditions. The moisture content of swollen soil in large soil tracts was practically identical both during wetting at depth through boreholes as well as wetting at the surface and, on average, con­ stituted 37% for Khvalynsk soils, 46% for Sarmatsk soils and 43% for Aral'sk soils. Investigations on deformation of large tracts soaked with water, electrolyte and sulphuric acid solutions were carried out on soils in the region of Dzhezkaz­ gan as well as alluvial soils in the vicinity of Sverdlovsk township by wetting them with water and sulphuric acid. Three trenches of 100m2 were prepared in Dzhezkazgan. The soil in trench No. 2 was soaked with water through 7-m deep boreholes. Trench No. 3 was soaked with electrolyte (10% sulphuric acid, 50% copper sulphate and 3% nickel sulphate) while trench No. 6 was filled with a 10% sulphuric acid solution. Boreholes of 3- and 5-m depth were drilled in trenches No. 3 and 6. Fig. 2.4 shows the displacement of surface markers in these trenches. In spite of the smaller thickness of soil layer subjected to wetting in trench No. 3, the heave of the soil surface during soaking by acid was more compared to that by water and occurred at a more rapid rate (Table 2.5). Table 2.5. Rate of surface heave of soil tracts Trench no. 2 3 6

Rate of heave, mm/month, over several months

10 14 14

2

3

4

5

6

9 14 14

8 13 13

7 15 16

6 14 18

5 14 25

The magnitude of relative swelling of the layers located at various depths is shown in Table 2.6. The relative swelling of alluvial soil when soaked with water and a 1% solution of sulphuric acid under an external load of 0.028 MPa was 4.2 and 10% respectively. Thus when a soil is wetted with sulp~uric acid solution, both expansion and rate of swelling increase. Similarly, when a large soil mass was

51

Fig. 2.4. Heave of the Soil surface as a function of time. 1, 2 and 3-heave of soil in trench Nos. 6, 3 and 2 respectively.

Table 2.6. Relative swelling of soil at various depths Trench no. 2 3 6

Relative swelling, %, of soil layers at various depths, m 0-1

1-2

2-3

3-4

4-5

5-6

6-7

1.6 8.3 8.6

1.4 3.8 5.1

1.0 3.1 4.2

0.9 0.6 3.4

0.8

0.7

0.6

2.1

1.1

soaked with a 10% solution of sulphuric acid at a depth of 5 m, the heave observed at the surface was 238 mm while when soaked with water at a depth of 7 m the heave was only 92 mm. The relative swelling of soil for soaking with acid solution was 1.5-5.5 times greater than that for water. It follows from this that during erection of structures on clayey soils where industries utilising sulphuric acid or other liquids are located, it is. necessary to soak the clayey soils with these fluids when carrying out soil tests.

2. Deformation of Soil Underlying Foundations during its Wetting The principles governing swelling of soil subjected to an external load were studied within a stressed zone under test footings. For instance, one test footing, each 2 x 2 m with a depth of 0.5 m, was installed in two 9 x 9 m ..trenches excavated in Sarmatsk soils. Depth markers were placed on the footings to determine soil displacement at depths of 5.6 and 6.5 m. Surface markers were also provided to measure displacement of the trench bed around the footing. The pressure at the base of footing No. 1 was 0.21 MPa while that for footing No. 2

52 was 0.1 MPa. The soil was soaked through the gravel layer at the surface as well as through boreholes of 7-m depth. Three footings of 1 x 1 m were installed in trench No. 9 whose dimensions were 8 x 15 m. The pressure at the base of these footings was 0.1, 0.2 and 0.3 MPa. The deformations "of successive layers at the base of these footings at depths of 0.25, 0.50, 0.75 and 1 m were measured using markers installed in a single borehole located under the centre of the footing. A simi~ar test procedure was adopted for testing Aral' sk, Maikopsk, Khva­ lynsk and other soils. Thus, in the case of Khvalynsk soils footings of 0.7 x 0.7 m were installed in a trench 20 x 20 m where the pressures at the base of the foot­ ings were 0.015, 0.025, 0.05, 0.1, 0.2 and 0.3 MPa. The soil was wetted through 3-m deep boreholes. Fig. 2.5 shows the uplift of the footing (Sarmatsk soils) and heave of the soil layers at its base as a function of time. It can be seen from the Figure that the nature of deformation of the soil layers under stress due to external loading is similar to that of layers deforming under their own weight. Thus, the maximum heave of the surface at the bed of the trench occurred at the place where the footing was installed. With increase in depth, heave of the soil layers decreased. In the present case the soil expanded due to the load acting on the base and the stresses due to the weight of the footing. Swelling did not occur in layers where the pressure corresponded to the inequality p + Pzg :::; Psw·

Fig. 2.5. Uplift of footing and heave of soil layers at its base as a function of time. !-heave of soil surface; 2-uplift of footing; 3, 4, 5, 6, 7 and 8-heave of layer at depths of0.7, 1.8, 2.5, 3.5, 4.5 and 5.6 m respectively.

Swelling.of the soil at the base of a foundation can be prevented by increas­ ing the external load. If soil loosening is to be prevented, then the external load

,53

must exceed the swelling pressure. Considering that swelling pressure depends on the state of the soil, such as for soils of high moisture content, deformation due to swelling may be prevented by reducing the load on the footing com­ pared to that on soils of very small moisture content. Hence attempts were made to reduce the swelling pressure of Sarmatsk soils by increasing their moisture content and monitoring the mechanism of deformation of the soil at the base for different external loads. For this purpose the moisture content of the soil in trench No. 10 was artificially increased from 38 to 43% at a depth of 3 m. A footing 1 x 1 m was placed on the moist and partially swollen soil with pressures developed at the base of the footing being 0.05, 0.1, 0.2 and 0.3 MPa. After the settlement due to load stabilised, the soil was wetted through the gravel layer at the surface and through boreholes of 8-m depth. It can be seen from Fig. 2.6 that the nature of deformation at the base of the footing at a pressure of 0.3 MPa differs from that for 0.05 MPa. A continuous heave of all the layers below the footing occurred in the case of the latter. The na­ ture of displacement of the soil layers below the footing with p = 0.3 MPa also differed. During the initial period an almost identical heave was observed for all the soil layers and the footing. Thereafter the heave of soil layers exceeded the displacement of the footing and the difference continued to increase with time. In this case the nature of deformation of the soil layers along the depth appeared to differ. Thus, at the top layer lying next to the base of the footing up to 0.25 m depth a reduction inJay~r thickness was seen, i.e., the soil comp~essed. The thick­ ness of this layer decreased by 15 mm as a result of wetting. In contrast to this the soil in the deeper layers (H > 0.25 m) loosened due to soil swelling. The mag­ nitude of deformation due to swelling of the soil in the layer lying at a depth of 0.25-1.5 m was 8 mm and the uplift of the footing was mainly due to the heave of the soil layers lying at a depth of up to 1.5 m below the base of the footing.

Fig. 2.6. Uplift of footing and heave of soil layers at (a) p = 0.3 MPa and (b) p = 0.5 MPa. 1-uplift of footing; 2, 3,4 and S-heave of soil layers at depths of0.25, 0.5 and 1.5 m respectively.

Consequently, increase of pressure from 0.05 MPa to 0.3 MPa at the base of the footing led to a decrease in uplift of the footing but did not completely

54 eliminate it in spite of the fact that the pressure acting at the base exceeded the swelling pressure of the soil of the given state. The relative swelling consistently reduced with an increase in pressure and was just about 1% in soil layers (at depth of 1.5 m) lying below the footing when p = 0.3 MPa while for p = 0.05 MPa it was about 4.2% on average. When the soil of natural moisture content of w = 0.38% in trench No. 9 was wetted, the deformations of layers below the test plates for pressures up to 0.3 MPa were similar to those under footings in trench No. 10 considered earlier for p = 0.05 MPa, i.e., swelling of soil was observed over the entire stressed zone. In this case the relative swelling of soil layers lying in the stressed zone was greater than that below the footing considered earlier. Thus, the relative swelling of soil layers lying at a depth of 0-1 m with a pressure of 0.1 MPa at the base of the footing was 0.9% in trench No. 10 and 3.5% in trench No. 9 while at the base of test plates at a pressure of p = 0.3 MPa it was 0.4% in trench No. 9 and 0.8% in trench No. 10 respectively. Experiments have shown that the uplift of a footing depends on the dimen­ sions of the soaked area and pressure at the base of the footing wherein the lift decreases with increasing area, type and state of soil and area of base of the footing. The load transmitted by the footing changes the nature of deformation of the wetted soil. Away from the footing the heave of the soil surface continues to increase until it reaches a maximum corresponding to the average heave of the soil at the bed of the trench. The distance from the edges of the footing (2 x 2 m size) to the point of maximum heave of the soil surface was 1.5a (where a is half the width of the footing) at a pressure of 0.1 MPa at the base of the footing and 2.5a at a pressure of 0.21 MPa. These investigations showed that the time required for stabilisation of uplift of the footing is less than that for heave of the soil at the bed of the trench. For instance, the uplift of footings placed on Sarmatsk soils (trench No. 10) ceased in almost 5 months while in trench No. 9 it ceased in 1.5 months, i.e., the same rules as in the case of self-weight appear to be applicable, namely the time required for swelling of the soil decreases with increase in the stresses acting on the soil mass. Investigations on a wetted soil mass with simultaneous measurement of deformation of soil layers subjected to an external load and their own weight. made it possible to establish a relationship between relative swelling and pressure or depth at which the soil layers are located (Fig. 2.7). The expression E. 8 w = f(p) for self-weight of the soil layers was plotted from results obtained from soaking soil in trenches of identical area while that for external pressure was plotted from the magnitude of expansion of the soil layers lying below the footings. The nature of variation of E. sw = f (p) for external loading was similar to that obtained from tests on soils in a consolidation test apparatus. However, the absolute value of E. 8 w for corresponding values of pressure in the latter case

55

Fig. 2. 7. Relationship between swelling of soil and pressure. !-during tests in a consolidation test apparatus; 2-during field investigations under external load­ ing; 3-during field investigations under self-weight of soil.

appeared to be greater due to different working conditions of the soil. It was established that up to a pressure of 0.3 MPa a linear relationship exists between the ratio c = Esw 1 /Esw l and the pressure acting on the soil (here E8 w 1 is the relative swelling ~f soil layers lying in the zone subjected to stress by th~ footing and Esw l is the relative swelling obtained in a consolidation test apparatus). Thi~ relationship takes the following form: Esw,f = Esw,z(co-

kp)

· · · (2.1)

where c0 is the ratio (E. sw 1 / E sw l) at p = 0, and k is a proportionality coefficient, cm2/kN. ' ' The values of coefficients c0 and k for various soils are as follows: Sarmatsk soils--0.9 and 0.036; Khvalynsk soils--0.87 and 0.037; Aral'sk soils--0.91 and 0.032 and Maikopsk soils--0.89 and 0.034. The nature of stresses in a soil mass caused by its own weight during swelling is almost similar to that due to an external load, i.e., similar to that in soil layers lying below footings. Hence the relative swellings obtained for self-weight of soil mass closely agree with those obtained from calculations for external loading. However, as can be seen from Fig. 2.7, this agreement is observed for pressures up to 0.1 MPa. At 0.09 MPa a sudden drop in the

56

value of relative swelling for self-weight of the soil occurred (the nature of this relationship did not change at high pressures). Consequently, the working conditions of the soil during swelling when subjected to high stress under its own weight (or at great depths from the surface) remain the same as in all other cases considered above. At the same time the sudden decrement of E.~w observed at 0.09 MPa or at depths exceeding 5 m from the surface may be attributed to the action of some additional pressure Pad· This is equivalent to such an external pressure at which the decrease in relative swelling [extension of the E. sw = f (p) curve for st>lf-weight of soil] is equal to the difference between the values of E.sw (see Fig. 2.7) for a change in depth from 5 m to 6 m. This additional pressure is due to the influence of the dry part of the soil mass on layers which undergo deformation because of swelling of the soil. 3. Zones and Phases of Deformation during Swelling

When the pressure at the base of a footing is increased, its uplift decreases but is not completely ruled out, although at a certain unit of pressure compres­ sion of the soil may be observed in some individual layers, i.e., the nature of deformation of the soil mass varies along its depth. Hence the principles gov­ erning uplift of footings and heave of surface of the soil mass during swelling should be considered together with the nature of deformation of soil layers along its depth. Only in such a case is one able to evaluate the influence of swelling of various soil layers and external load on the uplift of footings. Fig. 2.8 shows curves for the heave of soil layers at depth after swelling had stabilised. When Sarmatsk soils were soaked through 10-m deep boreholes, they swelled over the entire wetted thickness; when wetted through 5-m deep boreholes swelling occurred only to a depth of 12 m. The soil layers located below this depth underwent no displacement in spite of being wet. Consequently, for soil masses of large thickness soil swelling does not occur over the entire wetted layers but only to some specific depth in the wetted zone. That portion of the soil mass where displacement of successive layers and their heave due to swelling occurs is termed the swell zone. The lower boundary of the swell zone lies at a depth H sw where the pressure due to self-weight of the soil equals the swelling pressure, i.e., where the following condition is satisfied: Psw = "fHsw·

. . . (2.2)

Once the swelling pressure is known, the thickness of the swell zone Hsw may be easily ascertained. However, the pressure Psw for the self-same type of soil may differ depending on the working conditions of the soil. Table 2.7 shows the values of H sw obtained from equation (2.2) where the swelling pres­ sures p sw ,l, p sw ,J and p sw ,g were obtained from tests conducted on soils in a consolidation test apparatus, on large soil tracts subjected to external loads and on self-weight of the soil ("{ = 18 kN/m3 ).

57

Fig. 2.8. Heave of soil layers measured along depth. 1 and 2-Sarmatsk soils at depth of soaking h = 15 and 10 m; 3-Aral'sk soils at h = 8 m; 4-Khvalynsk soils at h

~

4 m; 5-K.immeriisk soils at h

=7 m; 6-for soils (Dzhezkazgan) soaked

with acid solutions at h

= 3 m.

Table 2. 7. Magnitudes of swell zones Types of soil Sarmatsk K.immeriisk Maikopsk A::al'sk Khvalynsk Quaternary

Experimental

Hsw,m

Hsw,J

Hsw.f

Hsw.f

Hsw,l

Hsw,2

Hsw,3

0.7 0.67 0.76

1.0 1.0 1.0 1.0

-

1.0

Hsw,l

Hsw,2

Hsw,3

Hsw,J

23 16 30 22 39 14

17 12

12 8 15

17 22

13

12 8 15 13

0.§2 0.5 0.5 0.59

14 11

11

0.78

-

-

-

Note: Values of H 8 w,~oHsw, 2 andH8 w, 3 calculated from swelling pressures Psw,l,Psw,f and Psw,g respectively.

It can be seen from Table 2.7 that the calculated value of the swell zone varies depending on the value assumed for the swelling presslire Psw (Table 2.8). Wllen the swelling pressure data are taken from consolidation tests; then the

58 Table 2.8. Swelling pressures, MPa

---

Pressure Psw,l Psw.f Psw~g

Psw,J/Psw,l Psw,g/Psw,l

Sarmatsk

Kimmeriisk

0.41 0.31 0.21 0.78 0.51

0.30 0.22 0.24 0.73 0.47

Types of soils Maikopsk Aral'sk 0.60

-

0.27

-

0.45

0.41 0.31 0.23 0.76 0.55

Khvalynsk

Quaternary

0.70 0.4

0.25

­

0.20

-

0.8

0.58

magnitude of the swell zone differs from the actual by two times. The nature of ·layer by layer deformation of the soil at the base of the footings differs from that observed in a large soil mass under its own. weight. For instance, Fig. 2.9 shows the displacement of layers of Sarmatsk soil at the base of footings. Curves 1-5 show the displacement of soils with initial moisture content of nearly 38% and curves 6-9 with initial moisture content of 43% at a wetting depth of hw = 7 m. When the moisture content of the soil at the base of the footing was 38%, the soil dispersion increased with decreasing pressure on it. At a depth of 2 m the heave of layers below all the footings was similar since the pressure exerted by the footings at this depth had no significant influence on soil swelling. At a moisture content of 43% deformation of successive layers showed a different trend. Thus, at p = 0.3 MPa over a depth of Q-1.0 m the soil was found to be compressed whereas in the layers further down the soil had dispersed. At p = 0.2 MPa the relative displacements of the depth markers over a depth of 1 m were found to be practically constant while in the deeper layers swelling of soil occurred. At a pressure of p = 0.05 MPa and 0.1 MPa at the base of the footing the nature of layerwise deformation was observed to be the same as in the case of a large soil mass under its own weight. Compressive deformations occurred because the pressures acting on the soil exceeded its swelling pressure for a given state of the soil. The absence of displacement indicates that external pressure is counterbalanced by the swelling pressure. Investigations showed that the deformation of successive layers in other types of soils was analogous. Thus in the case of Kimmeriisk soils at p =0.3 MPa in the upper portion of the foundation below the footing, the soil layers directly in contact with the base of the footing were compressed, no deformation was observe Psw)· The combination of zones as shown in Fig. 2.10,b corresponds to the condition wherein p = Psw while that shown in Fig. 2.10,c corresponds to the condition wherein p < p sw. The height cif the deformation zone depends not only on the external pressure, but also on the size and shape of the footings. When the external pressure and bearing area of the footings are increased, the size of zones I and 11 will also increase. When the self-weight of the soil alone acts on its layers, then for a large soil mass only a swell zone develops. The nature of layerwise deformation and demarcation of zones along the soil depth must be examined during site investigations and design since soaking of a soil mass over some limited portion, i.e., within the limits of zones I and 11, may lead to an erroneous c,.mclusion that the footings will be subjected to no uplift, whereas when the soil mass is soaked over the entire swelling depth the footings are liable to uplift.

60

Fig. 2.10. Deformation zones in a large soil mass due to swelling.

Let us consider the phenomenon occurring in a large wetted soil mass dur­ ing a change in its stressed condition. As can be seen from Fig. 2.11 ,a, when the footing was loaded up top= 0.124 MPa settlement took place due to consoli­ dation of the soil. After stabi1isation of this process the soil was further watered which led to uplift of the footing which ceased when swelling of the soil sta­ bilised. Thereafter the footing was unloaded but watering was not discontinued. After the footing was unloaded it began to lift further but stabilised after some­ time. The footing' was once again loaded, which resulted in its further settlement. Thus, when the state of stress of a soil is varied, different types of deformations are observed such as its consolidation or expansion, i.e., when a soil is loaded it goes through various phases of deformation. In contrast to usual soils the following phases of deformation may be de­ marcated in swelling soils (see Fig. 2.1l,b). Phase A corresponds to that of consolidation of a usual soil. Here if 0 < p Pis settlement takes place (curves IT and III). If the soil is watered after stabilisation of settlement, then phase B of swelling of the soil sets in at p < psw. In this case the wedging pressure of the water film overcomes the external pressure and structural bond of the soil. The clay parti­ cles move apart, leading to dispersion of the soil. This process is of a decaying nature. However, for a given- state of the soil one may select such a load that wetting the soil does not result in its additional deformation. This corresponds to the condition p = Psw (curve 11). Finally at p > Psw additional settlement may occur (curve Ill) while for certain types of soils the deformations observed are in the nature of subsidence (for slope wash loams in Kemerovo town which

61

Fig. 2.11.

Phases of soil deformation.

1-loading; 2-wetting; 3-unloading.

have a macroporous structure and are prone to collapse). In this case the soil showed subsidence when the pressure below the settlement plate was p = 0.2 MPa and swelled at p = 0.1 MPa. Two different processes, namely subsidence or expansion may occur dur­ ing interaction of soil with water depending upon the pressure acting on it. Such defonnations appear in the Kommunarsk, Berdyansk, Chemomorsk loams (Krasnodarsk border) and others. Here only swelling occurs when the pressure on the soil is reduced. The data available at present enable us to obtain a first approximation of the limiting pressures at which expansion or subsidence of argillaceous soils may commence (Table 2.9). Table 2.9. Nature of soil deformation Type of soil

Nature of soil deformation under pressure, MPa 0.01-{).06 0.06-{).18 0.18-{).30

Sandy loam Loam Clay

Expansion Expansion Expansion

Subsidence Expansion Expansion

Subsidence Subsidence Expansion

When soils which are capable of both expansion and subsidence are wetted, it is necessary to determine all possible defonnations over the entire range of pressures acting on the foundations. If the load on the footings is relieved after completion of swelling with­ out discontinuing wetting of the soil, then expansion phase C commences (see Fig. 2.11,b). It should be noted here that defonnation due to swelling at no load

62 would be greater than the total expansion of the soil under loading and subse­ quent unloading conditions. When the footings are subjected to an additional load after completion of swelling, the soil consolidates and the phase of secondary consolidation (phase D) commences (see Fig. 2.1l,b). In this case the maximum subsidence is ob­ served in the case of soils which swell most and the modulus of deformation during secondary consolidation is several times smaller than that during initial consolidation of the soil.

4. Lateral Deformations and Pressures acting on Protective Structures during Soil Swelling Most expansive soils have a microlayer texture which is responsible for their anisotropic properties besides their structural features. This results in un­ equal swelling in both vertical and lateral directions. Thus, for Sarmatsk soils deformation and swelling pressure in specimens along the stratification was 20% greater compared to that along the direction perpendicular to it. Hence, during swelling lateral displacements may even exceed vertical movement. Field investigations have shown that when a large soil tract which is under stress due to external loading or its own weight is soaked, there are no lateral displacements of soil in the wetted region. At the same time wetting the soil along one side of continuous footings of 4-m length resulted in a heave of 95 mm and lateral displacement through an average of 3 mm towards the side opposite to that being wetted. It was found that lateral displacements occur in a soil mass when vertical banks are present in it. Thus, soaking of the soil over a period of 80 days at the sides of a trench led to vertical heave of the soil surface and lateral displacement of the vertical side. The greatest lateral displacement was indicated by markers installed on the vertical side. With increasing distance away from the sides the magnitude of displacement diminished. At a depth of 1 m from the surface and at a distance of 7.5 m from the trench no lateral displacement was observed. At 2.5-m and 4-m depths there were no lateral displacements at distances of 6 and 4 m respectively from the trench. Fig. 2.12 shows the distribution of lateral deformations along the height at different sections of the soil. With increasing depth lateral displacements decrease and at some particular depth completely disappear. These diagrams show that with increasing distance from the walls of the trench, the depth at which lateral displacements cease decreases. The boundary of the zone over which lateral displacements may occur is enclosed by the curve MN. Because of swelling the vertical heave of the surface was 90 mm and verti­ cal displacements decreased with depth. The zone prone to displacements almost coincided with the zone over which moisture had spread. Hence vertical displace­ ments occurred over the region bounded by the curve SK. In the present case two characteristic zones may be distinguished: Zone SON where vertical and

63

Fig. 2.12.

Diagram of soil displacement during wetting.

!-vertical displacement of soil surface; 2, 3-vertical displacement at depth of 2.5 and 4 m; 4, 5, 6 and 7-lateral displacement of soil; 8-vector representing displacement of points 0, C and D; 9-boundary of region of lateral displacements; 10-boundary of region of vertical displacements.

horizontal displacements occurred and the zone bounded by the curves OK and ON where only vertical displacements occurred. At the boundary dividing these zones microshear areas might develop which promote the formation of sliding surfaces. The possible occurrence of lateral deformation must be taken into account during the design of protective structures on expansive soils. In the absence of displacement of vertical sides, for instance in retaining walls, additional forces begin to act on the latter due to soil swelling caused by its wetting. These additional forces primarily depend on the type"-and state of the soil and are governed by the swelling pressure (see para 4, Chapter 1). An underestimation of the additional lateral pressures due to swelling of soil during. construction leads to disruption of the st~bility of sheet piles and other protective constructions. For instance, in one factory the reinforced cement concrete retaining wall of a warehouse for finished products deformed due to swelling of the soil. This necessitated strengthening of the structure. Numerous cases of damage to canals with a variety of subsurface interconnections are known. Soils which tend to swell may develop pressures which act on retaining walls. In such cases the coefficient of active earth pressure (ratio of lateral and vertical pressures under active conditions) may exceed unity. This leads to

64

rupture or development of a tilt, i.e., displacement of the wall due to swelling of the soil. Extensive field investigations were conducted on Sarmatsk and Khvalynsk soils to ascertain the lateral pressure acting on structures during soil swelling. The lateral pressures that developed during swelling of Sarmatsk soils of disturbed and undisturbed structure were studied in a test area near Kerch' town. For this purpose the top humus layer was removed and a trench 2.5 x 4.5 m with a depth of 3.2 was excavated. The trench had vertical walls on two sides while the other two sides had a slope of 45°. An RCC well of 3.3-m height and 2.5 x 2.5 m in section was placed within the trench. One wall of the well was concreted to take the soil thrust while the opposite wall, away from the vertical wall by 0.4-0.5 m, facilitated subsequent installation of probes (Fig. 2.13).

Fig. 2.13. Cross-section of test well. 1-- = - constant·

. . . (2.21)

Let us select the distance Z from the soil surface to the depth at which ground-water lies as this constant. Then

,P(w) -Z+

(•+ I~dz) (;:) j~d ~

-Z

. . . (2.22)

Tests on soils in consolidometers correspond to one-dimensional loading. Consequently, the equilibrium condition following completion of the swelling process may be described by equation (2.22). Here the gravitation potential and load due to self-weight of the soil may be omitted due to the small height of the sample ring. In turn, the degree of saturation after expansion always equals unity and consequently

"'w (::)

ai

I "'d

= 1

. . . (2.23)

where "fw is the unit weight of water. Finally, the level of free water during wetting of the soil in the test set-up coincides with that of the surface and hence Z = 0. Taking these into consider­ ation equation (2.22) may be represented as

'l/J(wsw) = -Phw·

. . . (2.24)

This equation shows that completion of the swelling process occurs when equilibrium is achieved between pressure due to external load and wedging pressure. If the external pressure is less than wedging pressure, then swelling continues and correspondingly the moisture potential reduces. On the basis of experimental investigations in test apparatuses a functional relationship was obtained between the moisture potential and the moisture con­ tent for natural specimens of Khvalynsk and Sarmatsk soils; The following re­ lationships have been assumed for analysing the experimental data (Fig. 2.20): exponential function: log( -'ljJ) =log A+ a1og(w8 w- w);

. . . (2.25)

78

Fig. 2.20. Relationship between logarithm of the moisture potential '1\J and moisture content for: (1) Sarmatsk soil (2) Khvaiynsk soil.

logarithmic function: log( -'ljJ) = IogB + ~ (w 8 w- w)·

. . . (2.26)

The logarithmic function quite adequately describes the section where log( -'ljJ) exceeds 3 but gives excessive values of moisture content at low values of log( -'ljJ). Thus for Khvalynsk soil log( -'ljJ) = 0 corresponds to swelling moisture w 8 w = 0.507 which exceeds the average moisture content during free expansion of soil. The exponential relationship exactly describes the section 0 to log( -'ljJ) < 2.8 but is found to be inapplicable at high values of log( -'ljJ). Thus for Khvalynsk soils at w = 0 the value of log( -'ljJ) = 5.33 whereas it is seen from experi­ mental observations that log( -'ljJ) = 7 for w = 0. Hence while constructing the graph of the function 'ljJ(w) it was assumed that for the section log( -'ljJ) ~ 0 to the point of intersection between the logarithmic and the exponential rela­ tionships this graph is described by the exponential relationship and thereafter by the logarithmic relationship. Hence the relationship between log( -'ljJ) and w is given by log( -'ljJ) = 5.23 + 11.57 log(0.465- w) between 0 and the point of intersection and log( -'ljJ) = 2.29 + 16.26(0.469 -. w) after the point of in­ tersection [for Sarmatsk soils] and log( -'ljJ) = 6.54 + 3.041log(0.4 ~ w) and log( -'ljJ) = 1.8 + 16.81(0.4- w) respectively for Khvalynsk soils (here w is expressed as a fraction). · A continuous derivative 'ljJ( w) may be obtained if 'ljJ( w) is approximated as ­

'ljJ(w) = -A(w8 w- w)"'

1Qi3Cwsw-w).

. ..

(2.27)

79 The constants A, a and ~ are evaluated from the condition that the curve de­ scribed by equation (2.27) passes through three given points. The graphs drawn on the basis of such an expression with constants A, a and ~ almost coincides with the curves of 1\J(w) in Fig. 2.20. They are continuous functions with deriva­ tives at all points and pass through the point log( -1\J) = 7 at w = 0. The coefficient of porosity as a function of moisture content and pressure appears as a part of expression (2.22) for the absolute moisture potential It has been established that there exists a specific relationship between these quantities. Thus, Table 2.13 shows the values of coefficients for e = f(w) as a linear, parabolic, hyperbolic and logarithmic function. Given the above analysis; the following conclusions may be drawn: -For clayey soils a close correlation exists between the coefficient of poros­ ity and moisture content; -The magnitude of the gradient in the linear relationship is always less which is characteristic of soils existing in a three phase state; than 1/ -Experimental observations are better described by a parabolic equation, i.e., the relationship between e and w is non-linear. It may be noted that for large values of w the parabolic expression is practically coincident with the linear. Experiments were conducted on Khvalynsk and Sarmatsk soils in odometers to ascertain the relationship between porosity, load and moisture content. The specimens tested were dried to obtain different degrees of moisture content. The load was increased in steps until the desired pressure was obtained. Thereafter, the soil was wetted until completion of the swelling process. In the free expansion tests, i.e., when the external load was zero, the specimens were periodically weighed so that a graph could be plotted for e as a function of w in the range of we to wsw· When the initial degree of saturation Sr exceeded 0.65, the swelling moisture for a given stage of loading was almost independent of the moisture content of the soil. At the completion of the swelling process the degree of saturation Sr was almost unity, i.e., all the pores in the soil were inundated with water. Experiments on free swell showed that complete inundation of the pores during the swelling process is approached when the moisture content of the soil is less than the swelling moisture. The data obtained from consolidation tests were utilised to plot the rela­ tionship between porosity and moisture content at various pressures. The graph plotted from the parabolic expression served as the reference curve. The ini­ tial porosity coefficients e0 did not always fit the correlation curve for initial moisture contents w 0 • During loading of the specimens through steps of !lp the magnitude of !le was calculated on the basis of e( w 0 ) on the parabolic curve at w = w 0 (Fig. 2.21) and not from e0 • If soil is subjected-to loading and wetting, it will swell under constant pressure conditions. In this case, of the two independent variables (moisture content and pressure), only the moisture content varies during swelling. During such moisture variations the porosity coefficient increases. For instance, increase

"'w,

168 154 110 33 28 70 72

Type of soil

Mayotiche Khvalynsk Aral'sk Maikopsk Nizhnekarbonov Sarmatsk Yursk

No. of

data points

Type of correlation

2.552 1.975 3.027 2.633 2.417 2.072 2.648

k 0.117 0.256 0.012 0.119 0.050 0.314 0.047

a

(e =kw+ a)

Linear relationship

-1.367 7.291 2.449 12.001 0.667 1.881 -5.372

a 3.715 -1.805 1.591 -5.845 2.165 0.817 5.463

b

c -0.114 0.731 0.215 1.603 0.072 0.509 -0.305

(e = aw 2 + lrw +c)

Parabolic relationship

-0.422 -0.139 -0.254 -0.335 -0.080 -0.219 -0.170

a 2.264 1.319 1.798 2.006 0.966 1.706 -1.420

b

(c =!!:..+b)

2.293 1.070 1.949 2.087 0.947 1.474 1.555

a

0.088 1.403 1.954 1.997 1.209 1.732 1.662

b

(e = alogw +b)

Hyperbolic relationship Logarithmic relationship

Table 2.13. Values of coefficients ill, o, 6 and c in the expressions for porosity of clayey soils

0

00

81

Fig. 2.21. Porosity coefficient of Khvalynsk soil as a function of moisture content and pressure. 1, 2, 3, 4, 5 and 6-at pressures of 0, 0.05, 0.1, 0.2, 0.3 and 0.4 MPa respectively; 7-at fully saturated condition; 8-theoretically predicted curve.

in moisture content from 25 to 30% in Sarmatsk soil led to an increase in porosity coefficient through ~e = 0.092 at p = 0 and ~e = 0.088 at p = 0.3 MPa. The mean values of the derivative (dejdw)* for this interval of moisture content were 1.84 and 1.76 respectively for p = 0 and p = 0.3 MPa. The insignificant difference between these derivatives permits the elimination of pressure as an independent variable and consideration of (8ej8w)cr· as a function of moisture content only. Consequently, the partial derivative (8'ej8w)cr; transforms to the total differential (dejdw) and the expression for coefficient of porosity is given by . . . (2.28) e = f(w)· These assumptions enable us to simplify the computations. However, it is necessary to estimate the numerical value of the error introduced in the values obtained for soil displacements due to such assumptions. The influence of pres­ sure on porosity coefficient e in equation (2.28) and on equilibrium moisture distribution in the soil would be evident through a decrease in the moisture • Given as D..e/D..w in the Russian original-Translator.

82

content. Let us consider a swelling zone of 15-18 m depth for plotting the re­ lationship given by equation (2.28). It suffices to use the curves for the range 0--0.3 MPa. The curve shown by the broken line in Fig. 2.21 represents the function e( w) for which . . . (2.29) e = (ep=O + ep= 3 )/2· Equation (2.29) may be approximated as follows for Khvalynsk soils: (i) e= 0.6 for w :::; 0.15; (ii) e= 8.30w2 - 2.218w for 0.15 and (iii) · e= 2.77w for w 2: 0.32·

< w < 0.32; . . . (2.30)

For Sarmatsk soils (i) e= 0.725 for w:::; 0.15; (ii) e= 4.083w 2 - 0.767w + 0.748 for 0.15 < w < 0.4 and (iii) e= 2.74 at w > 0.4·

. . . (2.31)

During computations it is necessary that data be available on moisture varia­ tion during transition from its initial non-equilibrium moisture distribution to the state of equilibrium and the correlation between porosity and moisture content of expansive soil. The type of equation describing equilibrium moisture distribution along the vertical in a one-dimensional representation at constant temperature and reversibility of the wetting-drying process is similar to equation (2.22). This equation consists of two characteristic functions, 1(;(w) and e( w) which were obtained experimentally for Khvalynsk and Sarmatsk soils. Laboratory investigations revealed that e is a function of p and w for swelling soils. It was shown earlier that it is possible in principle to utilise the function e = e( w) to change over from an integral to a differential expression. Utilising equation (2.22) and substituting

J z

p

+

"fdz = "fd[z- Z -'t(y(w)Jie(w)

. . . (2.32)

0

we have dw dz

1­

1(;(w)

1 +w 1 + e(w) e'(w) e" (w)

. . . (2.33)

+ [z- Z -'t(J'(w)] e'(w)

Equation (2.33) can be solved by numerical integration for known boundary conditions wlz=O = w0 . The value of w0 is determined from the expression, pd I = -Z· 1(;(w0 ) + "fdw w=wo

. . . (234)

83 When the soil surface is shielded from the surroundings, the moisture dis­ tribution in the soil becomes uniform after some interval of time in conformity with the initial level of the ground-water table and pressure applied at the sur­ face. If the location of the ground-water table or pressure at the surface changes, then the moisture is redistributed corresponding to the new equilibrium condition and due to this the soil layer is displaced. While computing the soil displace­ ments caused by changes in moisture distribution in the soil, it was assumed that the time interval between two successive levels of ground-water or pressures at the surface was large enough for the new moisture distribution to be close to equilibrium conditions. · The theoretical conditions corresponding to this case are shown in Fig. 2.22. During wetting and drying the soil layers undergo displacement. However, the reduced co-ordinate for the given layer remains constant. This makes it possible to determine the displacement of a soil layer during a change in the level of the ground-water or a change in the pressure at the surface. The thickness of the swollen soil in actual practice will be maximum when z = 0 and p = 0. Let us designate this thickness by H00 x for the soil layer whose reduced co-ordinate at zero values of Z and pis x. Th~ reduced co-ordinate will be measured from the surface. Hence at Z = 0 and p = O,H00 0 is the true thickness of the entire soil layer which swells, while H 00 10 is the true thickness of the soil layer whose reduced co-ordinate x = 10 rrL Let us designate the true thickness of the soil layer for values of Z and p other than zero byHpz,x· Then the difference H 00 x - Hpz x represents the contraction of the soil layer with the reduced co-ordinate x d~ing change of external pressure from 0 to p and change in level of ground-water from 0 to Z. If Z == 0 while p =/= 0, then this difference corresponds to shrinkage caused by increase of pressure at the surface from 0 to p and conversely when p = 0 while Z i= 0 the shrinkage obtained is that due to the lowering of the level of the water-table from 0 to Z. The functional relationships 'ljJ(w) from equation (2.27) ande(w) from (2.31) were utilised while developing this method. of computation. For Sarmatsk soil, e as a function of w and p may be approximated by

= e 1 at w < w 1 ; == e 1 + (w- w 1 )(Aw2 +Bw +C) and e = 2.74w for w 3 < w· e e

for w 1 < w < w3 ;

(2.35)

The coefficients A, B and C are determined from the conditions de

elw=w2 = e2; elw=w3 = 2.74w3; dw lw=w3 = 2.74,

(2.36)

where e 1 , e 2 and e3 depend on the pressure. These may be approximated by the expressions: e 1 = 0.62 + 0.13e- 0·24P at w 1 = 0.204;} e2 = 0.72 + 0.15e-0 ·203P at w2 == 0.27; · and w 3 = 0.25 + 0.19e-0·25P.

. . . (2.37)

84

Fig. 2.22. (a) Theoretical method for determining soil displacement during change of equilibrium conditions; (b) relationship between true co-ordinate Z and reduced co-ordinate x.

Calculations of soil displacement using equation (2.35) were linked with the solution of equation (2.32) and computation of the true co-ordinate Z and pressure due to the soil layers

z

J"fdz. These computations were carried out on 0

an electronic computer in terms of reduced co-ordinates for a layer of Sarmatsk soil of an overall reduced thickness of x = 20 m underlain by bedrock. The true co-ordinate Z and the integral

z

J"fdz were determined from the expressions: 0

'h j zj

=

2 :~:::)2 + ei-1 + ei); i=l

. . . (2.38)

85

J Zj

"fdZ =

0

"fh

.

J

2 ~(2+wi-l +wi)

. . . (2.39)

~=I

where w is the moisture content expressed as a fraction. The overall reduced thickness of soil layer x and the interval h are related to each other by

x=nh·

. . . (2.40)

The magnitude of moisture content w0 was. determined at the surface Z = 0 for given values of p and z. Thereafter the value of wj was calculated by the method of successive approximations with the desired accuracy at each step as follows: k -

k-1

3

3

w. - w.

~(w~- 1 )- z. +Z+ Pje~(w~- 1 ,p·)

J J J

- --- - - -J= - - -"'- ' - - --ol•'(wk-t) + Pj e" (w~-t p ·) '+'J

. . . (2.41)

"jWJ'J

The value of wj-! obtained for the previous step is given as the zeroth approximation. Fig. 2.22,b shows the relationship between the true soil layer thickness H 00 x and the reduced coordinate x. It can be seen that this relation­ ship is linear 'in nature, which may be explained by the fact that the derivative (dxjdH00 x) = -(1 - e)- 1 changes but little. Thus at w = 0.465, e = 1.274 and w = 0.35, e = 0.959, the derivatives are 0.44 and -0.51 respectively. Fig. 2.23 shows the relationship between settlement S = H00 x - HpZ x and the level of ground-water at various pressures applied at the ~urface. At p = 0.1, 0.2 and 0.3 MPa these curves do not emanate from the origin of the co-ordinates but make an intercept of (H00 0 - Hpo 0 which equals the settlement caused by an increase in pressure from 0 to p at the surface at Z = 0. As the magnitude of the reduced co-ordinate x increases these curves be­ come flatter. Nevertheless the soil layer thickness should not be taken to be constant, i.e., when the level of groundcwater changes, the ·lower boundary to which shrinkage (swelling) extends becomes a variant. · The curves shown in Fig. 2.23 may be utilised to evaluate the magnitude of swelling or shrinkage both for the entire soil mass as well as its individual layers for variations in the level of ground-water. Let us determine the displacement of soil at the surface by the method developed here for the case of lowering of the ground-water level (the initial data used in the example are assumed). Let us consider that the ground-water level drops from 0 to 20 m. Up to a depth of 18 m from the surface the soil consists of expansive Sarmatsk clay overlying sand and sandy loam. Setting off the thickness equal to 18 m towards the left from 42.5 m on the abscissa (see Fig. 2.22,b), the reduced thickness is found to be x = 8 m. Hence the displacement at the surface due to shrinkage caused by drop in the ground-water level from 0 to 20 m would be equal to the difference

86

Fig. 2.23. Relationship between displacement of layers of Sarmatsk soil and ground-water level and pressure at the surface.

between S1 for x = 0 and S2 for x = 8 m. From the curves shown in Fig. 2.23 at p = 0 we have S = 100 - 44 = 56 cm.

87 Let us compare the displacements obtained from the approximate theory utilising the function e( w) (broken line) an:d the values computed from a mme rigorous method where the void ratio is a function of both moisture content and pressure, i.e., e = e(w,p) (solid lines). It can be seen from Fig. 2.23 that the maximum discrepancy in displacement occurs at x = 0 and p = 0.3 MPa. If the soil displacements for small variations in ground-water level are compared, the difference is seen to be relatively small. Thus, for a rise in the level of ground-water from 20 m to 0 m the displacement at the soil surface (x = O,p = 0.3 MPa) calculated by the rigorous method for x = 20 m is 181 - 132 = 49 cm but 160 - 116 = 44 cm by the approximate method. The situation described earlier is not constrained by the initial natural mois­ ture profile. While calculating the lift due to effect of shielding the surface, it is necessary to proceed from the moisture profile existing in the soil mass just be­ fore commencement of construction. The magnitude of expansion of the given soil layer should be determined by comparing its thickness after transition to the equilibrium state of moisture distribution with that of the same layer at the time of construction. Hereafter a distinction shall be made between two types of systems, namely 'closed' and 'open', to describe the nature of the relationship between the level of the ground-water table and the total moisture content of a system. If the location of the ground-water table after shielding the soil surface de­ pends upon the total moisture content of a soil mass at the time of construction and its additional ingress during subsequent service, then such systems are clas­ sified as 'closed' systems. In 'closed' systems in the absence of any additional sources of moisture, the location of the ground-water table under equilibrium conditions may be determined by applying the condition that the total moisture content in the soil remains constant, i.e.,

J J H

Ho

9dz =

0

eodz·

. . . (2.42)

0

The upper limit of integration corresponds to the depth up to the bedrock for soils of restricted thickness. For soils of unrestricted thickness the depths H and H 0 are replaced by the distance from the horizons where there are no fluctuations in the level of the ground-water table. The suffix o corresponds to the condition of the soil mass at the time of construction. The symbol represents the volumetric moisture content, i.e.,

e

w 9 = Pd 1 + e

. . . (2.43)

88 If additional moisture M enters the soil, then the level of the ground-water under equilibrium conditions is determined from the expression H

j

H

9dz =

0

j

. . . (2.44)

90 dz +M·

0

A numerical solution to the problem of determining the level of ground­ water in 'closed' systems under an equilibrium state for the conditions given by equations (2.42) and (2.44) was obtained on an electronic computer. In this case the entire thickness of the soil mass was divided into n layers of thickness h so that H 0 = nh. The total moisture content M0 at the time of construction, the reduced co­ ordinates of individual layers xj and of the entire layer of the swelling soil x were determined from the equations

J Ho

Mo =

n

90 dz =

~ tt(So,i-1 -

0

z

x · = jdz/(1 +e)= J

0

hn[

1

2L (1 + e-_ 1) i=1 z

. . . (2.45)

9o,i);

1]

+ (1 + ei) .

. . . (2.46)

The solutions to these equations were obtained by utilising the functions 'ljJ(w) and e(w) determined experimentally for Khvalynsk and Sarmatsk soils. Equation (2.33) was integrated in constant steps of h with boundary condi­ tion wlz=O = w 0 determined by equation (2.34). At xj > x, the true thickness of the swelling zone and the total moisture content M of the soil layer under equilibrium conditions were obtained by linear interpolation at the point where the value of the reduced co-ordinate was x. The ground-water level determined for 'open' systems is specific and does not depend upon the moisture content at the time of construction. In 'open' systems the location of the ground-water level is fixed relative to the lower boundary of the swelling soil layer. Let us assume that at the time of construction the thickness H0 of the swelling soil and the level of the ground-water Z0 are known from the data derived from engineering and geological investigations. It is required to determine such an equilibrium condition that the difference between the new ground-water level Z and the thickness of swelling soil layer H equals the difference (Z0 - H 0 ): Z-H=Z0 -H0 •

. . . (2.47)

At Z = Zk_ 1 the function Hk = Hk(Zk-d was determined and the modules 1Zk_ 1 -Hkl were compared with IZ0 -H0 1.

89 If it was found that the difference between these moduli was greater than 8, where 8 is the accuracy with which Z is determined, then the kth value of the ground-water level was calculated from the expression

Zk = Zk-1 -

(Zk 1 -Hk)- (Zo -Ho) Hk(Zk_ 1+ ~) - Hk(Zk-1) '

1~

. . . (2.48)

and the procedure was repeated. In equation (2.48) ~ is the small increment in ground-water level which was utilised for approximate calculation of the derivative oH I

oz z=zk-1

~ Hk(Zk-1

+ .6-Z)- Hk(Zk-1) ~

. . . (2.49)

During computations it was found that the derivative oHI oZ at .6-Z = 5 cm was trivial to the third order (10- 3 ) while the desired value of Z was obtained in the very first step. Neglecting the second term in the denominator of equation (2.48), repre­ sented by the derivative oHI oZ of equation (2.49) we have Z ~ Z 1 = Z 0 -H0

+H1(Z0),

. . . (2.50)

i.e., it is sufficient to specify the ground-water level as Z0 during calculations. When the calculations are completed, one obtains the thickness of the swollen soil layer under equilibrium conditions for a fixed location of the ground-water level and its depth from the surface calculated from equation (2.50). Let us consider the effect of seasonal variation of moisture and heat at the soil surface on moisture migration and displacement of the swelling soil when it is exposed to the surroundings' as well as shielded from them. The unsteady moisture migration processes appear due to filtration, evap­ oration, redistribution of moisture and temperature fluctuations. Combining the above factors and rearranging them in a specific order it is possible to model the processes of moisture migration during seasonal variation of thermal and moisture conditions. In order to develop models describing the moisture and thermal conditions of a given region the following initial conditions at the soil surface need to be specified: amount of atmospheric precipitation and duration, the nature of annual variation of temperature at the soil surface; the annual variation of relative humidity of the atmospheric air and the discharge coefficient. The thickness of the soil layer undergoing seasonal processes of expan­ sion and contraction is determined theoretically by comparing the natural non­ equilibrium moisture profile with the equilibrium moisture distribution or expri­ mentally from the observations of the displacements of depth markers installed in 'open' areas.

90 A constant moisture distribution at the lower boundary is taken as the boundary condition. This condition is satisfied, firstly, when the thickness of the swelling soil layer is greater than that of the zone of seasonal variation of moisture content (here the migration of moisture at the lower boundary of the soil layer equals zero) and, secondly, when the swelling soil at some small depth is supported by impervious soil, in which case the moisture migration at the lower boundary becomes negative (this is observed during drainage of water from the lower horizon). This is resolved by consi~ering the problem as one-dimensional wherein the hysteresis phenomenon due to wetting and drying is ignored. The temperature distribution in the swelling soil is obtained with the help of the Fourier heat conduction equation as follows:

at at

=

a [at2 (z) az at] . az

. . . (2.51)

Equation (2.51) includes the term a~, the thermal diffusivity of swelling soil, which is not a constant. The average natural moisture content of the soil wa is utilised for calculation of at when it is assumed that ~ = const. Thus for Khvalynsk soils it may be assumed that wa = 25% and a~ = 23 cm2/h while for Sarmatsk soils wa = 37% and a~= 27 cm2/h. When the thermal diffusivity is a constant, equation (2.51) transforms to

at 2 a2t at= at az2 •· The temperature at the surface of the soil at any given instant may be represented as a sum of two terms, the annual average temperature to and the temperature deviation tp (t) from the annual average

t(z, t)lz=O =to+ tp(t),

(2.52)

where t =time. If tp(t) is approximated by n

tp(t)

= LAi sin[(i211t/T) + ai],

. . . (2.53)

i=l

then from equation (2.52) the temperature distribution along the depth at any instant of time may be obtained as

t(z, t) = to(z) + tAi exp (- :t z=l

/0)

x· sin (i 2; t -

:t /0 + ai),

. . . (2.54) where T is the time period expressed in years; ai is the phase shift; and Ai is the amplitude of the harmonics.

91

The function to(z) corresponds to the solution [of the steady-state equation]

82to

az2 = 0.

. . . (2.55)

If the annual average temperatures to at the soil surface z == 0 and ton at z = H are known, then the solution of the steady-state equation (2.55) is obtained as z . . . (2.56) to(z) =to+ (toH- to)"k

The temperature distribution at different depths and different periods of time was obtained experimentally for Sarmatsk soils. It was found that the annual average temperature at various depths remains practically constant at 13°C, i.e.,

to(z)

=to = 13°C,

. . . (2.57)

while the temperature deviation at the soil surface from its annual average is described fairly well by the sinusoidal function

i.p(t) = 15 sin 2; t·

. . . (2.58)

The reference point for time was selected in such a way that phase shift a = 0. Then the instantaneous temperature distribution along the depth described by equation (2.54) is t (z, t) = 13 + 15 exp

( -zy{7(\ m)

. ( Tt2TI zy{"2:rr) m ·

X Sill

. . . (2.59)

The moisture flow j is made up of a liquid portion and a vapour portion j = Jw + Js· · ·. (2.60) In the case of weak transients, which holds true for variation in moisture and thermal conditions of swelling soils, migration of moisture in a liquid form in a direction perpendicular to the z axis through a unit area in unit time may be given by the Darcy equation .

Jw =

-Pw

ka h 1, apart from the stresses due to self-weight "fZ of the soil mass and that due to footing a zp• there is yet another additional stress caused by the nature of deformation of the soil due to its expansion. Then the total stress in the ith layer is given by: