soil mechanics in engineering practice 3rd edition karl terzaghi ralph b peck gholamreza mesri 1996...

CE264-GEOTECHNICAL ENGINEERING SOIL MECHANICS IN ENGINEERING PRACTICE-3RD EDITION-KARL-TERZAGHI-RALPH-B-PECK-GHOLAMREZA-MESRI-1996

100 HYDRAULIC AND MECHANICAL PROPERTIES OF SOILS

Frost action in humid regions with severe winters constitutes a counterpart to the annual volume changes due to desiccation in semiarid regions with hot summers, such as central Texas. It not only damages roads but also displaces retaining walls (see Article 45.5) and lifts shallow foundations. However, by inserting a layer of gravel between the highest water table and the frost line, the body of soil subject to freezing can be transformed from an open into a closed system, and frost heave can usually be kept within tolerable limits.

Selected Reading

Casagrande, A. (1931 ). "Discussion: A new theory of frost heaving," Proc. Hwy. Res. Board. 11, pp. 168-172.

Beskow, G. (1935). "Tjiilbildningen och Tjallyftningen med Siirskild Hiinsyn till Vagar och Jiirnviigar" (Soil freezing and frost heaving with special application to roads and railroads). Sveriges Geologiska Undersokning, Stockholm, Series Cv, No. 375, 242 pp.

Osterberg, J. 0. (1940). "A survey of the frost-heaving problem," Civil Eng., 10, pp. 100-102. Contains a condensed bibliography on the subject.

Physics of the Earth-Part IX. "Hydrology" (1942). Edited by 0. E. Meinzer, New York, McGraw-Hill, 1st ed., pp. 331-384. Review of present knowledge concerning soil moisture.

Yong, R. N. and B. P. Warkentin (1966). "Soil freezing and permafrost," Chapter 12 in Introduction to Soil Behavior. New York, MacMillan, pp. 391-428.

Frivik, P. E., N. Janbu, R. Saetersdal, and L. I. Finborud (1980). "Ground freezing 1980," Developments in Geotech. Eng., vol. 28, Elsevier, Amsterdam, 411 p.

ARTICLE 16 COMPRESSffiiLITY OF CONFINED LAYERS OF SOIL

16.1 Introduction

Fills and embankments that are wide compared with the thickness of the underlying compressible ground produce a one-dimensional state of compression of the ground. When a large area is loaded uniformly, every element of soil at every depth is confined by adjacent elements that are subjected to the same state of stress. There is no horizontal deformation of the soil except near the boundaries of the loaded area. A state of one-dimensional compression is also approximated in a clay layer loaded by a foundation, if the layer is overlain and confined by a desiccated crust or granular layer thick enough to minimize heave of the clay around the foundation. A similar deformation boundary condition exists when a foundation is placed deep enough that the surrounding overburden prevents lateral deformation of the clay located directly below the foundation. The thicker the overlying layers and the thinner the compressible clay, the more closely the deformation condition in the clay approximates one-

dimensional compression. The one-dimensional compression condition is also favored when the compressible ground is underlain by a stiff layer such as a dense granular soil or bedrock. Horizontal shearing resistances at the top and bottom boundaries of confined clay strata appreciably restrain the strata from stretching in horizontal directions.

Beneath embankments, storage facilities, and footings of limited size in comparison with the thickness of the compressible ground, the ideal one-dimensional state of compression does not exist. Some settlement is then caused by lateral displacement of soil from under the loaded area. However, inclinometer measurements of the lateral deformation of soil at the boundaries of embankments and storage facilities show that settlements resulting from lateral deformation are generally small compared with those resulting from compression if the factor of safety against undrained instability during construction or loading remains greater than about 1.4. The settlement caused by flow of soil from under the structure is then likely to be less than 10% of the end-of-primary settlement (Article 16.3) resulting from compression of the voids (Mesri et al. 1994).

Hence, the information required for computing settlement due to compression of clay strata under confined or other conditions that approximate one-dimensional compression can be derived from compression tests on laterally confined specimens. The tests are known as consolidation tests, and the apparatus in which they are conducted is termed an oedometer, Article 16.9. If the computed settlements are found to exceed a tolerable amount, the foundation is redesigned.

16.2 One-Dimensional Compression

In this section, the compressibility of soil is described for the condition of one-dimensional compression. The discussion is most applicable to transported saturated clays and silts. Settlement due to one-dimensional compression results only from decrease in the volume of the voids and can be analyzed in terms of effective vertical stress.

Every natural soil is characterized by its composition and structure (Articles 3 and 4). These two attributes are not completely independent of each other, because certain compositions favor particular types of structure. For example, a soil composed of quartz tends to have equidimensional rounded or angular particles and under natural conditions stabilizes at relatively low void volumes, whereas a soil composed of illite has plate-shaped particles and the potential to exist at high void volumes. However, even a soil with a particular composition may have different structures. An obvious example is a natural soil in its undisturbed and remolded states.

In addition to the mechanical and physicochemical conditions of deposition and to postdepositional changes


in composition, soil structure is determined by the effective-stress history. The effective vertical stress CJ'~ is defined by the total vertical stress CJ' v and the porewater pressure u, both of which are external to the soil structure (Article 15.3). Because of the particulate nature of soil and the existence of various interparticle bonds, some of which are viscous, the internal structural response to a change in the external effective stress is time-dependent. Thus, a soil's structure is determined not only by the effective stress but also by its time-history or aging. The existing state of consolidation of a natural soil is defined by the in situ void ratio e0 and the effective overburden pressure CJ'~0 •

Any combination of composition and structure that allows a soil to exist at a high volume of voids, as indicated by a high natural water content or void ratio, results in the potential for large volume changes. In most settlement problems the composition of a soil is not altered by the construction or loading, and compression takes place exclusively in response to an increase in effective vertical stress. The natural soil structure adjusts to a new external condition of effective stress by experiencing a decrease in the volume of voids. The compression response to the initial increments of effective stress is strongly influenced by the natural structure of the soil. However, after the initial compression begins to alter the natural structure, the compressibility increasingly reflects the composition. The effective vertical stress at which major changes in the natural soil structure begin to take place is called the preconsolidation pressure and is denoted by CJ';. In the range from CJ'~m to CJ';, designated the recompression range, the soil structure accommodates the increased effective stress without significant interparticle displacement. In this stress range, the compression results from the deformation of the soil structure, which involves only minor slip at interparticle contacts. The greater the interparticle bonding and cementation, the greater is the resistance to compression in the recompression range, and the more abrupt is the transition from recompression to compression, because major interparticle slip begins the process of destructuration at the preconsolidation pressure.

In the range beyond CJ';, known as the compression range, significant particle rearrangement is required to develop interparticle resistance to the increased effective stress. In highly bonded soils this rearrangement involves considerable compression, not only to accommodate the additional effective stress but also to compensate for the interparticle bond resistance destroyed by the compression beyond CJ';. This is especially true for deposits of marine clay and silt that were leached by seepage or diffusion subsequent to the development of a preconsolidation pressure by aging (Mesri 1993). Because the chemical alteration took place at a CJ'~0 less than CJ';, the fabric and void ratio of these clays remain substantially

ARTICLE 16 COMPRESSIBILITY OF CONFINED LAYERS 101

unchanged and correspond to their composition before leaching. When these clays are destructured by consolidation beyond CJ';, a major change in fabric and thus large compression take place in the transition from the fabric and structure of the original unleached clay to those of the present leached clay. In general, however, for all soils in the compression range, the compressibility decreases continuously as the effective stress and the corresponding compression increase.

16.3 Void Ratio-Effective Stress Relationship

Even in the absence of time-dependent changes in total stress and groundwater level or reference porewater pressure, the compression of saturated soils is time-dependent because it is the result of two separate mechanisms, each of which is time-dependent. This can be illustrated by the following basic equation relating void ratio, effective stress, and time

de ( ae ) dCJ'~ (ae) dCJ'~ dt = a(J'~ dt + at ' = avs dt + avt

t av

( 16.1)

where the subscripts v, s, and t denote vertical, stress, and time, respectively. The first term is time-dependent because the increase in effective stress always requires time due to the finite permeability of soils. This component of the time-lag is minimal for relatively permeable granular soils compared with silts or clays. The second term expresses the effect of the various internal components of effective stress; after an increase in effective stress, time is required to reach internal equilibration among the interparticle forces. This component of timedependent behavior is also less important for coarsegrained than for fine-grained soils because of the limited types of interparticle forces in coarse-grained soils compared with the forces acting between particles of the very fine fraction.

The first term in Eq. 16.1 represents the hydrodynamic, and the second term the structural time-dependent mechanism. Inasmuch as both mechanisms are related to the development of the internal components of effective stress in the soil, both are controlled by effective stress. However, it is not possible to evaluate the time-dependent responses of the various internal components of CJ'~ separately. Consequently, the compression rate deldt is for convenience expressed separately with respect to effective stress by avs and with respect to time by aw. The distinction is entirely arbitrary, however, because there are no differences between the mechanisms of volume change due to the changes in external effective stresses and those due to the redistribution of internal interactions. All the mechanisms of volume change, including the deformation, displacement, and aggregation or dispersion of particles; the distortion of adsorbed water films; and

the contraction or expansion of double layers, can operate during changes in external effective stress and with time.

When an increment Acr v of total vertical stress is applied to a saturated soft clay or silt, a porewater pressure Au develops. In one-dimensional compression at the instant of loading, Au is equal to Acr'" because the compressibility of the soil structure far exceeds the compressibility of both the water and the soil solids (Article 4). This increment of porewater pressure is termed excess porewater pressure, because it is in excess of an equilibrium porewater pressure. Given time, the excess porewater pressure dissipates, with a corresponding increase in effective stress. The period of time during which the excess porewater pressure dissipates is called the primary consolidation stage. The secondary consolidation stage corresponds to the period after the dissipation of the excess porewater pressure. Although it is true that, during secondary compression, water is discharged from the soil by a porewater pressure gradient generated by the tendency of soil structure to compress as indicated by av1,

the excess porewater pressure producing this gradient is so small that it need not be considered in analysis of secondary compression. On this premise, primary and secondary compression can be unambiguously defined by integrating Eq. 16.1 to obtain the total compression from the instant at which Acrv is applied to any elapsed timet. Thus

It ftp [ dcr' ] fr 0 de = 0 avs dtv + avt dt + t avt dt

p

The first integral from t = 0 to tp, at which the excess pore pressure is practically zero, is the primary compression, and the second integral from tP to any elapsed time tis the secondary compression. During secondary consolidation, when the effective vertical stress cr~ is essentially constant, the only contribution to the volume decrease comes from av1, whereas during primary consolidation both avs and avt contribute to the compression.

During primary consolidation, avs and av1 are not constants; both vary with elapsed time and with the location of the soil element with respect to the drainage boundary. Furthermore, there is no obvious relationship between values of av1 during secondary compression and those of avr during primary compression. Although it is possible to observe the settlement as a function of time during secondary consolidation and to evaluate avt• it is not yet possible to separate the contributions of avs and avt to the observed settlements during primary consolidation. For most practical applications this does not create a serious difficulty, because the void ratio-effective vertical stress relationship corresponding to the end-of-primary (EOP) consolidation has been found to be independent of the duration of the primary consolidation stage. This finding is known as the uniqueness of EOP e vs cr~ (Mesri and

Choi 1985b). Consequently, the EOP e vs cr~ data from small-scale laboratory samples can be used directly to compute the magnitude of the settlement of layers in the field without the need to evaluate avs and av1 separately. In contrast, modeling the time rates of settlement and porewater pressure dissipation during the primary consolidation stage requires assumptions regarding the behavior of avs and av1 (Mesri and Choi 1985a) (Article 25).

Examples of EOP void ratio-effective vertical stress relationships for typical samples of three natural clays are shown in Fig. 16.1. The procedures for developing the relationships in the laboratory are discussed in Article 16.9. The composition of Mexico City clay, w1 = 500%, wP = 150%, allows it to exist at unusually high natural void ratios; natural water contents in the range of 200 to 600% are not uncommon. Even at such high void ratios, the structure of the clay initially resists compression until the preconsolidation pressure cr; is exceeded. Beyond

1.0

60

50

18

16

1.4

2.4

2.2

2.0

18

1.6

M~xlco Clly Cloy trj,/t:r:o ~ 1.5

Louls~ville Clay t:rp/t:r:D: 2.8

Slop~= av

San Fronc1sco 8o! M~d tTp/tTvo ~ 1.3

(b)

Slo~<Cc

14o 80 t60 240 320 400 48030!:;--'-so~--L.l.-':loo!:::---2-:::!oo:-;:---'---'-s~oo Effectivl! Vutlcal Pr11ssur11 ftr;, kPa)

Figure 16.1 Relation between end-of-primary void ratio and effective vertical pressure for natural clays from Mexico City, Louiseville, and San Francisco (top to bottom). Effective vertical pressure plotted (a) to natural scale and (b) to logarithmic scale.


a;, the large compressibility in the compression range reflects the high natural void ratio. Louiseville clay, w1

= 65%, wP = 28%, is one of the highly sensitive clays of eastern Canada that have a highly bonded structure. Unless significant mineralogical changes occurred after deposition, the bonds most likely developed early during deposition and consolidation and thus allowed the clay to stabilize at a relatively high natural water content. In the broad recompression range from a~0 to a; the structural bonds resist compression until the recompression strains break them, whereupon the compressibility increases dramatically. For such clays at a given initial void ratio, the higher the preconsolidation pressure, the larger is the compressibility beyond a;. Because of its composition, the sample of San Francisco Bay mud, w1

= 89%, wP = 37%, stabilized at a relatively high water content. Its preconsolidation pressure is slightly higher than the present effective overburden pressure, possibly because of aging. In the compression range beyond a;, the compressibility of all soils decreases continuously with the increase in effective vertical stress.

Curves expressing the relation between void ratio and effective stress, such as those in Fig. 16.1, do not necessarily correspond to EOP consolidation. They may be plotted, for example, for a timet greater than tP. Under these conditions they will include not only the primary but also a portion of the secondary compression.

16.4 Preconsolidation Pressure

The preconsolidation pressure a;, at which major structural changes including the breakdown of interparticle bonds and interparticle displacement begin to occur, is one of the most important properties of soft clays. It defines the boundary between stiff and soft deformation response of a soil to loading. The magnitude of the preconsolidation pressure is best expressed in terms of the value of a;/a~0, known as the overconsolidation ratio, OCR. Measured magnitudes of a;/a~0 for a variety of natural soft clays are in the range of 1.2 to 3 except within the desiccated crust, where they may be much higher. One or more mechanical and physicochemical mechanisms contribute to the development of the increased interparticle resistance to compression in soft clays and thus to the magnitude of a;. Geologically, the best-known process is preloading, in which the increased resistance to compression is the result of previous consolidation of the clay under past effective vertical pressures higher than that of the existing effective overburden. Geological loading and unloading by thick sediments or glacial ice have produced the most highly overconsolidated clays. In soft clays and silts, fluctuations of the water table, underdrainage, minor erosion of sediments, and light ice and snow loads may have contributed to preconsolidation. Preconsolidation is also produced by desiccation of soils located above the water table (Article 15.6.3). Other processes


such as freezing and thawing, and chemical changes caused by precipitation and oxidation, also operate within the zone above the water table, known as the crust or weathered zone, and influence interparticle bonding and the preconsolidation pressure. If a layer of stiff clay is located above a layer of soft clay of the same type, it is likely that the upper layer has been precompressed by desiccation. Furthermore, if the upper layer was exposed to the atmosphere for a long time, it is also likely to be discolored by oxidation. In some instances, stiff crusts may have formed below the water table by subaqueous weathering or cation exchange (Mourn and Rosenqvist 1957).

Increased interparticle resistance and therefore preconsolidation pressure also develop when a soft clay or silt experiences secondary compression. For example, postglacial marine and lacustrine clays have experienced 5 to 10 thousand years of secondary compression. In these clays, values of a;/a~o as high as 1.4 to 1.6 may have developed by secondary compression alone. Thixotropic changes in structure and improved interparticle bonding through chemical changes with or without cementing agents also contribute to the magnitude of the preconsolidation pressure. The highest values of a;/a~00 such as those in the very sensitive and brittle clays of eastern Canada, have probably developed with the help of cementing by silicate or carbonate complexes. No other type of interparticle resistance is strong and brittle enough to produce the very flat recompression curves and abrupt transition to the compression range characteristic of these clays. A decrease in the volume of voids is not needed to produce the thixotropic increase in structural resistance that results from the reorientation of plate-shaped clay particles to edge-face short-range interaction, from the reorganization of ions, or from chemical changes such as cation exchange and cement bonding.

It is likely that more than one mechanism contributes to the development of increased resistance to compression of a natural soft clay. Soils that are known not to have been subjected to effective vertical stresses higher than the present effective overburden pressure and that display values of a;/a~0 = 1 are called normally consolidated. Only very young soil deposits, or those that either in the field or laboratory have just completed primary consolidation in response to a recent loading, can be expected to lack a recompression behavior and to have values of a;/a~o equal to unity. Soft clays that have experienced one or more mechanisms of secondary compression, thixotropic strengthening, or chemical increase in interparticle resistance, have values of a;/a~o greater than unity.

Soils that have been subjected to effective vertical pressures in excess of the present effective overburden are called precompressed or overconsolidated. The degree of overconsolidation is expressed as the overconsolidation ratio, OCR = a~ /a~o• where a~ is the maximum max max

past pressure. Overconsolidated soils include those that are lightly or heavily preloaded by snow, ice, or sediments, as well as soils that have been preconsolidated as a result of earlier water table lowering or underdrainage. They also include desiccated crusts in which the maximum past pressure is the equal all-around suction that developed in dry environments. If the maximum past

Pressure a~ was smaller than about 400 kPa, the clay max

may still be soft. If it was much greater, however, the clay is stiff. Since the magnitude of a~max cannot be readily determined for natural soil deposits, the OCR is defined by a~/a~m irrespective of the cause of the precompression pressure.

In summary, the precompression behavior of a clay can be due to the weight of soil strata that were removed by erosion, to the weight of ice that melted away, to desiccation, or to aging by processes such as secondary compression. If the precompression is due to a uniform load that has been removed, a~ - a~o is the same at every point along a vertical line below the ground surface, and a~ /a~o gradually decreases with depth. If the precompression is due to desiccation, a~ - a~0 and a~/a~o decrease in a downward direction from the former surface of evaporation. However, if precompression is due to secondary compression aging, a~/a~o remains constant and a~ a~" increases with depth.

16.5 Coefficient of Earth Pressure at Rest

A condition of laterally constrained one-dimensional deformation prevailed during sedimentation-consolidation and erosion-rebound of most natural soil deposits and currently exists in most soils with a level ground surface. The coefficient of earth pressure at rest Ko is the ratio of the effective horizontal pressure a/, to the effective vertical pressure a~ in a soil that currently exists under the condition of zero horizontal deformation, with principal planes that are horizontal and vertical. That is,

a/, K=-o I

av (16.2)

The fraction of the force of gravity that is transmitted to the vertical planes is a function of the angle of internal friction mobilized under the laterally constrained deformation condition. Consequently, the external horizontal support required to maintain the condition of zero horizontal deformation decreases with an increase in the mobilized angle of internal friction. Jaky (1944) developed an equation relating K, and the maximum available angle of internal friction ' by analyzing a talus of granular soil standing at the angle of repose. He assumed the angle of repose to be equal to the angle of internal friction '. This is a reasonable assumption for sedimented, normally consolidated young materials for which the angle of repose is equal to the constant-volume friction angle

<l>~·v (Article 19.1) (Cornforth 1973). For these soils <!>;v is practically equal to <j>'. Thus, Jaky's equation for Ka applies to sedimented normally consolidated young clays and granular materials that have not been densified by aging, precompression, or preshearing, for example, by vibration. This condition exists in the oedometer test (Article 16.9) at the end-of-primary consolidation in the compression range. The corresponding a/,/a~ is denoted by Kop· The Jaky (1944) analysis, after a simplification (Jaky 1948, Mesri and Hayat 1993b), leads to

Kap = 1 - sin ' (16.3)

Oedometer tests with horizontal pressure measurements, on loose granular soils as well as clays and silts in the compression range, lead to values of Kap that generally agree with Eq. 16.3. Values measured for clays and silts and for granular soils correspond to a range in ' of 18° to 43°, and measured values of Kap range from 0.31 to 0.67 (Mesri and Hayat 1993b).

The foregoing statements are illustrated by Fig. 16.2, which presents the results of an oedometer test with horizontal pressure measurements on a sample of Saint Alban clay, a material with a well-developed structure, for which w1 = 43%, JP = 22%, ' = 30°. Its in situ OCR, a;ta~o (Article 16.4), is 2.42. The progress of consolidation is shown by the EOP relation between the void ratio and the effective vertical pressure a~;

the corresponding effective horizontal pressures a/, are shown as a function of a;. The value of Ka (Eq. 16.2) can be obtained from the stress path, which starts from the in situ stress condition a:.a = 33 kPa and a/,0 = K,a;o = 27 kPa, at which Ko has the value of 27/33 = 0.82. At a vertical stress a; structural breakdown occurred, whereupon the stress path assumed a slope Kop corresponding to that of an unstructured material, and because of the lack of structure the backward projection of the stress path passes through the origin. The slope, 0.48, of the stress path above a; is therefore equal to Kap· However, after a waiting period of 33 days during which secondary compression aging occurred, the value of a/, increased and the stress path, although again approaching the slope K"P' remained permanently above the projection of the portion between a~ and the pressure at which the waiting period began.

Because most natural soil deposits have experienced some degree of densification by aging, precompression, or preshearing, rarely is the in situ K0 equal to Kop· For example, for the Saint Alban clay (Fig. 16.2), field and laboratory measurements (Tavenas et al. 1975, Mesri and Feng 1988, Me sri and Hay at 1993b) lead to an in situ Ko in the range of 0.77 to 0.85, and most soft clay deposits of marine or lacustrine origin display values in the range of 0.6 to 1.2. In soft clay and silt deposits, values of Ko greater than Kap result from secondary compression aging

Figure 16.2 Results of oedometer test with horizontal pressure measurements on undisturbed sample of soft, sensitive St. Alban clay.

and from precompression effects of erosion, porewater pressure fluctuation, and desiccation.

Field and laboratory methods for direct measurement of in situ cr/,0 and thus of K0 in natural soil deposits are quite difficult to carry out and require special expertise and considerable care. Hence, various empirical procedures have been proposed. The following equation is suggested for estimating the in situ Ko in marine or lacustrine soft clay and silt deposits that have not been presheared (Mesri and Hayat 1993b).

(16.4)

where k, is the slope of cr;, vs cr~ in the recompression

range, as illustrated in Fig. 16.2. A value of k, = Ka/2 is typical and leads to

K=-K -+1 1 ((]"; ) 0 2 op cr:,o

(16.5)

The Jaky Eq. 16.3 can be substituted into Eq. 16.5, and thus only cr;Jcr~o and <J>' are required for estimating the in situ K0 •

For estimating the coefficient of earth pressure at rest for highly overconsolidated stiff clays, shales, and granular soils that have not experienced preshearing, the following empirical equation is applicable:

(

1 )sin <!>~v K 0 = (1 - sin <l>~v) rr;

CTvo

(16.6a)

or, alternatively,

(16.6b)

The upper limit of Ko from Eq. 16.6 is the coefficient of passive earth pressure Kp (Article 27). Although Eq. 16.6 and even Eq. 16.5 are applicable to granular soils as well as to clays, undisturbed sampling, especially of clean granular soil deposits, for the measurement of cr; is quite difficult.

Preshearing of soils by vibration or compaction leads to a significant increase in Koo Simple empirical equations, however, are not available for estimating the Ka of compacted clays, or granular soils that have been densified by vibration (Peck and Mesri 1987, Peck 1993, Mesri and Hayat 1993a, Mesri et al. 1993). Moreover, preshearing of natural soil deposits by such processes as ice movement

soil mechanics in engineering practice 3rd edition karl terzaghi ralph b peck gholamreza mesri 1996...

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