Shearing Strength of Soils

SHEARING STRENGTH OF SOILS

SYMBOLS

Notation Dimensional Analysis

b = a length L c = the cohesion intercept M L-1 T-2

Ip = the plasticity index - P = a force M L T-2 u = the pore fluid pressure ML-1 T-2 θ = an angle Angle

µ1 = shear strength reduction factor related to time effects - µ2 = shear strength reduction factor related to fissuring - σ = the normal stress on a plane M L-1 T-2 τ = the shearing stress on a plane M L-1 T-2 φ = the angle of internal friction Angle ψ = an angle related to cohesion Angle

Subscripts etc. where not identified above ´ = parameter measured in terms of intergranular or effective quantities c = preconsolidation values cu = consolidated undrained parameters d = drained test parameters i.e. dissipated pore pressures e = so-called true parameters f = failure values max = maximum values n = normal to plane values nc = normally consolidated values o = overburden values u = unconsolidated undrained test parameters 1 = major principal values 2 = intermediate principal values 3 = minor principal values

1. INTRODUCTION Stability analysis in geotechnical engineering includes all studies which attempt to determine whether or not the average shearing strength of soil over the assumed failure surface has a sufficient factor of safety against failure. Basically such studies consist of comparisons between all the forces which are or may act to cause failure and the resisting forces provided by the soil's shearing strength. The shearing strength of a soil sample is generally defined as its maximum resistance to shearing forces. In special cases an ultimate, Figure 1. Stress-strain curves for sand. residual or post peak value is used. The peak and ultimate values are shown on the normal stress-strain plot of test results in Figure 1. The residual value (Skempton, 1964) may be taken as the value recorded on a presheared sample or on an intact sample which is subject to excessive shearing, such as in a ring shear apparatus (Bishop et al, 1971), where the Coulomb's original shearing strength equation or Law is shown on soil particles can rearrange themselves into preferred orientations. Figure 3 and was expressed in terms of total stresses by Normally stability problems are solved by approximating the stress-strain behaviour by an ideal rigid-plastic material as shown in Figure 2. Where such an assumption is made the stability can be expressed in terms of τf ' c % σn tan φ (1) some definition of the shearing strength τf alone (this need not be a maximum value of τ). In actual fact the failure strength varies with the normal stress on the failure plane. Coulomb is credited with being the first person to express this variable It should be noted that unless φ = 0 the value of τ is not equal to the failure strength in terms of two engineering properties or parameters, f maximum shearing strength stress τ . This relationship expresses both namely: max the variation of strength of a single sample to changing external stresses (1) cohesion (c), or the resistance due to the forces tending to bond or or the locus of test results using different samples of the same type soil. hold the soil particles together in a solid mass; Another point worth noting is that the equation must have some limitation (2) internal friction (φ), or the rate of change of the resistance due to an otherwise soil slopes with slope angles less than φ could theoretically be increase of normal stress (σ ) on the failure plane. n infinitely high. Particle crushing will obviously occur first.

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 99 remoulded soils, showed that the cohesion intercept was dependent on the moisture or water content of the failing soil sample. This led to what has

become termed the true cohesion (ce) and true angle of internal friction

(φe) which are determined as shown in Figure 4 and a restatement of equation (1) by

τf ' ce % σ´n tan φe (4)

ce ' σ´nc tan ψe (5)

where σ´nc is the effective intergranular pressure which would have to be applied normally to the failure plane of a normally consolidated sample of the same soil to give a failure water content of the same value as the

failing sample, and ψe is an angle which relates the true cohesion to σ´nc. Hvorslev's proposals are useful as an academic model for soil strength but are normally not used in practice.

Figure 2. Stress-strain curve for ideal rigid-plastic material.

Figure 3. Coulomb's law.

2. EFFECTIVE STRESS CONCEPT Unfortunately the values of c and φ were not found to be constant values. Their usefulness was not universally accepted until Terzaghi's concept of effective intergranular stress (σ´) was postulated. This related the soil's behaviour to the difference between the total stresses (σ) and soil fluid pressure (u) by σ´ ' σ & u (2) Figure 4. Hvorslev's concept of true cohesion and friction angle (e.g. Gibson, 1953) In accordance with Terzaghi's concept the shearing strength of a soil may be expressed as 4. PRACTICAL CONSIDERATIONS τ ' c´ % (σ & u)tanφ´ ' In nature soil has been affected by weathering and other phenomenon f n (3) c´ % σ´n tan φ´ so that fundamental relationships, such as suggested by Hvorslev, have not found general acceptance in practical engineering. In addition the where the primes signify that the soil parameters are determined using shearing strength of soil is, like most other engineering material, effective stresses or equivalent intergranular stresses. dependent on factors such as creep and fatigue. For these and other more complex reasons the shearing strength parameters used in practice are 3. TRUE PARAMETER CONCEPT generally based on simplifying conditions of determining the stability Hvorslev (e.g. Gibson, 1953) working with multiple samples of against immediate failure and (or) long term failure depending on the

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 100 nature of the problem. expression for shearing strength (equation (1)) and then apply the result to practical problems in terms of short term undrained or total stress In the analysis of immediate stability it is assumed that the soil has a parameters (equation (6)) or long term drained or effective stress very low permeability and the moisture content of the soil will remain parameters (equation (13)). unchanged during the course of the engineering works. For such conditions the soil is tested rapidly enough to ensure undrained conditions. 6. RELATIONSHIP BETWEEN PRINCIPAL STRESSES AND Interpretation of the test results is then based on considering the soil as a FAILURE SHEARING STRESS single phase material much as most other engineering materials (i.e. steel, The relationship between the principal major and minor stress and concrete and the like). Analysis is then performed by working in total failure shearing stress using the Coulomb failure criteria is illustrated by stresses. The shearing strength equation for immediate, total stress or resolution of the forces on the element shown in Figure 5. (Note that the undrained stability analysis for a soil at a given moisture content intermediate principal stress has no theoretical effect on the Coulomb failure criteria). τf ' cu % σn tan φu (6) where cu = the undrained cohesion φu = the undrained angle of internal friction It has been shown by Skempton (1948a) and Bishop and Eden (1951) that when soil samples at the same moisture content and same stress history are fully saturated and the pore fluid and soil solids are incompressible in comparison with the soil skeleton

φu ' 0 (7)

This result is extensively used when dealing with immediate stability problems involving saturated or near saturated clays and relatively impermeable saturated silts for which, very simply (further corrections Figure 5. Elemental stresses on random plane. may be required prior to application) for the identical saturated samples Resolving forces (P) normal to any assumed plane making an angle θ τf ' cu (8) with the plane on which the major principal stress acts

For saturated samples with different moisture contents cu would, of course, Pn ' P1 cos θ % P3 sin θ (14) vary. Thus in a natural soil deposit cu may vary with depth. b On the other hand where the permeability of the soil is high and rapid σn ' σ1 b cos θ % σ3 b tan θ sin (15) dissipation of pore fluid pressures occur, such as with clean sands and cos θ gravel, or in low permeability soils where a change in moisture content is likely during loading, the shearing strength is expressed in terms of 2 2 ˆ σn ' σ1 cos θ % σ3 sin θ (16) effective intergranular stresses as given by equation (3). The parameters are sometimes referred to as drained (more logically dissipated pore fluid where subscripts 1 and 3 refer to major and minor principal values, and b pressure) parameters is a length over which P1 acts. Resolving forces parallel to any assumed plane to find the shear force τf ' cd % σn tan φd (9) Pτ on the plane In a drained test the pore fluid pressures are zero (or used as the zero Pτ ' P1 sin θ & P3 cos θ (17) datum when not zero) so that

c ' c´ b d (10) τ ' cos θ (18) σ1 b sin θ & σ3 b tan θ cos θ σn ' σ´n (u ' 0) (11)

ˆ τ ' (σ1 & σ3)sinθ cos θ (19) φd ' φ´ (12)

Thus equation (9) becomes identical to equation (3) or If the assumed plane is the failure plane and Coulomb's relationship is

τf ' c´ % (σn & u)tanφ´ (13) taken as being valid on the plane

It should be clearly understood that the term "drained" refers to the τ ' τf ' c % σn tan φ (20) dissipation of pore fluid pressures and not to the drainage under gravity of pore fluid from the soil. Basically what is being referred to is the open Substituting equation (19) with suitable subscripts to indicate failure and position of the drainage cock leading to the pore water of the soil. With equation (16) for σn in equation (20) the cock open pore water may (drain) enter or leave the sample to maintain (σ & σ ) sinθ cosθ ' zero pore pressure. A fully saturated soil specimen subject to a drained 1 3 f laboratory test remains fully saturated. In clean sands, gravels and c % [(σ ) cos2θ % (σ ) sin2θ]tanφ (21) normally consolidated clays c´ is generally close to and assumed to be 1 f 3 f zero. c % σ3 tan φ σ1 ' σ3 % 5. THEORY VERSUS APPLICATION sin θ cos θ & cos2 θ tan φ (22) From a simple engineering mechanics point of view it is appropriate to at failure develop theoretical engineering solutions in terms of Coulomb's

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 101 The plane of least resistance would make this value of σ1 a minimum value to produce failure or For the case of a saturated soil tested in an undrained condition φu = 0. The total stress criterion using equation (31) then gives sin θ cos θ & cos2 θ tan φ ' Maximum (23) σ1 & σ3 To find the location of θ it is necessary to differentiate with respect to θ τ ' c ' { } (32) f u 2 f and equate to zero. d The other simple condition is for clean sands and gravels where c´ = 0. (sin θ cos θ & cos2 θ tan φ) ' 0 (24) The effective stress criterion using equation (31) then gives d θ σ´ 1 ' N´ 2 2 φ (33) cos θ ' sin θ % 2cosθ sin θ tan φ σ´3 (25) ' 0 7. MEASUREMENT OF SHEARING STRENGTH The shearing strength of a soil can be determined in situ or in the & cot 2 θ ' tanφ (26) laboratory. In situ tests are often preferred in the practice of engineering because great care and judgement are required in the sampling, transportation, storage and handling of laboratory samples prior to testing. π φ φ 9θ ' % ' 45E % (27) Furthermore, cohesionless soils are badly disturbed during sampling and 4 2 2 handling. Such disturbance makes correlations between laboratory testing Substituting back into equation (22) gives (at failure) and field performance questionable. Fortunately for granular soil c´ may be taken as zero and field testing is then correlated with φ´ only. The high permeability of most granular soil generally means that undrained failure σ1 ' σ3 Nφ % 2 c Nφ (28) is unlikely. For cohesive soils, however, the long term parameters cannot where be satisfactorily determined in situ and these soils are often sampled and tested in the laboratory. Laboratory testing must also be relied on to 1 % sin φ determine the parameters of placed and compacted soils where testing of Nφ ' 1 & sin φ these soils is required. φ ' tan2 (45 % ) Although c and φ are not true constants in practice they are generally 2 (29) regarded as constant at any given point (or depth) over the stress range 1 ' likely to be encountered in the field problem being analyzed. φ Consequently, testing should be carried out at stress magnitudes tan2 (45 & ) 2 appropriate to the solution and location being considered. For example in a φu = 0 analysis cu is constant at a given depth but may vary, often Also substituting equation (27) in equation (19) linearly, with depth. The values of c and φ, if assumed constant may be determined by φ φ τf '(σ1 &σ3)f sin (45% )cos(45% ) (30) carrying out two or more (generally three is considered minimum) tests 2 2 with different normal pressures acting on the plane of shear failure. If the only when φ = 0 does the Coulomb failure shearing stress equal the shearing strength on the failure plane is measured directly, as in the shear maximum shearing stress. This may easily be seen on the Mohr circle box text shown in Figure 7, the shearing strength may be plotted directly shown in Figure 6. The Mohr circle is a useful method of verifying the against the normal stress on the induced failure plane to give c and φ as above equations. It may be seen that the radius of the Mohr circle which shown in Figure 3. must touch the failure locus shown in Figure 6 is (at failure)

σ & σ c σ % σ 1 3 ' { % 1 3 }sinφ (31) 2 tanφ 2 which may be rearranged to give equation (28).

Figure 7. Principle of direct soil-shear testing apparatus.

Alternatively where the external stresses are controlled, such as the principal stresses in the triaxial tests shown in Figure 8, the results may be plotted on a Mohr circle as shown in Figure 9. Once two or more failure circles are drawn a common tangent determines the values of c and φ.

Normally the triaxial test is done in compression with σ2 = σ3 however an extension test is sometimes done in research or expensive projects

where warranted. In such cases σ1 = σ2. In either case the value of σ2 has no theoretical effect on the Coulomb failure criteria, although in fact some differences have been noted (Bishop, 1966). Because of these differences Figure 6. Failure stress interrelationships from Mohr's a number of different laboratory testing equipment are available for circle. research and special projects. The shear box and triaxial test equipment

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 102 are the mainstay of a commercial laboratory particularly where both c and complex equipment are also available (e.g. the plate test and in situ shear

φ are required. A special form of triaxial test where σ3 = 0 is known as the box used by Marsland, 1971). unconfined compression test. 8. TYPES OF SHEAR TESTING Three main types of tests are performed on soils dependent on the dissipation of pore pressures (termed drainage) from the specimens under test.

(A) Immediate or Undrained Test (also known as Quick Test): the samples are subject to an applied pressure (under conditions of no drainage) and as quickly thereafter sheared. Care is taken to prevent (in fact this is difficult) any dissipation of pore pressure since the results assume none has occurred. The test is most applicable to clays with low permeability where drainage is very slow and negligible if the test is performed quickly. If the soil samples being tested have the same stress

history and are fully saturated then at failure φu = 0 as shown in Figure 12. This is one way of establishing that a soil is fully saturated. Clays with fine sand lenses where cavitation of air from the pore fluid often occurs prior to failure and partially saturated soils with high degrees of

saturation generally give low values of φu. The undrained immediate Figure 8. Stresses acting on triaxial compression sample. strength is also obtained in situ with the vane equipment. This test is most applicable to soft saturated soils. For such a result φ = 0 is assumed.

Similarly in the laboratory when the unconfined compression test σ3 = 0 is done φu = 0 is assumed and (σ1 - σ3) = 2 cu. For different sets of samples (i.e. from different depths) different values of cu will obviously be obtained.

Figure 10. Experimental determination of c and φ.

Where either c or φ is assumed several tests are available both for in situ and laboratory testing. The most common in situ tests are the vane shear test shown in Figure 10 for use in soft clays to measure cu (φu = 0) Figure 11. Main characteristics of standard penetration test. and the standard penetration test shown in Figure 11 for use in sands where the number of blows of a standard sampling spoon is related to φ´ (c´ = 0). Other common field equipment includes the static or dynamic (B) Consolidated Undrained Tests: the samples are allowed to cone penetrometer for sands (Sanglerot, 1972) and the pressure meter consolidate under an applied pressure. Once equilibrium is reached the (Baguelin et al, 1978) for stiff clays and soft rocks. Numerous more drainage cock is closed and they are then sheared at constant moisture content under conditions of no drainage. The total stress parameters,

obtained by using different consolidation pressures, ccu, φcu are of little value in practice so pore fluid pressure is generally measured during the test. Where the pore fluid pressures are measured the test must be performed slow enough to allow equalisation of pore pressure (normally 95%) since the sample may not be perfectly uniform in composition or external loading. This allows the effective or long term strength parameters c´ and φ´ to be obtained as shown in Figure 13. Because of the slow rate of consolidation of soils having low permeability this test is generally preferred for obtaining the c´ and φ´ values of clays. There is no equivalent in situ test. The value of c´ and φ´ is affected by the consolidation pressure used in relationship to the soil's preconsolidation pressure. When the consolidation pressure greatly exceeds the preconsolidation pressure c´ is normally observed to be close to zero which is a characteristic of normally consolidated remoulded clays.

(C) Drained Tests: the samples are allowed to consolidate as in the consolidated undrained test and then sheared slowly enough that any Figure 11. Principle of vane shear apparatus. excess pore pressures dissipate completely (normally 95% dissipation is

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 103 acceptable). In highly permeable material this test is preferred because of material generally result in c´ = 0. On dense material, as shown in Figure the difficulty of ensuring no escape of water in the consolidated undrained 14, the anomaly c´ … 0 is often obtained due to the fact that φ for dense test. In soils of low permeability such as clays the time required to ensure cohesionless soils tends to decrease with increasing confining pressure. 95% dissipation of all pore pressures becomes excessive. This test is Indeed if the confining pressure is excessively too high severe particle particularly suited for granular cohesionless materials. In the field it is crushing occurs. The decrease in φ is important for high earth dams and performed indirectly in the form of a standard penetration test (SPT) or the like. Under normal foundation engineering loads c´ = 0 is generally cone penetration test in which case c´ = 0 is assumed and correlations exist assumed. Thus from one test result to establish φ´. Since the effective and total stresses are the same, results similar to the effective stress construction shown in Figure 13 are obtained. Small differences, which are generally neglected, sometimes exist.

Figure 12. Undrained results on saturated soils with identical histories.

Figure 15. Typical shearing strength of rockfill (e.g. Leps, 1970).

For dense clean granular soils, particularly gravel sized material and larger, this often leads to the nonsensical result of φ´ > 45E. This is clearly not the friction between two surfaces but includes energy required for dilation. Nevertheless, because of established usage of the c´ = 0 approximation and the fact that the energy to cause dilation would be required to cause failure in situ this convention is maintained herein. An increase in density (decrease in porosity or void ratio) at a constant value

Figure 13. Consolidated undrained test results. of σ´n thus causes an increase in φ´ The effect of increasing the confining pressure on granular materials at a given density results in a decreasing value of φ´ as shown by Taylor (1948) for sands (Figure 15) and by Leps (1970) for larger size particles (Figure 16). Leslie (1963) has shown that well (or broadly) graded granular soil has a higher value of φ´ than a uniformly graded (single sized or well sorted) soil with the same maximum particle size. In addition a higher φ´ is recorded for the larger particle sized soils of two similarly graded soils. Soils composed of angular particles generally have higher values of φ´ than soils composed of rounded particles as shown in Table 1 (Sowers and Sowers 1951). Typical values of φ´ for granular soils loaded at normal engineering foundation stresses are given in Table 2. These values would decrease under the high pressures associated with high dams and the like. In the field values of φ´ are normally obtained from either the standard penetration test (SPT) or cone penetrometer. Typical test correlation values for sands at σ´ = 200 kPa are shown in Table 3. The values of φ´ Figure 14. Triaxial compression tests on crock ballast n should be decreased 5 for non-plastic (plastic index less than 6) silt size (e.g. Raymond and Davies, 1978) E soils and silty sands and increased 5E for gravel sand mixtures. Silts and sands with plastic fines should be evaluated as cohesive soils.

9. SHEARING STRENGTH OF COHESIONLESS SOILS τ The mobilisation of shearing resistance of cohesionless soils is &1 f φ´ ' tan ( ) (34) illustrated by the stress-strain curves shown in Figure 1. For dense σ´n granular materials the resistance increases to a peak value and then decreases as the strain increases further to an ultimate value. During this post peak period the soil particles gradually loosen to a condition 10. SHEARING STRENGTH OF COHESIVE SOILS approximately the same as that of the granular material in the loose state. The selection of the shearing strength parameters appropriate to an The value of φ for loose granular soil often being called the angle of engineering works built in cohesive soils is one of the most complex and repose. Several tests conducted at different confining pressures on loose difficult decisions facing the Geotechnical engineer. It is the intent herein

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 104 to deal only with the strength of cohesive soils in a simplistic manner. Other factors such as anisotropy are also important but are generally not Cohesive soil properties need selection for three types of common analysis specifically determined in routine commercial investigations. depending on the appropriateness of the problem

Table 1. Effect of Angularity and Grading on Peak Effective Friction Angle of Coarse Sand in Degrees (e.g. Sowers and Sowers, 1951).

Shape and Grading Symbol Loose Dense

Rounded, Uniform SP 30 37 Rounded, Well Graded SW 34 40 Angular, Uniform SP 35 43 Angular, Well Graded SW 39 45

Figure 17. Relation between sensitivity and salt concentration in pore-water of marine clays (e.g. Skempton, 1953).

The undrained strength classification, often termed consistency, varies as shown in Table 4 from very soft to hard. These terms have no relationship to stress-strain properties since soft clays may, in some cases, be extremely brittle. It will be noted that the strength range covered by each higher consistency level is twice the range and values of the directly lower level.

Very soft and soft cohesive soils are generally intact and show little or no fissuring. Stiff to hard consistency clays, on the other hand, are very frequently fissured. Indeed as the strength increases some of the fissures may become classified as joints and these hard soils become indistinguishable from soft rocks. Clearly there is no clear cut division between these definitions and great care must be exercised in dealing with problems where fissures or joints are likely to be important in any stability analysis. Medium strength clays are likely to be either intact, showing no signs of a fissured pattern, or be clearly fissured. Their behaviour will be very much dependent on their physical nature. Figure 16. Typical friction angles from direct shear tests on sub-rounded sand (e.g. Taylor, 1948). The sensitivity of a cohesive soil is defined as the ratio of its undisturbed undrained strength to the remoulded undrained strength of the same soil. A sensitivity classification (Skempton and Northey, 1952) may be made and is shown in Table 5. It should be clearly understood that determination of a soil's sensitivity is not standardized. For the higher (i) the total stress or undrained stability, which for a saturated soil, yields values of sensitivity there will normally be considerable differences in the

some appropriate proportion of cu … 0 and φu = 0, values determined in the laboratory and in the field. The value determined (ii) the peak effective stress analysis in terms of some appropriate by field vane is often less than that obtained by a laboratory triaxial or, proportion of c´ and φ´ more commonly, unconfined compression test. Further complications

(iii) the residual effective stress analysis in terms of c´r and φ´r. occur due to the fact that sensitive clays show different degrees of strength regain (known as thixotropic strength regain or thixotropy) after 11. STRENGTH CLASSIFICATION OF COHESIVE SOILS remoulding. Thus the time between remoulding and testing may have an Because cohesive soils often present serious stability problems the appreciable effect on the measured value of sensitivity. further classification of these soils beyond that established using the Unified System is most common. Three main characteristics of immediate One of the best known type of clay deposits exhibiting high interest in any stability analysis are sensitivities are those deposited in a sea water environment and then

(i) Variation of undrained shearing strength cu of the soil deposit leached by fresh water. Sensitivity in these deposits are sometimes related (ii) Nature of fissuring within the soil deposit to residual salt content (Figure 17). (iii) Sensitivity of the various soil layers within the deposit.

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 105 Table 2. Typical Values of Frictional Angles for Granular Soils for σ´n = 100 kPa

Soil Type Symbol Loose Medium Dense

Silt (non-plastic) ML, MH (PI<6) 26 - 30 28 - 32 30 - 34 Uniform Sand and Silty Sand SP, SM 26 - 30 30 - 34 32 - 36 Well Graded Sand SW 30 - 34 34 - 40 38 - 46 Gravel GW, GP, GM 32 - 36 36 - 42 40 - 48

Table 3. Relationship for φ´ and In situ Tests in Clean Sands

Sand Density (SW,SP) Relative Density Standard Penetration Static Dutch-Cone Angle of Internal Test N - blows/300 mm Resistance Friction*

qc - MPa φ´ Degrees

Very Loose < 0.2 < 4 2 < 28 Loose 0.2 - 0.4 4 - 10 2 - 4 28 - 30 Medium 0.4 - 0.6 10 - 30 4 - 12 30 - 37 Dense 0.6 - 0.8 30 - 50 12 - 20 37 - 42 Very Dense > 0.8 > 50 > 20 > 42

* Decreases 5E for non-plastic silts (ML,MH with PI < 6) and silty sands (SM) Increase 5E for gravel or gravel sand mixtures (GW,GP,GM)

In a new, fresh or young deposit of uniform, fully consolidated soil the Table 4. Consistency of Saturated Clay Soils effective overburden pressure in most practical cases, increases relatively uniformly with depth (Skempton, 1948a) though, due to positive or Consistency Unconfined Shearing Standard negative artisan water pressure, this may be slower or faster than given by Compressive Strength Penetration a static water table assumption. In such a normally consolidated soil Strength-kPa (kPa) Blows/300 mm deposit this uniform increase in effective overburden pressure (σ´o) is associated with a decrease in moisture content of the soil and a uniform

Very Soft < 25 < 12.5 < 2 increase in undrained shearing strength (cu). Note that if three samples of Soft 25 - 50 12.5 - 25 2 - 4 soil from the same depth are tested in an unconsolidated undrained test φu Medium/Firm 50 - 100 25 - 50 4 - 8 = 0, cu = constant for the given depth. On the other hand if a series of Stiff 100 - 200 50 - 100 8 - 15 such sets of tests are performed, each set from different depths, and the

Very Stiff 200 - 400 100 - 200 15 - 30 value of cu for each depth is compared with the effective overburden (σ´o) Hard > 400 > 200 > 30 then (in practice cu is obtained with an in situ vane test or unconfined compression test)

cu ' constant (35) Table 5. Sensitivity of Clays σ´o (after Skempton and Northey, 1952). This very important relationship is characteristic of young normally Classification Strength Ratio consolidated clay deposits. Where erosion of a young normally consolidated clay deposit has occurred the deposit becomes lightly Insensitive < 1 overconsolidated. Because the expansion index of a soil is very much Low Sensitivity 1 - 2 smaller than its compression index a small decrease in effective stress (due Medium Sensitivity 2 - 4 for example to erosion) has little effect on the soil's moisture content and Sensitive 4 - 8 on its undrained shearing strength cu at a given depth. It does, however Extra Sensitive 8 - 16 have an effect on the effective overburden pressure. In lightly Quick > 16 overconsolidated young deposits of clay equation (35) must be modified to

cu ' constant (36) σ´c 12. STRENGTH CHARACTERISTICS IN SOFT CLAYS Very soft and soft clays are generally intact, rarely exhibiting any where σ´c = the preconsolidation pressure (in effective stresses) fissures. They have a liquidity index over 0.5 depending on their sensitivity and strength. Sensitive soils have a liquidity index close to or As the amount of erosion increases the assumption of no change in cu greater than 1.0 and insensitive soils a liquidity index less than 1.0. The at a given depth becomes less valid and thus equation (36) decreases in liquidity index decreases as the strength (consistency) increases and for correctness. stiff and very stiff clays reduces to a value close to zero.

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 106 Obviously both equations (35 and 36) will be valid although the constants will be different. An example of a deposit exhibiting this quasi- preconsolidation due to aging is shown in Figure 18. For glacial and post glacial clays the constants of equations (35 and 36) generally range with the limits shown in Figure 19.

Figure 18. Example of 'aged' normally consolidated clay (e.g. Raymond, 1968).

Figure 20. Post failure factors of safety from undrained total

stress analysis using full values of cu (e.g. Bjerrum, 1973)

Figure 21. Variation of φ' with plasticity index for normally Figure 19. Typical characteristic values of glacial and post consolidated remoulded clays (e.g. Gibson, 1953). glacial normally to lightly overconsolidated clays (e.g. Bjerrum, 1973). Normally consolidated deposits may also be aged by other factors such as the bonding of particles by chemical action. These soils may also show Normally consolidated clays may exhibit a continuing consolidation at a relationship expressed by equation (36) and it is common engineering approximately constant effective stress (known as secondary practice in normally consolidated and lightly overconsolidated clay to consolidation). This causes a slow decrease in moisture content and a check the validity of both equations (35) and (36). slow increase in shearing strength. This rate of increase in strength has been shown by Bjerrum (1967) to be dependent on the effective Very soft and soft clay deposits of saturated or near saturated soils are overburden pressure such that in some aged normally consolidated clays generally intact (do not exhibit fissures). Their short term undrained both equations (35 and 36) are valid (the constants are different). For strength is based on φu = 0, cu … 0 with a correction for the difference in normally consolidated deposits aged and modified by secondary rate of testing (Casagrande and Wilson, 1951), soil anisotropy and other consolidation only, the induced preconsolidation pressure, known as factors. The correction to be made to the value of cu has been the subject quasi-preconsolidation, increases uniformly with depth so that of an extensive study by Bjerrum (1973). The correction factor was correlated, with sufficient accuracy for practical purposes, to the soil's σ´c ' constant (37) Plasticity Index (Ip). This is shown in Figure 20 and may be expressed by σ´o

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 107 1 µ1 ' (38) 0.84 % 0.08 Ip where the engineering undrained stability strength is given by

τf ' µ1 cu (39)

It is recommended that µ1 should not be taken as greater than 1. LaRochelle et al (1974) have suggested that the value of µ1 may be obtained by using the post peak strength (termed, by them, the undrained residual) recorded at relatively low strains since this strength could drop drastically on remoulding. Limited data is presently available on this procedure. The long term or effective stress stability of very soft and soft normally consolidated and lightly overconsolidated clays are based on the peak values of c´ and φ´. Great care must be taken to determine the parameters over the stress range applicable to the field since in aged clays the parameters change quite abruptly if the soils are subject to in situ shear stresses close to failure or close to or above the preconsolidation pressure. According to Bjerrum (1973) the correction for rate of loading is similar in magnitude to that expressed by equation (39).

τf ' µ1 (c´ % σ´n tan φ´) (40) Figure 22. Typical results for fissure clay (e.g. Ward et al.). Gibson (1953) has given a tentative relationship for φ´ of normally consolidated remoulded clays, Figure 21. Further data confirming the guide has been presented by Kenney (1959). Sensitive soils are particularly prone to major changes in their long term strength parameters if loaded close to their preconsolidation pressures along with major changes in their settlement parameters. These changes may result in large long term deformations due to creep and (or) consolidation. Sensitive soils may be treated, in terms of stability analysis, like insensitive soils except that higher factors of safety should be required particularly where failures are likely to cause large and possible catastrophic deformations.

13. STRENGTH CHARACTERISTICS OF STIFF TO HARD CLAYS Intact, non-fissured very stiff to hard clays may be considered such a rarity that where they are reported it is recommended that a careful check be undertaken or they be regarded as fissured. Fissured clays exhibit weaknesses along the fissures which in random testing depends on the size of specimen. Where selected testing is done results similar to those shown in Figure 22 are obtained. For random testing the strength decreases as the specimen size increases since larger specimens are more likely to include more representative fissures of field scale. Considerable scatter must be expected in a testing program and this is illustrated in Figure 23 which shows the strength profile for a deep deposit of very stiff to hard London clay. Provided that, in the field, water cannot enter the fissures and cause rapid softening a total stress or undrained analysis in fissured clay may be performed in the same way as any other undrained strength analysis except that a factor (µ2) for fissures needs to be included.

Thus Figure 23. Strength-depth profile for london clay (e.g. Ward et al, 1965). τf ' µ1 µ2 cu (41)

Little information is available on the variation in values of µ2 for different soil types. Generally local or regional information exists where a record In reality the undrained stability of stiff to hard clays is not generally of case histories has been kept by local engineers. Quite often there are a major consideration since the strength is more likely to decrease in the Governmental records since Governments are the major clients dealing long term. Short term considerations should be centred on preventing the with public works. fissures from opening. If the fissures do open then water enters the fissures and softens the clay adjacent to the fissures. The strength of the

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 108 soil adjacent to the fissures decreases and also controls the 'global' strength of the deposit. Under such conditions the strength drops to values closely associated with the residual strength parameters. This may occur quite rapidly particularly where the prevention of fissure opening cannot be or is not engineered.

For long term stability involving increases in compressive lateral forces it is reasonable to assume that any fissures would remain closed and the long term stability may be based on peak effective stress parameters modified for time effects and fissure spacing.

τ ' µ1 µ2 (c´ % σ´n tan φ´) (42)

Figure 25. Decrease in φr' with increasing clay fraction (e.g. Skempton, 1964)

Figure 24. Comparison of drained strength of intact and failed overconsolidated clay (e.g. Skempton, 1964)

Figure 26. Properties of an overconsolidated clay On the other hand when considering the long term stability involving (e.g. Skempton and Larochelle, 1965) decreases in compressive lateral forces the possibility of fissure opening is of major concern. In such circumstances the long term strength should 15. SOILS WITH STRUCTURALLY UNSTABLE SOIL FABRIC be based on residual effective stress parameters. Since theses should be Although not stated so far in the discussion of shearing strength it has obtained at very slow rates of loading and along presheared failure planes, been implicitly assumed that the soils under discussion have a soil fabric as illustrated in Figure 24, no time or fissure coefficients are necessary structure which is sufficiently stable that it may be simplistically and thus modelled. These soils are characteristic of those found in post glacial regions and in alluvial deposits. They are composed in the main of relatively inert, natural or artificially compacted materials which are over τf ' c´r % σ´n tan φ´r (43) 90% saturated. Of more complexity are the soils of diverse characteristics occurring in climatic regions which produce occasional or continuing

A rough guide, shown in Figure 25, to the value of φ´r has been presented aridity. Present fundamental knowledge of these soils is limited but has by Skempton (1964) who found the value to be very much affected by the been summarized by Aitchison and Tokar (1973) under the term known clay content of a soil. as 'structurally unstable soils'. There is no clear definition of a 'structurally unstable soil' however such soils have stress-strain responses 14. STRENGTH CHARACTERISTICS OF MEDIUM TO STIFF which cannot be quantified simply in terms of the applied stress level and CLAYS an applied stress dependent pore fluid response. The definition includes Medium to stiff intact clays should be treated in much the same way as high void ratio sands, silts and clays which are unsaturated and lightly soft and very soft clays. On the other hand medium to stiff fissured clays cemented and which collapse or expand on wetting or leaching in the should be treated in much the same way as stiff to hard clays. The scatter unloaded or lightly loaded condition. They also include those high void in strength data may be expected to increase as the strength increases and ratio soils which may be subject to dynamic loading and respond by as the overconsolidation ratio increases. In a strength depth profile a liquefaction. general curve in the data, as shown in Figure 26, may be expected due to the reduction in strength with loss of overburden or increase in The solution to a problem on a 'structurally unstable soil' generally overconsolidation ratio. takes on one of the following (a) to design for collapse (swelling) as quantified

Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond© 109 (b) to design for avoidance of collapse (swelling) by precluding the American Society of Civil Engineers, Volume 85, No. SM3, June 1959, operation of the triggering mechanism pp. 67-79. (TA710.A1 A57). (c) to induce collapse (swelling) prior to construction (d) to apply soil stabilization processes to modify or remove the LaRochelle, P., Trak, B., Tavenas, F. and Roy, M., (1974) "Failure of a susceptibility of the soil to collapse (swelling). Test Embankment on a Sensitive Champlain Clay Deposit", Canadian At the present time a practical scientific approach to the problems Geotechnical Journal, National Research Council of Canada, Ottawa, involving 'structurally unstable soils' has not been developed which is Volume 11, No. 1, February 1974, pp. 142-164. (TA1.C213). generally accepted. This is mainly due to the fact that the hazard to life and injury is largely absent in these soils and thus research funding has Leps, R.M., (1970) "Review of Shearing Strength of Rockfill", Journal of been noticeably minor. Nevertheless it should be understood that property the Soil Mechanics and Foundation Division, American Society of Civil damage due to collapsing and swelling soils in terms of damage to houses, Engineers, Volume 96, No SM4, Proceedings Paper 7394, July 2970, pp. buildings, roads and pipelines is conservatively estimated for the U.S.A. 1159-1170. (TA710.A1 A57). by Jones and Holtz (1973) to be more than twice that due to damage from floods, hurricanes, tornadoes and earthquakes. Leslie, D.D., (1963) "Large Scale Triaxial Tests on Gravelly Soils", Proceedings of the Second Panamerican Conference of Soil Mechanics These soils will not be dealt with herein but the interested reader is and Foundation Engineering, Brazil, Volume 1, 1963, pp. 181-202. referred to the State-of-the-Art statements in various Proceedings of the (TA710.P187). International Society of Soil Mechanics and Foundation Engineering Conferences as a suitable starting point. Marsland, A., (1971) "Large In situ Tests to Measure the Properties of Stiff Fissured Clays", Proceedings of the First Australian - New Zealand 16. REFERENCES Conference on Geomechanics, Melbourne, 1971, Volume 1, pp. 180-189. Aitchison, G.D. and Tokar, R.A., (1973) "Problems of Soil Mechanics and (TA710.A83t). Construction on Soft Clays and Structurally Unstable Soils (Collapsible, Expansive and Others)", Proceedings of the Eighth International Raymond, G.P. (1968) "Construction Method and Performance of an Conference on Soil Mechanics and Foundation Engineering, Moscow, Embankment on Deep Muskeg", Proceedings Third International Peat August 1973, Volume 3, pp. 161-190. (TA710.I6t). Congress, Quebec City, pp. 51-56. (TA710.A1 N27).

Baguelin, F., Jezequel, J.F. and Shields, D.H., (1978), "The Pressuremeter Raymond, G.P. and Davies, J.R., (1978) "Triaxial Tests on Dolomite and Foundation Engineering", Trans Tech Publications, Germany. Railroad Ballast", Journal of the Geotechnical Engineering Division, (TA775.B22 1987t). American Society of Civil Engineers, Volume 104, No GT6, June 1978, pp. 737-751. (TA710.A1 A57). Bishop, A.W., (1966) "The Strength of Soils as Engineering Materials", Geotechnique, The Institution of Civil Engineers, London, Volume 16, Sanglerat, G., (1972) "The Penetrometer and Soil Exploration", Elsevier No. 2, June 1966, pp. 91-128. (TA1.G3). Publication Co., Amsterdam. (TA710.5 S2523).

Bishop, A.W. and Eldin, G., (1950) "Undrained Triaxial Tests on Skempton, A.W., (1948a) "A Study of the Immediate Triaxial Test on Saturated Sands and Their Significance in the General Theory of Shear Cohesive Soils", Proceedings of the Second International Conference on Strength", Geotechnique, The Institution of Civil Engineers, London, Soil Mechanics and Foundation Engineering, Rotterdam, Volume 1, June Volume 2, No. 1, June 1950, pp. 13-32. (TA1.G3). 1948, pp. 192-196. (TA710.I6t).

Bjerrum, L., (1967) "Engineering Geology of Norwegian Normally- Skempton, A.W., (1948b) "The Geotechnical Properties of a Deep Stratum Consolidated Marine Clays as Related to Settlements of Buildings", of Post-Glacial Clay at Gosport", Proceedings of the Second International Geotechnique, The Institution of Civil Engineers, London, Volume 17, Conference on Soil Mechanics and Foundation Engineering, Rotterdam, No. 2, June 1973, pp. 81-118. (TA1.G3). Volume 1, June 1948, pp. 145-150. (TA710.I6t).

Bjerrum, L., (1973) "Problems of Soil Mechanics and Construction on Skempton, A.W., (1953) "Discussion on Theories and Hypotheses of Soft Clays and Structurally Unstable Soils (Collapsible, Expansive and General Character, Soil Properties, Soil Classification, Engineering Others)", Proceedings of the Eighth International Conference on Soil Geology", Proceedings of the Third International Conference on Soil Mechanics and Foundation Engineering, Moscow, August 1973, Volume Mechanics and Foundation Engineering, Zurich, Volume 3, 1973, pp. 115- 3, pp. 111-159. (TA710.I6t). 116. (TA710.I6t).

Casagrande, A. and Wilson, S.D., (1951) "Effect of Rate of Loading on Skempton, A.W., (1964) "Long Term Stability of Clay Slopes", the Strength of Clays and Shales at Constant Water Content", Geotechnique, The Institution of Civil Engineers, London, Volume 14, Geotechnique, The Institution of Civil Engineers, London, Volume 2, No. No. 2, June 1964, pp. 77-101. (TA1.G3). 3, June 1951, pp. 251-263. (TA1.G3). Skempton, A.W. and LaRochelle, P., (1965) "The Bradwell Slip: A Short- Gibson, R.E., (1953) "Experimental Determination of the True Cohesion Term Failure in London Clay", Geotechnique, The Institution of Civil and True Angle of Internal Friction in Clays", Proceedings of the Third Engineers, London, Volume 15, No. 3, September 1965, pp. 221-242. International Conference on Soil Mechanics and Foundation Engineering, (TA1.G3). Zurich, Volume 1, August 1953, pp. 126-130. (TA710.I6t). Skempton, A.W. and Northey, R.D., (1952) "The Sensitivity of Clays", Jones, D.E. and Holtz, W.G., (1973) "Expansive Soils - the Hidden Geotechnique, The Institution of Civil Engineers, London, Volume 3, No. Disaster", Civil Engineering, American Society of Civil Engineers, 1, June 1952, pp. 1-16. (TA1.G3). Volume 43, No. 8, August 1973, pp. 49-51. (TA1.C58). Sowers, G.B. and Sowers, G.F., (1970) "Introductory Soil Mechanics and Kenney, T.C., (1959) "Discussion on Geotechnical Properties of Glacial Foundations", Third Edition, The MacMillan Co., New York, p. 556. Lake Clays", Journal of the Soil Mechanics and Foundation Division, (TA710.S67).

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Ward, W.H., Marsland, A. and Samuels, S.G., (1965) "Properties of the London Clay at the Ashford Common Shaft: In situ and Undrained Strength Tests", Geotechnique, The Institution of Civil Engineers, London, Volume 15, No. 4, December 1965, pp. 321-344. (TA1.G3).