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In this article we will discuss about how to determine the shear strength of soil.

**Shear Tests: **

The shear strength parameters (c, ɸ) are determined under definite test conditions. Depending upon the drainage conditions, three types of shear tests have been developed.

**They are:**

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(i) Unconsolidated undrained test (or simply undrained test) UU- No drainage of pore water is allowed during the entire test. Also called short-term test (During construction)

(ii) Consolidated undrained test, CU, (for long term) – Drainage and full consolidation of sample is allowed under a cell pressure σ_{3}. It is then sheared by applying deviator stress without allowing drainage.

(iii) Consolidated drained (CD) – Drainage is allowed throughout the test, first under σ_{3} and then while applying σ_{d}. Thus, pore pressure u is always zero and the stresses are effective stresses. The pore pressure during the undrained condition (UU and CU test) can be measured and the effective stresses can be calculated [σ_{d} = deviator stress = σ_{1} – σ_{3}]

**i. Direct Shear Test: **

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The specimen of the shear box is sheared under a normal load N. The shearing strain is made to increase at a constant rate, and hence the test is called the strain controlled shear box test.

The shear force F, at failure, corresponding to the normal load N is measured with the help of the proving ring. A number of identical specimens are tested under increasing normal loads and the required maximum shear force is recorded. The size of the box is 6 cm cube.

A graph is plotted between the shear force as the ordinate and the normal load as the abscissa. Such a plot gives the failure envelope for the soil under the given test conditions. Figure. 12.5(c) shows a plot given the failure envelope plotted as a function of the shear stress and the normal stress.

Any point F(σ, τ) on the failure envelope represents the state of stress in the material during failure, under a given normal stress. In the direct shear test, the failure plane MN is predetermined and is horizontal.

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In order to find the direction of principal planes at failure, we first locate the position of the pole on the Mohr circle on the principle that the line joining any point on the circle to the pole P gives the direction of the plane on which the stresses are applied.

Hence, through point F a horizontal line is drawn to intersect the circle at that point P which is the pole. Since points A and B represent respectively the major and minor principal stresses, PA and PB give the directions of major and minor principal planes.

Dividing the shear force and the normal force by the cross-sectional area of the specimen, we obtain the shear stress as well as the normal stress on the failure plane.

**ii. Unconfined Compression Test: **

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The resultant failure envelope is horizontal and the corresponding shear strength parameters defining this horizontal line are limited to an intercept value c_{u}, ɸ_{u} being zero.

When the Mohr circle is drawn, its radius is equal to σ_{1}/2 = C_{u}. The failure envelope is horizontal. PF is the failure plane, and the stresses on the failure plane are –

Where q_{u} = unconfined compressive strength at failure. The compressive stress is calculated on the basis of changed cross-sectional area A_{2} at failure, which is given by –

**iii. Triaxial Compression Test (Undrained): **

In CU test porous disc is used – L/D = 2

As per IS Code = 37.5 mm dia

L = 75 mm

A specimen 37.5 mm in dia and 75 mm long is generally used. The specimen is encased by a thin rubber membrane and placed inside a plastic cylindrical chamber that is usually filled with water or glycerin.

The specimen is subjected to a confining pressure by compression of the fluid in the chamber. To cause shear failure in the specimen, one must apply axial stress through a vertical loading ram (sometime called deviator stress).

**The stresses can be applied in one of the two ways: **

1. Application of dead weights or hydraulic pressure in equal increments until the specimen fails.

2. Application of axial deformation at a constant rate by means of a geared or hydraulic loading press. This is a strain controlled test.

The axial load applied by the loading ram corresponding to a given axial deformation is measured by a proving ring or load cell attached to the ram.

Connections to measure drainage into or out of the specimen, or to measure pressure in the pore water are also provided.

Note — If L/d > 2.5 specimen act as column.

The advantage of this method (modified failure envelope) of plotting the failure envelope is that averaging of scattered test result is facilitated to a great extent, giving the mean value of the parameters.

**Skempton’s Pore Pressure Parameters: **

In many problems involving deformation of soil masses, it is essential to estimate the magnitude of the changes in pore water pressure resulting from change in the state of stress. In a saturated soil, changes in the principal stresses of σ_{1}, σ_{2} and σ_{3} result in a change in pore water pressure, Δu_{w}, for no drainage condition.

The change in pore water pressure. Δu_{w} is due to isotropic stress increase Δσ_{3 }together with an axial stress increases (Δσ_{1 }– Δσ_{3}) as in Triaxial Shear Test. Hence, coeff. B = Δu_{1}/Δσ_{3}

Change in pore pressure due to change in cell pressure.

The sample is saturated when it exhibits B-factor of 1.0 but not less than 0.9

During undrained condition, σ_{3} is held constant and σ_{1} is increased. The change in pore pressure. Δu is measured and then A Factor is computed.

**Vane Shear Test: **

The shearing strength of a soil can also be determined by using a device called the shear vane, which consists of four plates welded orthogonally to a steel rod. The test may be conducted either in the laboratory or in the field. The field vane will be larger in size than the laboratory shear vane as shown in Fig. 12.12.

The failure of the soil is induced by applying a torque to the vane introduced into the soil. The torque may be measured by a calibrated torsion spring, and the shearing strength s may be obtained as follows —

(If only one end of the vane partakes in shearing the soil)

Where T = torque, D = diameter of vane, H = height of vane. The vane shear test is particularly suited for soft and sensitive clays for which suitable cylindrical specimens cannot be easily prepared.

**Torvane Shear Test: **

The modification of vane shear, called Torvane, is convenient for investigating the strength of clays in the walls of test pits in the field or for rapid scanning of the strength of tube or split spoon samples.

The vanes are pressed to their full depth into the clay below a flat surface, whereupon a torque is applied through a calibrated spring until the clay fails along the cylindrical surface circumscribing the vanes and simultaneously along the circular surface constituting the base of the cylinder. The value of the shear strength is read directly from the indicator on the calibrated spring.

**Pocket Penetrometer: **

Pocket penetrometer can be used to determine undrained shear strength of clay soil both in the laboratory and in the field. The procedure consists in pushing the penetrometer directly into the soil and noting the strength on the calibrated spring.

**Ring Shear Test: **

In this test, the residual strength of an undisturbed clay can be determined under drained condition using ring shear apparatus. In this test a laterally (confined normally) loaded annular specimen is twisted with the confined rate of displacement or torque as shown in Fig. 12.12(a).

In order to ensure that no excess pore water pressure develops in the specimens, the rate of rotation has to slow and the specimen remains under drained condition. The shear displacement may be continued to a desired level and there is no restriction to the magnitude. Shear stress is plotted against shear displacement and is to be calculated from the applied torque as shown in Fig. 12.12 (b)

**Shear Strength of Clay Soils: **

In cohesive soils, the drainage of pore water under loading takes longer time than sandy or gravely soils. In granular soils, volume changes occur quickly under shear loads because of their high permeability.

In case of clayey soils, loads are applied faster than the rate of drainage taking place in actual engineering practice. This inevitably leads to the development of pore water pressure.

The pore water pressure gradually dissipates leading to volume change in the soil, if loading does not lead to failure in the soil. On the other hand, shear failure may occur in the soil, if the pore water pressure becomes sufficiently high.

The simple reason being that soil skeleton alone can carry the shear stress and not the pore water. The strength is a function of the effective stress alone. Pore water pressure, however, plays an important role in computation of effective stress.

Stress history of the soil is another important consideration influencing the shear strength of a cohesive soil. Normally consolidated or over-consolidated soil will influence the drained strength as well as undrained strength.

**Undrained Strength from Unconsolidated Undrained Test: **

In UU test, drainage is not permitted during application of the deviator stress. There is no dissipation of excess pore pressure.

There can be no volume change in the sample under applied stresses in saturated clay since the water and the soil grains are virtually non-compressible and the sample contains no air.

When cell pressure is applied to the sample, the additional stress is entirely carried by the water in the voids and the pore pressure is increased by an amount equal to the cell pressure increment.

Increasing the total stress does not alter the effective stress and in an ensuing compression test the measured shear strength does not depend on total stress. Several samples tested under different confining pressures will all give practically the same peak deviator stress at failure.

Mohr circles of total stress as shown in Fig. 12.13 give the similar horizontal envelope (ɸ_{u} = 0) characteristic of saturated clays, the cohesion intercept ‘C_{u}‘ being the total shear strength.

The Mohr circle of effective stress at failure as shown in Fig. 12.13 is found to be virtually the same circle for all values of total stress.

The undrained shear strength C_{u} of normally consolidated clays (ɸ= 0) is found to increase uniformly with decreasing water context, which decreases uniformly with increasing depth below the ground surface.

If the soil is partly saturated, the deviator stress at failure will increase with increase in cell pressure and the failure envelope will no longer be a horizontal line. Application of cell pressure increment σ_{3} to a partly saturated sample causes the pore pressure to increase by an amount less than σ_{3}; consequently there is an increase in effective stress.

Mohr circles of failure in terms of total stress for a set of partly saturated samples are shown in Fig. 12.14. The deviator stress at failure increases with increasing cell pressure at low pressure. At higher confining pressure the air in the voids becomes more compressed and more air passes into the solution in the water.

**Consolidated Undrained Strength (CU Test): **

A normally consolidated saturated clay sample is considered to the desired effective stress before applying the deviator stress and loading to failure. After consolidation is over, the drainage line is closed and the sample sheared up to failure under an undrained condition keeping the cell pressure constant.

After the consolidation is over, there is no excess pore water pressure in the specimen at that consolidation pressure. When there is tendency towards volume decrease during shear, such volume change is not allowed to occur and a positive pore water pressure develops.

Normally consolidated clays which would decrease in volume where drainage allowed exhibits pore water pressure while over-consolidated clays. Which have a propensity for volume increase under drained condition are likely to manifest negative pore water pressure during the second stage of the CU test as shown in Fig. 12.15.

**Drained Strength: **

No excess pore pressure builds up within the specimen at any stage in a drained test. The total stresses are the effective stresses. In this test a specimen is first consolidated under a certain confining pressure. It is then sheared sufficiently slowly so as to allow full dissipation of pore pressure, the confining pressure or the normal load being kept the same as used for consolidation.

The failure envelopes of drained tests are very similar to those obtained from consolidated undrained test in terms of effective stresses. For normally consolidated conditions, the failure envelope passes through the origin of stress and for pre-consolidated conditions, gives an effective cohesion intercept as shown in Fig. 12.18.

The shear strength equation for drained test is written as —

τ = C’ d + σ tan ɸ’_{d}

where C’_{d} = zero for normally consolidated conditions.

**Shear Strength of the Cohesionless Soils: **

Cohesionless soils when unconfined have little or no strength in the air dried state and little or no cohesion when submerged. In these soils the interparticle surface forces are of little significance and their strength properties are essentially governed by effective stresses.

The stress-strain relationship in granular soils depends much upon the initial state of compactness or the density index. In a triaxial test, the deviator stress is plotted against axial strain and in a shear box test, the shear stress is plotted against shear displacement or strain as shown in Fig. 12.19.

Dense sand shows a relatively high initial tangent modulus; stress reaches a maximum value at comparatively low strains and then decreases rapidly with increasing strain. With further increase in strain the stress becomes more or less constant it is then known as the ultimate stress. Loose sand shows a relatively slower rate of increase in stress with strain, the stress becoming maximum at comparatively large strains and decreasing very slowly thereafter.

In a loose sand, the maximum stress is the ultimate stress occurring at relatively large strains, whereas in a dense sand, the maximum stress is the peak stress which occurs at low strains. The peak stress is usually taken to define the shear strength in dense sands.

In loose sands, either the maximum stress or the stress value at any arbitrary chosen strain is taken as the strength of the soil.

The volume change characteristic depends on various factors, such as particle size shape and distribution, density index, orientation of principal planes, principal stress ratio, minor principal stress and the previous stress history. Dense sand expands and loose sand compresses during shear as shown in Fig. 12.20.

At sufficiently high strains, both dense and loose sand may be thought to attain approximately the same void ratio at which further shear strain will occur with no volume change. Such a void ratio is termed the “critical void ratio”.

**Selection of Test Procedure for Determining Shear Strength of Soils: **

The choice of which test conditions to use during testing is usually dependent on the drainage conditions expected to exist at the project site. If the soil is sandy, excess pore pressure resulting from new loads can usually be expected to dissipate rapidly and drained condition should be employed during the test.

On the other hand, if the soil to be stressed in the field is a saturated clay, excess pore pressure will dissipate slowly and ɸ = 0° conditions are likely to govern; thus, a UU test is the proper choice.

The excess pore pressure tends to dissipate by drainage. The rate to which they can dissipate, and hence the shear strength can be developed in the field, depends to a considerable extent on the permeability and on the dimensions of the mass of soil influenced by the shear stresses.

They also depend on the rate at which the stresses are applied; a very slow change in the stress applied to a soil mass of low permeability may not produce any greater pore pressure than a rapidly stress in a highly permeable soil. These considerations provide a basis for estimating the shear strength in practical problems or for selection test procedures appropriate to the problems.

In case of sands and gravels, if the stresses are applied very rapidly, having permeability in the range 10^{–3} to 10^{–4} cm/sec, and especially if the mass of sand has large dimensions, the stresses may induce pore pressures but cannot be dissipated quickly enough to maintain the shearing strength.

If the sand is dense, its strength may be temporarily increased; it is then conservative to use the S-test (consolidated drained) value. However, if it is loose its strength may be temporarily reduced to the R-test (consolidated undrained) value.

The period of construction for a building during which the footing loads are built up, may be relatively short in comparison with that required for consolidation of the soil Hence, Q condition prevail and ɸ = 0 concept is applicable. The shear strength is then readily determined as half the unconfined compressive strength of undisturbed samples.

If the change in stress will ultimately lead to swelling, the shear strength may decrease with time, the use of the unconfined compression or triaxial Q-tests (unconsolidated undrained) may give satisfactory results for the construction period and immediately thereafter. For evaluating the long-term stability of cut-slopes in stiff clay, Q-tests are not suitable.

Strongly over-consolidated clays with plasticity indices greater than about 40 require special consideration. Such material almost always contains joints and slickenside; the presence of these defects may control the strength of the entire deposit. Hence, Q condition do not apply.

In many instances it is uneconomical or impracticable to carry out the studies necessary to take advantage of the decrease of pore pressure resulting from consolidation and drainage; under these circumstances, triaxial Q-test give conservative values of shear strength. Unconfined compression tests are not likely to be suitable because capillary stresses may have a considerable influence on the results.

The shear strength of partially saturated soils depends largely on whether the soil is coarse-grained or fine-grained. For gravels and sands the apparent cohesion due to capillary moisture is usually neglected for permanent construction and values of ɸ are determined from drained triaxial tests.

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