Joshua P. HumirangBSCE IV- GC

COMPRESSIBLIY OF SOILSWhen a soil mass is subjected to a compressive force, its volume decreases. The property of the soil due to which a decrease in volume occurs under compressive force is known as the compressibility of soil. The compression of soil can occur due to:

Compression of solid particles and water in the voids Compression and expulsion of air in the voids Expulsion of water in the voids

The compression of saturated soil under a steady static pressure is known as consolidation. It is entirely due to expulsion of water from the voids.

INITIAL, PRIMARY AND SECONDARY CONSOLIDATION

Initial Consolidation

When a load is applied to a partially saturated soil, a decrease in volume occurs due to expulsion and compression of air in the voids. A small decrease in volume occurs due to compression of solid particles. The reduction in volume of the soil just after the application of the load is known as initial consolidation or initial compression. For saturated soils, the initial consolidation is mainly due to compression of solid particles.

Primary Consolidation

After initial consolidation, further reduction in volume occurs due to expulsion of water from the voids. When a saturated soil is subjected to a pressure, initially all the applied pressure is taken up by water as an excess pore water pressure. A hydraulic gradient will develop and the water starts flowing out and a decrease in volume occurs. This reduction in volume is called as the primary consolidation of soil

Secondary Consolidation

The reduction in volume continues at a very slow rate even after the excess hydrostatic pressure developed by the applied pressure is fully dissipated and the primary consolidation is complete. The additional reduction in the volume is called as the secondary consolidation.

Imposed stress distribution below foundations

The distribution of stresses in the ground under a foundation due to applied loading is not uniform. Changes in vertical stress decrease with both depth and horizontal distance from the load; but can be predicted with reasonable accuracy using elasticity theory (and sometimes simpler approximate methods).

Boussinesq's solution

According to Boussinesq (1885), the vertical stress v in the ground due to a point load Q is

where z is the depth below the load and r is the horizontal distance from the load.

Simple solutions are available for stresses below strip footings, below the centre of circular footings and below a corner of a rectangular footing. The latter can be used to calculate the stress at any point by dividing the rectangle into two or more rectangles and summing the stresses due to each part. For example, to find the stress under the centre of a (B x L) rectangular base, find the stress under the corner of a (1/2B x 1/2L) rectangle, then multiply by 4.

Stress below a circular foundation

The vertical stress at a depth z below the centre of circular base of radius R isv = q .Ic where q is the bearing pressure and

The stress value below the centre is a maximum for a given depth. The expressions for stresses off-centre are much more complex. Over deep soil layers, the average value will be between 0.85 and 0.6 of the centre-line value according to the stiffness of the footing.

Stress below a strip foundation

The vertical stress at a depth z below a uniformly loaded strip footing of width B=2b isv = q .Is

where q is the bearing pressure andIs = [ + sin .cos(  + 2 ) ] / 

Stress below a rectangular foundation

The vertical stress at a depth z below the corner of a rectangular subject to uniform pressure isv = q. IR where q is the bearing pressure and

Approximate methods

For settlement calculations (but not necessarily for other geotechnical problems), sufficient accuracy is usually obtained by assuming a simplified pressure distributuion. The two methods given below are in common use.

Tomlinson's methodTomlinson suggests using an approximate pressure distribution for small foundations on stiff clay:

Settlement,  = ( 1.5 B) x ( 0.55 qn) x mv

whereB is the breadth of the foundationqn is the net bearing pressure

2 : 1 distribution methodThe vertical stress on horizontal planes is assumed to remain uniform, but decrease linearly with depth below the foundation, thus:

For a strip footing:

For a rectangular footing:

where:qn = applied net bearing pressure B = breadth,L = lengthz = depth from underside of footing

SHEAR STRENGTHShear strength is a term used in soil mechanics to describe the magnitude of the shear

stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle contacts. Due to interlocking, particulate material may expand or contract in volume as it is subject to shear strains. If soil expands its volume, the density of particles will decrease and the strength will decrease; in this case, the peak strength would be followed by a reduction of shear stress. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. The theoretical state at which the shear stress and density remain constant while the shear strain increases may be called the critical state, steady state, or residual strength.

A critical state line separates the dilatant and contractive states for soil.

The volume change behavior and interparticle friction depend on the density of the particles, the intergranular contact forces, and to a somewhat lesser extent, other factors such as the rate of shearing and the direction of the shear stress. The average normal intergranular contact force per unit area is called the effective stress.

If water is not allowed to flow in or out of the soil, the stress path is called an undrained stress path. During undrained shear, if the particles are surrounded by a nearly incompressible fluid such as water, then the density of the particles cannot change without drainage, but the water pressure and effective stress will change. On the other hand, if the fluids are allowed to freely drain out of the pores, then the pore pressures will remain constant and the test path is called a drained stress path. The soil is free to dilate or contract during shear if the soil is drained. In reality, soil is partially drained, somewhere between the perfectly undrained and drained idealized conditions.

The shear strength of soil depends on the effective stress, the drainage conditions, the density of the particles, the rate of strain, and the direction of the strain. For undrained, constant volume shearing, the Tresca theory may be used to predict the shear strength, but for drained conditions, the Mohr–Coulomb theory may be used. Two important theories of soil shear are the critical state theory and the steady state theory. There are key differences between the critical state condition and the steady state condition and the resulting theory corresponding to each of these conditions.

Direct Shear Test

Dry sand can be conveniently tested by direct shear tests. The sand is placed in a shear box that is split into two halves (figure 1.32a). A normal load is first applied to the specimen. Then a shear force is applied to the top half of the shear box to cause failure in the sand. The normal and shear stresses at failure are

Where A= Area of the failure plane in soil-that is, the area of cross section of the shear box Several tests of this type can be conducted by varying the normal load. The angle of friction of the sand can be determined by plotting a graph of s against σ′(=σ)

For sands, the angle of friction usually ranges from 26° to 45°, increasing with the relative density of compaction. The approximate range of the relative density of compaction and the corresponding range of the angle of friction for various coarsegrained soils is shown in figure 1.33.

Triaxial Tests

Triaxial compression tests can be conducted on sands and clays. Figure 1.34a shows a schematic diagram of the triaxial test arrangement. Essentially, it consists of placing a soil specimen confined by a rubber membrane in a Lucite chamber. An all-round confining pressure (σ3) is applied to the specimen by means of the chamber fluid (generally water or glycerin). An added stress (∆σ) can also be applied to the specimen in the axial direction to cause failure (∆σ=∆σf at failure). Drainage from the specimen can be allowed or stopped, depending on the test condition. For clays, three main types of tests can be conducted with triaxial equipment:

1. Consolidated-drained test (CD test)

2. Consolidated-undrianed test (CU test)

3. Unconsolidated-undrained test (UU test)

Table 15 summarizes these three tests. For consolidated-drained tests, at failure, Major Principal effective stress =σ3=∆σf=σ1=σ′1

Minor Principal effective stress =σ3=∆σ′3 Changing σ3 allows several tests of this type to be conducted on various clay specimens. The shear strength parameters (c and ϕ) can now be determined by plotting Mohr’s circle at failure, as shown in figure 1.34b, and drawing a common tangent to the Mohr’s circles. This is the Mohr-Coulomb failure envelope. (Note: For normally consolidated clay, c≈0). At failure

For consolidated-undrained tests, at failure,

Major Principal total stress =σ3=∆σf=σ1

Minor principal total stress =σ3

Major principal effective stress =(σ3+∆σf)−uf=σ′1

Minor principal effective stress =σ3− uf=σ′3

Changing σ3 permits multiple tests of this type to be conducted on several soil specimens. The total stress Mohr’s circles at failure can now be plotted, as shown in figure 1.34c, and then a common tangent can be drawn to define the failure envelope. This total stress failure envelope is defined by the equation

Where ccu and ϕcu are the consolidated-undrained cohesion and angle of friction respectively (Note: ccu≈0 for normally consolidated clays) Similarly, effective stress Mohr’s circles at failure can be drawn to determine the effective stress failure envelopes (figure 1.34c). They follow the relation expressed in equation (82).

For unconsolidated-undrained triaxial tests

Major principal total stress=σ3=∆σf=σ1

Minor principal total stress =σ3

The total stress Mohr’s circle at failure can now be drawn, as shown in figure 1.34d. For saturated clays, the value of σ1−σ3=∆σf is a constant, irrespective of the chamber confining pressure, σ3 (also shown in figure 1.34d). The tangent to these Mohr’s circles will be a horizontal line, called the ϕ=0 condition. The shear stress for this condition is

Where

cu=undrained cohesion (or undrained shear strength)

The value of the pore water pressure parameter A at failure will vary with the type of soil. Following is a general range of the values of A at failure for various types of clayey soil encountered in nature.