Articles - THE CONCEPT OF EARTH MATERIAL SHEAR STRENGTH

Strength generally is defined as resistance to deformation. In considering earth materials, it is shear strength that is most significant. The shear strength model almost universally used in analyzing such matters as the safety factor of a slope is that of the Mohr-Coulomb model that defines shear strength as the sum of two different kinds of strength according to the following equation:

s = c + p tan φ

where s is the shear strength, c is the cohesive strength, p is a the normal load acting on a potential surface shear, φ is referred to as the angle of internal friction, and its tangent is referred to as the coefficient of friction. In this model, cohesive strength (or simply "cohesion") can be analogized to the kind of strength afforded by glue or cement. As such, cohesion is considered to resist deformation regardless of the direction in which a force is applied. Friction strength, on the other hand, is considered to be a function of a friction coefficient which is characteristic of the surface along which shearing acts. Every corporeal surface has its own unique coefficient of friction. Since force inducing shear must act on a surface, the physical variable of concern is actually a stress. Whether the frictional coefficient considered is that characteristic of, say, rubber on concrete, or sandstone on shale, or indeed, exactly the same material on either side of a postulated plane through such material, the principle is the same.

STRENGTH DATA DETERMINATION

The coefficient friction can only be determined experimentally. In earth materials, this commonly is done by loading a sample of earth material, thus creating an infinite number of stressed surfaces, and increasing the load until rupture occurs. The most common test is that using the direct shear machine. In direct shear, a sample is placed in a special box which can be loaded normally and sheared laterally at a controlled rate of strain. Because the lateral area of the sample in the box subject to shearing and normal loading is known, both the normal and shear stresses, as well as the strain can be measured. Data from repeated trials under varying normal loads produces data from which two Cartesian coordinate curves are plotted, one of normal stress versus shear stress, and the other of shear strain versus shear stress. The slope of the former curve is interpreted as the angle of internal friction, and the shape of the latter is used to interpret peak and ultimate shear strength.

Direct shear data of this sort almost invariably is what is produced in the geotechnical engineering phase of an investigation in support of an application for a grading or building permit. Direct shear test data, if used judiciously by an experienced practitioner is satisfactory for determining the friction angle and cohesion even though it is technically objectionable in certain respects. A better means to test materials is that of the triaxial machine because it permits control of lateral as well as normal loading and allows for accurate determination of neutral stress within the sample. However, triaxial testing is considerably more costly that that of direct shear.

EFFECTIVE STRESS LANDSLIDE MECHANISM

The model universally used to determine the safety factor against slope failure is that of a vertical cross-section taking transverse to a slope in the direction most likely to be the one in which the driving forces are maximum. The earliest models assumed a circular arc of failure and calculated failure and resisting moments with respect to the center of the circle. This was followed by the method of "slices," actually adjoining prisms, aligned along any assumed or existing surface of shear failure. The sum of the calculated resisting and driving forces applied to the bases of the prisms is assumed, quite incorrectly, to represent the total resisting and driving stresses for the section considered acting homogeneously along the shear surface and therefore, failure will occur along the entire surface essentially instantaneously. This could be true only if the slope material is mechanically entirely homogeneous. This is seldom the case.

As is apparent from a consideration of the safety factor of a stable slope, failure cannot occur unless there is a change in slope conditions. Such changes are those induced by a reduction in the resisting forces due to ground water in the slope in the static case and those due to increasing driving forces, either statically by over-steepening a slope or dynamically particularly during an earthquake. Although earthquakes are the most common cause of dynamically induced landslides, it is fairly well established that seismic vibrations such as those from the mechanical operation of heavy grading equipment, also can cause landsliding, especially if occurring repetitiously.

It is well established that the mechanism of effective stress is the most common cause of landsliding to be considered in terms of property development. The Terzaghi effective stress model is given by the following modification of the Mohr-coulomb model:

s = c + ( p-u) tan φ

where u is referred to as the neutral stress. As the equation shows, a sufficiently large value of u can reduce frictional strength to near zero resulting in almost certain failure. Mechanical application of neutral stress can occur in two ways. In a simple case, it acts on a sloping essentially impermeable section of shale resting on a permeable section of sandstone. The frictional strength along that surface may be considerable in the dry state, but if ground water enters the sandstone and rises, the hydraulic head thus developed results hydraulic pressure acting on the shale surface the force of which is simply the ratio of the pressure to the unit weight of the water. A sufficiently high hydraulic head then acts much as does a hydraulic jack to reduce p.

A more common mechanism is simply that where a section of a slope is infiltrated by ground water. When this happens, a buoyant force is imparted to the section that is saturated. This force is calculated as the product of the saturated mass volume and the unit weight of the water.

As a result, the saturated mass can exert less force on any surface within it and hence frictional strength along such surface is reduced possibly to the point where the total remaining sum of the frictional and cohesive strength is overcome by the stress due to the total driving force.

By way of analogy, consider a model consisting of a cable the total strength of which is the sum of the individual strengths of many strands of which it is composed. If the cable is capable of supporting a maximum of 1,500 pounds, and the weight it supports is 1,000 pounds, the safety factor against the cable breaking is 1.5. Suppose further that the cable is supported by a scale attached to a beam. The scale will register 1,000 pounds. Now begin cutting individual cable strands. Since each strand contributes to the total cable strength, that strength is reduced incrementally more and more with the parting of each strand. In other words, the more strands that are cut, the less strength of the cable is capable of mobilizing. Nevertheless, during this process, the scale still registers 1,000 pounds. Finally, suppose the strands are of some elastic material such as copper. At some point, when enough strands are cut, the remaining strands begin to deform elastically by lengthening and the suspended mass beings to move downward and the cable may be said to be in a condition of incipient failure, and when more strands are removed, the supported 1,000 pounds causes those remaining to exceed their combined elastic limit. The result is that the remaining strands suddenly lengthen plastically which is the model equivalent to the development of a landslide.

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