Mohr–Coulomb theory

A shear Act specifies in the materials science of how a material behaves under the influence of shear forces. Shear laws are used in technical fields such as engineering and construction, to estimate the maximum load capacity of a structure. In geotechnical engineering, they serve to determine the maximum load capacity of the soil and for the prediction of subsidence.

Shear law of Charles Augustin de Coulomb

At a shear stress of a body both in the direction of shear as well as those occur perpendicular to it. A voltage perpendicular to the shear inhibiting effect on the shear. The bigger it turns out, the larger the shear stress are before permanent deformation occurs. This is similar to the friction, which is able to prevent a body on an inclined plane of movement. In addition, interaction between grains or molecules of the body a holding force that must be overcome before a part of the body shears. The stress caused by these forces is called cohesion.

The voltage above which a permanent deformation occurs, can be determined for a particular material using the shear of Coulomb Law:

It is dependent on the material cohesion and also dependent on the material parameters. The acting perpendicular to the shear stress is proportional to the pressure at the point considered of the body.

This shaving law, all types of soil and rocks are described. Even for metals and other natural materials (bulk and storage materials with solid consistency ) it is applicable.

Application on soils with pore water

A special feature of granular media such as soil, the pore water. Pressing on a dry soil, the pores are mainly compressed. The individual grains are thus moving closer together and take the pressure. Now, if the pores are filled with water, the situation is somewhat more complicated. The water is incompressible and first takes the external load on the pore water pressure. Since the side of the load there is a lesser pore pressure, the water flows from the low pressure and the pores may deform ( decrease ), and so the stress on the grains of the soil can be derived. This process is called consolidation of the soil. The pore water pressure caused by the load, is called the pore pressure. This is broken down in the consolidation.

In a water-saturated soil, the weight forces of grain is transferred to grain. This transfer is based on the constitutive law of Coulomb. If now a water-saturated soil impacted by an additional load, as created by the additional load an excess pore water pressure. The granular structure feels initially unaware of this additional burden, as the water absorbs the pressure. Thus, the grain - to-grain tension in the first moment is the same as without the additional burden. Only with time, when the pore water runs off, the grain - to-grain stresses increase so until the auxiliary voltage is fully absorbed by the grain - to-grain tension. This must be taken into account during the shearing law, ie. The shear law of Coulomb applies only to grain - to-grain stresses. For the calculation of grain - to-grain tension of the pore water pressure must be deducted from the total voltage:

So to get to the extended property law of Coulomb:

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