Friction strength envelope

Dividing the forces by the contact area, the equation of friction strength envelope is obtained in the following form ... 

Fig. 7. Tectonic interpretation showing accretion of mafic and ultramafic oceanic sequences, juvenile volcanic arcs, and accretionary prisms against an older crustal nucleus. Inset shows strength envelopes for the lithosphere showing differential stress (oj-as, MPa) against depth (km) for granite, granulite and dunite (see Jelsma et al. 2001) and Byerlee s (1978) friction relation.

The strength envelope at critical state of Kaolin clay at ambient temperature shows a straight line, with a slope M = 0.8 that corresponds to a friction angle of ( ) =21°. Figure 3 combines the results of drained shear tests at critical state obtained at ambient and high temperatures (90°C). It is clearly shown that the strength envelope at critical state is independent of testing temperature. 

Fig. 3.21a. Shear stress as a function of horizontal displacement measured in the shear box test at various normal pressures (10, 20, 50, 100, 200, 300 kN/m ). The bottom diagram shows the static friction stress (maximum of the shear stress-displacement curve) as a function of normal pressure (strength or failure envelope). Shear-stress vs. displacement curves wiA sliding friction nearly eqirivalent to static friction are typical for embossed stractures in combination with a clay-mineral liner. Source of data is (Bliimel and Bmnunermarm 1994)...

Figure 7.11 shows as an example Mohr s diagram for the Muderong shale, a relatively weak material with a cohesive strength of 2.75 MPa and a friction coefficient of 0.34. The envelope delivers the equation (Dewhurst and Hennig, 2003) ... 

The limit equilibrium method determines the forces required for equilibrium, taking into account the geometry of the slope, the pore pressure u, and the loads. When layers of reinforcement are introduced, it is possible to define the envelope of the maximum strength available in each layer, which depends on the friction between the reinforcement and the soil, the characteristics of the reinforcement, and the compatibihty of deformations with the functionality of the project. The diagram of the available forces must overlap that of the required forces, as shown in Fig. 15.4. 

---