Threshold Strain Concept

Cyclic loading of contractive specimens of both sand (a) and clay (b) leads to failure when pore pressures increase sufficiently. Numbers indicate cycle number. (After Sangrey, D.A. et al.. Cyclic loading of sands, silts and clays. Proceedings of the ASCE Special Conference on Earthquake Engineering and Soil Dynamics, Pasadena, CA, 2, pp. 836-851,1978. Reprinted with permission of ASCE.) 

CubicaUy packed assemblage of spheres subjected to normal stress, a, and shear stress, x, which produce interparticle contact forces N and T. (After Dobry, R. et al.. Prediction of Porewater Pressure Buildup and Liquefaction of Sands during Earthquakes by the Cyclic Strain Method, NBS Building Science Series 138, U.S. Department of Commerce, National Bureau of Standards, 1982.) 

When a tangential force, T is applied, elastic distortion causes the centers of the spheres to be displaced perpendicular to their axis (Mindlin and Deresiewicz, 1953 Dobry et al., 1982) by an amount given in the equation below  

The shear strain corresponding to the initiation of gross sliding is called the volumetric threshold shear strain. This relationship is given below assuming T =fN. 

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The mechanical concepts of stress are outlined in Fig. 1, with the axes reversed from that employed by mechanical engineers. The three salient features of a stress-strain response curve are shown in Fig. la. Initial increases in stress cause small strains but beyond a threshold, the yield stress, increasing stress causes ever increasing strains until the ultimate stress, at which point fracture occurs. The concept of the yield stress is more clearly realised when material is subjected to a stress and then relaxed to zero stress (Fig. Ih). In this case a strain is developed but is reversed perfectly - elastically - to zero strain at zero stress. In contrast, when the applied stress exceeds the yield stress (Fig. Ic) and the stress relaxes to zero, the strain does not return to zero. The material has irreversibly -plastically - extended. The extent of this plastic strain defines the residual strain. 

The concept focuses on an accelerated 24 h test using a rising step load-modified, slow strain rate testing protocol to measure the threshold. An equivalence vies established between the >75 % threshold acceptance level for the specimens and the >90 % threshold for product at 45 HRC. 

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