Mathematic expression method of strain softening and its application

Strain softening widely exists in the geo-materials. This kind of evolution can be expressed by an incrementally formulated curve. Firstly, a reference curve with positive function value, who monotonously decrease and finally tends to be constant, is defined in plane rectangular coordinate system. Then a curve starting from the origin is formulated incrementally. The gradient of the formulated curve is determined by the difference between the function values of the formulated curve and the reference curve. In this way, the formulated curve increases initially for that the function value is lower than that of the reference curve. Until the formulated curve meets the reference curve, it stops increase and begins to decrease. Finally the function value of the formulated curve tends to be constant with that of the reference curve gradually approaches constant. This mathematic expression method is implied in the unified hardening model (UH model) describing the over-consolidated soil. Making use of the same method, an isotropic compression model for the structured soil can also be extended.