An Improved Hyperbolic Model for Silty Clay Considering Strain Softening of Soil and Freeze-Thaw Cycle Effects

In order to describe the stress-strain characteristics of strain-softening soil subjected to freeze-thaw cycling, an improved hyperbolic model was proposed. Based on the traditional Kondner hyperbolic model and the definition of secant modulus, the basic relation between dimensionless secant modulus E_s/E_i and dimensionless deviation stress q/q_max was deduced through transformation of the hyperbolic model function. A set of triaxial tests were conducted on compacted silty clay specimens subjected to different confining pressures and freeze-thaw cycles. The q/q_max-E_s/E_i relations before and after strain softening could be fitted by the power function, respectively. An improved hyperbolic model, which contained 8 parameters including c, φ, K, n, f, g, α and β, was proposed to reflect the strain softening characteristics. The influence of freeze-thaw cycles on soil characteristics was formulated by determining the laws of the model parameters changed with freeze-thaw cycles. The results showed with the increase of freeze-thaw cycles, the peak strength of specimens and cohesion c decreased gradually, the internal friction angle φ increased ceaselessly; the initial secant modulus decreased increasely, and the corresponding parameter K decreased at the same time, the parameter n increased steadily. The parameters f and α were the limit values which reflected secant moduli of picewise functions in the period of strain-softening, they increased or decreased gradually respectively with increase of freeze-thaw cycles.The parameters g and β reflected the shape of E_s/E_i-q/q curves before and after strain-softening, and g decreased steadily with the increasing of freeze-thaw cycles and β changed in fluctuation. The relations of the above parameters to freeze-thaw cycles could be fitted by the Logistic function. The improved model and representation expressions for model parameters were programmed into a calculation software, which taking the confining pressure and freeze-thaw cycles as the variables. The calculation results by the model could reflect the influence of confining pressure and freeze-thaw cycles on the mechanical properties of soil.