Analysis of the dynamic characteristics and nonlinear earthquake response of soil-underground structures
Abstract: The underground tunnels in Nanjing are distributed in a soft soil foundation, and the seismic performance of soil-underground structures is an urgent problem in practical engineering. To describe the dynamic characteristics of soft soil under cyclic loading, this study modifies a defect of the traditional Davidenkov model and establishes a dynamic constitutive model of viscoplasticity for a nested surface with memory. To compensate for the lack of interaction data between soft soil and subsurface structures, a large-scale shaking table model test was conducted to study the nonlinear seismic response of soil-underground structures in deep-field soft soils with a liquefied soil layer in the Nanjing area. The results show that when the ground vibration propagates through the soil medium, the Fourier spectrum of acceleration at low frequencies is larger than that of high frequencies, and the amplification coefficient of the surface peak acceleration decreases with increasing intensity of the input ground motion of the bedrock surface.
Keywords: Deep field soft soil; nonlinear dynamic; soil-underground structure interaction; large-scale shaking table model tests; nonlinear earthquake response
2 Materials and Method
2.1 The nonlinear dynamic constitutive model of soil
The following equation for the estimation of dynamic shear modulus ratio was proposed by Hardin (1972):
where is expressed as
and is the reference shear strain.
Martin (1982) used the Davidenkov model to describe the above relationship，with rewritten as
where A, B, and are curve curve fitting parameters related to soil properties. It should be noted that is no longer a reference shear strain amplitude with definite physical meaning, and is only a fitting parameter (Dong et al., 2015).
The Davidenkov skeleton curves of the stress-strain relationship of soil can be expressed as follows:
When the values of the curve fitting parameters are A = 1, B = 0.5, and = , the stress-strain curve described by the Davidenkov model is degenerated to the Mashing hyperbolic model. Per (2) and (3) of the Mashing rule (established in 1926 by Mashing in proceedings of the 2nd international congress on applied mechanics and can describe the one - dimensional dynamic stress - strain relationship of rock and soil mass under constant cyclic loading), when the value of the reference shear strain amplitude is = 0.1%，taking different curve fitting parameters produces a hysteresis loop, as in Fig. 2-1.
Fig.2-1 The dynamic shear stress-strain curves given by Davidenkov skeleton curves
The damping ratio is a quantitative description of the energy dissipation characteristics of the rock and soil under cyclic loading. Based on the equivalent nonlinear viscoelastic model damping ratio, the damping ratio is expressed as follows:
where is the hysteresis loop area, which is expressed as the energy consumption in the cyclic stress system, and is the triangular area expressed as the elastic strain energy. According to these definitions, when the stress-strain relationship skeleton curves use the Davidenkov model, the corresponding hysteretic curves are constructed according to the Mashing rule. Thus, the soil damping ratio equation can be derived as follows (Chen et al., 2006):
is the shear strain amplitude corresponding to the loading and unloading turning point of shear stress-shear strain hysteretic curve.
The actual stress-strain relationship curves of the soil should be as follows. When and , is the upper limit of the shear stress. When B < 0.5, the skeleton curves according to formula 6 are , which i