基于混合物理论的饱和介质体应变本构模型

为了解决饱和多孔介质的建模问题，采用工程混合物理论建立了饱和多孔介质体积本构理论框架。首先，假定多孔固相与流相基质体积变形功相互独立，采用Terzaghi有效球应力、孔压和流体基质压力作为本构模型的应力状态变量，获得了固相、固相基质和流相基质体应变的余能表达式。其次，根据Lade和De Boer模型试验加卸载测试数据，建立了加卸载阶段饱和多孔白塞木立方体流固两相体积本构方程，推导了固相体积切线模量、Biot切线系数和流相Biot切线模量等力学参数计算公式。分析了加载阶段固相体积切线模量，Biot切线系数，流相Biot切线模量等力学参数随Terzaghi有效球应力和孔压变化规律。最后，根据本文体积本构模型和静力平衡方程建立了饱和多孔介质的一维固结方程，数值分析了饱和多孔白塞木立方体的固结特性，获得了固结度和沉降随时间变化曲线。研究表明，固相体积切线模量随Terzaghi有效球应力的增大而增大，随孔压 的增大而减小。Biot切线系数介于0.42~0.95之间，随Terzaghi有效球应力和孔压的增大而减小。流体Biot切线模量随Terzaghi有效球应力增大而先减小后增大，随孔压增大而减小。孔压切线系数在大多数情况下小于1.0。考虑固相基质变形时饱和多孔介质的初始孔压不等于外荷载，因此饱和多孔介质在外荷载作用下存在瞬时沉降。本文提出的建模方法可用于非线性饱和多孔介质的建模和数值分析工作。

Bulk Strain Constitutive Models of Saturated Media Based on Mixture Theory

In order to solve the modeling problems of saturated porous media, the engineering mixture theory is used to formulate the bulk constitutive theoretical framework of saturated porous media. Firstly, Supposing that the bulk deformation works of porous solid and fluid matrix are mutually independent and using Terzaghi''s effective spherical stress and pore pressure and fluid matrix pressure as stress state variables of constitutive model, the expressions of bulk stains of solid phase and solid matrix and fluid matrix are obtained in the complementary energy. Secondly, the solid and fluid bulk constitutive equations of saturated porous cubes of balsawood in the loading and unloading stages are founded on the basis of the loading-unloading measuring data of model test conducted by Lade and De Boer. The calculating formulae of mechanical parameters are deduced such as solid bulk tangent modulus, Biot''s tangent coefficient and fluid Biot''s tangent modulus and so on. The change rules of mechanical parameters along with Terzaghi''s effective spherical stress and pore pressure are analyzed in the loading stage for solid bulk tangent modulus, Biot''s tangent coefficient and fluid Biot''s tangent modulus and so on. Finally, the one-dimensional consolidation equation of saturated porous media is derived from the bulk constitutive models of the paper and static balance equation. The consolidation behaviors of saturated porous cubes of balsawood are numerically analyzed and the change curves of consolidation degree and settlement with time are obtained. The researches show that, the solid bulk tangent modulus increases along with Terzaghi''s effective spherical stress and decreases along with pore pressure. The Biot''s tangent coefficient is between 0.42~0.95 and decreases along with Terzaghi''s effective spherical stress and pore pressure. The fluid Biot''s tangent modulus first decreases and then increases with the increase of Terzaghi''s effective spherical stress, and decreases with the increase of pore pressure. The tangent coefficient of pore pressure is less than 1.0 in most cases. The initial pore pressure is not equal to the external load in saturated porous media when considering the compressibility of solid matrix. Thus the immediate settlement exists in saturated porous media after external load is applied. The modeling method provided in the paper can be used to model and numerical analyze nonlinear saturated porous media.