目的 研究地铁隧道衬砌背后注浆复合材料的等效弹性模量,使力学模型更符合工程实际.方法 将注浆材料当成理想弹性体,利用均匀化方法,研究单胞的宏细观尺度函数性质.利用摄动技术,将宏观结构中一点的位移、应力等展开为与细观结构尺度相关的渐进展开式,得到一系列摄动控制方程.结合弹性力学基本方程,联立求解得到等效刚度矩阵.将两种材料的三维弹性刚度矩阵的具体形式代入前面推出的公式,求出复合材料的等效弹性模量的具体计算解析解.结果 由任意弹性模量的两种材料以任意配比混合而成的隧道衬砌复合材料都可以直接应用公式求解等效弹性模量.对于各种配比的复合材料,当砂砾所占体积为0时,复合材料的等效弹性模量都是混凝土本身的弹性模量；当砂砾所占体积比率为1(混凝土体积为0)时,复合材料的等效弹性模量都是砂砾本身的弹性模量；其他配比时在曲线上呈规则分布.复合材料的等效弹性模量小于用体积平均法求得的等效弹性模量.当砂砾和混凝土的弹性模量相差越大时,回填层的等效弹性模量和用体积平均法求解结果相差越大.随着砂砾弹性模量的增大,复合材料的等效弹性模量呈增大趋势.结论 用均匀化方法求得的复合材料的等效弹性模量值小于用体积平均法求得的数值,更能真实反映材料力学性能.%Equivalent elastic modulus of post grouting composite around metro tunnel lining is studied so that the mechanical models can coincide with the actual case. Homogenization theory is used to study macro-scale and meso-scale function qualities of unit cell, when grouting materials are considered as ideal elastomers. Displacement and stress functions in macro-scale are turned asymptotically into expansion forms in meso-scale by perturbation technology. Some perturbation control functions are gotten. Equivalent modulus matrix is obtained through combining and solving the above equations. Then 3-dimensional equivalent modulus matrix of each material is substituted by the above equations, then the calculating equation of equivalent elastic modulus are obtained. When any two materials in any ratio are mixed into composites for tunnel lining,the equivalent elastic modulus can be worked out directly with the formulas. The equivalent elastic modulus of composite is the same as elastic modulus of the concrete when the size of gravel is zero;on the contrary,it is the same as of the gravel when the size percent of gravel is 1. Equivalent elastic modulus regularly distributes on the curve. The value for equivalent elastic modulus is smaller than that got through volume averaging,and the gap is more,the value difference is bigger. Equivalent elastic modulus becomes bigger as the value of gravel increases. The value obtained by homogenization theory is smaller than hat by previous volume optimization method,and reffected more actual mechanics qualities of composites.
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