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中文摘要：
混凝土、岩石等工程材料是典型的多孔介质材料，孔隙或微裂纹的存在对材料的弹性模量及强度等力学参数产生很大影响。该文基于三相球模型确定了含孔隙复合材料的有效体积模量，提出采用空心圆柱形杆模型推导得到了含孔隙复合材料有效剪切模量的理论公式，并在各向同性材料的假设条件下确定了材料的有效弹性模量及泊松比；推导并得到了含孔隙材料的有效抗拉、抗压强度及有效抗剪强度与孔隙率之间的定量关系公式，并进一步得到了含孔基质在达到有效强度时的临界应变与孔隙率之间的定量关系。结果表明该文方法能较好的预测含孔混凝土材料的有效力学性能，且公式简单，易于应用。
英文摘要：
Concrete and rock are typical porous mediums which have a great influence on the elastic modulus, strength and other mechanical parameters of concrete material. The effective bulk-modulus of a composite with hollow spheres in a matrix is determined by a three-phase sphere model, and the theoretical formula of an effective shear modulus is deduced and obtained by a hollow cylindrical rod model proposed in the paper. Based on the assumption of isotropic materials, the effective Young＇s modulus and Poisson＇s ratio are derived. Besides, the relationships between porosity and effective tensile strength, effective compression strength and effective shear strength are deduced, and the formulas of a quantitative relation are given. Furthermore, the relation between porosity and critical strain when the material with pores reaches the effective strength is deduced. The results show that the method proposed in the paper can predict the effective mechanical properties of concrete greatly, and the formula is simple and easy to use.
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