The modified Cam-clay model has been widely adopted as the theoretical framework for constitutive modelling of clays. However, there is so far no such model for sands on the basis of which further development can be carried out. Based on the main differences in the behaviours exhibited during isotropic compression and shear processes between sands and clays, a basic constitutive model for sands is proposed by introducing the compressive hardening parameter \(p_{{\text{s}}}\) and the critical state parameter \(\chi\) into the formulations of normal compression line and elliptic yield surface of the modified Cam-clay model respectively. When the new compressive hardening parameter and critical state parameter both equal 0, the normal compression line and yield surface of the proposed model for sands can degrade into the corresponding ones of the modified Cam-clay model for clays. The comparison between test data and the model prediction indicates that the proposed model can predict the stress–strain relationship of normally compressed sands (i.e. the loosest sands without structure) well. The proposed model can be considered as the basic framework for further research on constitutive modelling of sands due to its clearly defined assumption, simple structure and good capability in model prediction.

修正的 Cam-clay 模型已被广泛用作粘土本构建模的理论框架。然而，迄今为止还没有这样的砂模型，可以在此基础上进行进一步的开发。基于砂土和粘土在各向同性压缩和剪切过程中表现出的主要差异，通过引入压缩硬化参数\(p_{{\text{s}}}\)和临界状态参数\(\chi\)分别代入修正 Cam-clay 模型的法向压缩线和椭圆屈服面的公式。当新的压缩硬化参数和临界状态参数都等于0时，砂土模型的法向压缩线和屈服面可以退化为相应的粘土修正Cam-clay模型。试验数据与模型预测结果对比表明，该模型能够较好地预测常压砂岩（即最松散的无结构砂岩）的应力应变关系。该模型假设明确、结构简单、模型预测能力强，可作为进一步研究砂岩本构模型的基础框架。