It is well known that the compressibility of crushable granular materials increases with the moisture content, due to the decrease of particle strength in a humid environment. An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work. But how the material humidity can affect this relationship is not clear, and experimental evidence is quite scarce. Based on compression tests on dry and saturated crushable sand recently reported by the present authors, a new non-linear relationship is proposed between the amount of particle breakage and the plastic work. The expression contains two parameters: (1) a material constant dependent on the grain characteristics and (2) a constant depending on the wetting condition (in this study, dry or saturated). A key finding is that the relationship does not depend on the stress path and, for a given wetting condition, only one set of parameters is necessary to reproduce the results of isotropic, oedometric, and triaxial compression tests. The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression. The breakage ratio is introduced into the expression of the elastic stiffness, the critical state line and the hardening compression pressure. Incremental stress-strain computations with the model allow the plastic work to be calculated and, therefore, the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations. Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained.

众所周知，由于潮湿环境中颗粒强度的降低，可破碎颗粒材料的可压缩性随水分含量的增加而增加。考虑本构模型中晶粒破碎的影响的现有方法是将晶粒尺寸分布的演变与塑性加工联系起来。但是，材料湿度如何影响这种关系尚不清楚，而且实验证据还很匮乏。根据作者最近报道的对干燥和饱和的可破碎砂的压缩试验，提出了一种新的颗粒破碎量与塑性功之间的非线性关系。该表达式包含两个参数：（1）取决于晶粒特性的材料常数和（2）取决于润湿条件的常数（在本研究中，干燥或饱和）。一个关键的发现是，这种关系不取决于应力路径，对于给定的润湿条件，只需要一组参数即可重现各向同性，测压和三轴压缩试验的结果。该关系已被引入到基于临界状态概念的弹塑性本构模型中，该模型具有用于塑料滑动和压缩的双屈服面。将破损率引入弹性刚度，临界状态线和硬化压缩压力的表达式中。该模型的增量应力-应变计算可以计算塑性功，因此，可以通过提出的非线性关系来预测颗粒破碎的演变，并将其重新引入本构方程。