临界状态土的物理标度律

Scaling laws for quasi-static granular sand at critical state

土的临界状态理论描述了土有效应力、抗剪强度与土密实度之间的对应关系,大量土力学试验还揭示了土体强度与加载速率存在相关性。考虑到颗粒物质是自然土体的实际载体,从颗粒物理本源出发,将流态颗粒惯性数I发展为考虑砂土密实程度(即初始颗粒体积分数Ф0)的准静态颗粒物理惯性数Q=Ф0[ln(I)+α]。以砂土的经典三轴试验数据为基础,探究了处于临界状态土的颗粒物理标度律,发现颗粒的摩擦系数μ与准静态颗粒惯性数Q之间满足简单的μ=ξQ线性关系。新建立的简单物理标度律能够统一刻画处于临界状态砂土的密实状态、剪切速率、围压和粒径等因素与土内摩擦角间复杂的经验关系。为描述受剪颗粒准静态变形的体变规律,进一步探索了临界状态下土颗粒体积分数与准静态颗粒惯性数间的相关性。对三维应力状态情况,引入一个新的无量纲量“中主应力数”对标度律进行拓展,可揭示中主应力对临界状态砂土摩擦特性的影响。

The critical state theory of soils describes the correspondence between effective stress,shear strength and soil density.Numerous soil mechanics experiments have also revealed a correlation between soil strength and loading rate.Considering that the granular matter is the actual medium of natural soils,a quasi-static inertia number is proposed,i.e.,Q=ϕ0[ln(I)+α],for the granular soils considering the particle volume fraction.Based on the classical triaxial test data of soils,the scaling laws of quasi-static deforming sand at the critical state from the perspective of granular physics are explored,and a simple linear relationship i.e.,μ=ξQ,is found between the friction coefficient and the quasi-static particle inertia number.The newly established scaling laws can quantitatively describe the influences of the volume fraction,shear rate,confining pressure and particle size on the frictional properties of sand when reaching the critical state.In addition,to quantify the volumetric deformation laws of sand under quasi-static shear,a correlation is obtained between the particle volume fractionϕat the critical state and the quasi-static inertia number Q.In attempt to characterize the scaling laws of the three-dimensional stress state,a new dimensionless number(i.e.,the intermediate principal stress number)is defined to reveal the influences of the intermediate principal stress on the frictional properties.Thus,the scaling laws are extended.