A sphere packing model for shear bands in dense soils

The rhombic sphere packing can be used to model the biaxial test on granular soils in a very simple way. According to the angle of assemblage, the packing is dilatant or contractive. Correspondingly, overall stresses are transmitted as chains of forces or oblique forces of contact. The connection of the soil stress-strain behaviour and the packing void ratio is achieved by mapping both of the plots. The mapping shows that dense soils are dilatant and loose soils are contractive, separated by the critical state. It also shows that the bifurcation point and the peak strength are features only of dense soils. The band of strain localization is analysed in the elastic regime, and its inclination is found maximizing the intensity of the mobilized stress ratio. The stresses within the shear band are obtained by assuming a partially coaxial packing rotated to reach the full plastic state. The equilibrium of the overall stress at the line of discontinuity reveals a relationship between the peak friction angle and the coefficient of lateral pressure at rest. As long as these parameters are obtained independently of each other, they allow the validation of the theory.

Features of formation of karst falls on the earth’s surface

Karst manifestations are widespread in many regions and pose a significant danger to residence and economic activity. Failing funnels arise during the collapse of rocks over underground voids (caves, workings, etc.), formed during karst formation or in the process of anthropogenic doing in the rock massive. However, not every karst or technogenic cavity gives rise to a failure of the earth’s surface, and as a rule, its occurrence is unexpected. In this work, we consider the dynamics of the formation of dips of the earth’s surface in the form of a collapse pipe. To do this, the geomechanical problem is solved by the meshless code Smoothed Particle Hydrodynamics (SPH). The method allows to obtain a solution to the problem taking into account large deformations and possible discontinuities in the process of changing the stress-strain state. The Drucker-Prager fracture criterion is used, the parameters of which change over time in accordance with the accumulation of damage, which determines the temporary development of the fracture process, its beginning and speed. Various options for the formation of a vertical dip are considered depending on the geometrical parameters of the initial cavity, its depth and materials composing the rock mass, as well as the features of the destruction of various materials composing the mass during the formation of the dip. Relations are obtained that relate the depth of the cavity, the horizontal size of the hole, the strength properties of the rocks (adhesion, angle of internal friction), the coefficient of lateral pressure in the array. The features of wave processes generated by the formation of a dip are considered, for which a velocity field is obtained near the fracture zone at various time points in the fracture process.

Compression of granular materials

Compression data on over 100 sands were examined to clarify the role of particle rearrangement through interparticle slip and rotation and particle damage on primary compression, including the yield stress, secondary compression, and coefficient of lateral pressure at rest. During the increase in effective vertical stress, mechanisms such as tighter packing that promote particle locking and interparticle slip and particle damage that promote particle unlocking together determine the relationship between void ratio and effective vertical stress. Three levels of particle damage together with interparticle slip and rotation determine three types of compression behavior and a yield stress at the abrupt onset of particle fracturing and splitting. The ratio of secondary compression index to compression index is independent of whether compression results from overcoming interparticle friction through interparticle slip, from overcoming particle strength through particle damage, or both; and therefore it is a constant independent of the effective stress range. The coefficient of lateral pressure at rest of an initially dense sand starts with a value defined by the Jaky equation and the maximum friction angle and remains constant up to the abrupt onset of particle fracturing and splitting, at which point it begins to increase with an increase in effective vertical stress.