Failure criteria for structurally heterogeneous materials

Abstract

Purpose. To analyze the current research regarding rock failure criteria and justify the analytical failure criterion for structurally heterogeneous materials in three dimensional stress-strain state.Methods. The study is based on an integrated approach with the use of analysis and synthesis of literature on the issues related to failure of the rock with heterogeneous structure, and application of analytical and empirical failure criteria to assess the strength of rocks. Findings.The analytical failure criterion is compared with the results of testing rocks in three dimensional stress-strain state. It is proposed to assess the degree of danger of the rock media failure for any point of homogeneous rock mass in the vicinity of mine working through the safety factor n , by comparing the value of equivalent stress e σ with tensile strength in uniaxial compression c R . Application of structural attenuation coefficient c k allows to pass from assessment of the rock sample strength to the evaluation of strength of the real structurally inhomogeneous rock mass.Originality. Failure criterion for structurally heterogeneous bodies with defects in the form of joint system which allows to adequately assess stability of the rock mass is proposed. Practical implications.Comparison of the analytical criterion with the results of laboratory testing of structurally heterogeneous materials in three dimensional stress state allows to predict rock failure in the massif with the accuracy of 94%. Keywords: failure criteria, structurally heterogeneous material, safety factor, tensile strength in uniaxial compression, equivalent stress, coefficient of the rock mass structural attenuation ВВЕДЕНИЕПри монотонном нагружении критерий разруше-ния представляет собой точечное условие потери несущей способности нагруженного твердого тела. Выбор адекватного критерия разрушения горных пород является одной из ключевых проблем в геоме-ханике. В случае одноосного напряженного состоя-ния критерий разрушения оценивается предельным (нормативным) значением напряжения, при котором теряется структурная целостность исследуемого тела. Это пределы прочности на одноосное сжатие, растя-жение и сдвиг. В геомеханике объектом исследова-ния, как правило, является объемное напряженно-деформированное состояние неоднородного массива горных пород, поэтому от выбора и применения кри-терия разрушения зависит точность геотехнических расчетов. Приоритет дается тем критериям, которые достаточно хорошо описывают поведение как одно-родного, так и неоднородного породного массива находящегося в объемном напряженном состоянии.Цель данной работы заключается в анализе суще-ствующих исследований критериев разрушения гор-ных пород и обосновании аналитического критерия разрушения для структурно неоднородных материа-лов, находящихся в объемном напряженно деформи-рованном состоянии.

Determining the influence of physical nonlinearity of soil strength properties on the estimated base resistance

“…A variety of non-linear models of strength are used to solve the problems on strength and stability, specifically a Shashenko failure criterion [1]. Accounting for the nonlinearity makes it possible to represent the strength properties of soil as a function of pressure under which they were determined, thereby significantly expanding the region of their change.…”

“…At the same time, for the convenience of presenting the material, we did not compare the estimated resistances regulated by standards. This is due to the fact that the standardized R st and the estimated base resistance R differ only in a multiplier (γ с1 •γ с2) /k, where γ с1 , γ с2 and k are the empirical coefficients, depending on many factors) [1,12,13].…”

“…where s z is the vertical normal stress; τ xy , τ xz , τ yz are the tangential stresses; ξ = ν/(1-ν) is the rebuff ratio; v is the Poisson coefficient [1,14]. When the soil approaches its limiting state, its Poisson coefficient tends to a value equal to 0.5.…”

“…Currently, the estimated soil resistance R [1,12,13] is used to determine the region of pressures applying which it is accepted to perform base calculations within the linear model. The issue is related to that, at present, in determining the estimated resistance of soil one does not take into consideration the non-linearity of dependence of the soil strength properties (that is specific cohesion, grip, and an internal friction angle) on normal pressure.…”

“…Many scientific papers addressed the impact of vertical loads on the bearing capacity of foundations on soils; their comprehensive analysis is of practical interest [1]. However, the increasing pace of construction in the world and the high safety and reliability requirements to modern buildings necessitate critical analysis and evaluation of existing building codes.…”