基于BQ的破碎岩体注浆加固强度增长理论

正确评估破碎岩体注浆加固后的强度对于岩石工程设计十分重要。基于莫尔库仑强度准则,建立了注浆前后破碎岩体强度增长理论,推导出单轴抗压强度增长率、单轴抗拉强度增长率、内摩擦系数增长率和内聚力增长率之间的关系方程。根据已有的基于BQ的岩体内聚力和内摩擦角的经验公式,推导出注浆后破碎岩体内摩擦系数增长率和内聚力增长率随岩体质量指标增长量（ΔBQ）变化的表达式。再根据已有的注浆后破碎岩体单轴抗压强度增长率的经验公式和各强度增长率之间的关系方程,得到隐含ΔBQ的非线性方程,可通过数值解法求出了ΔBQ的值,进而很容易求得各强度增长率的值。分析表明,随着岩体质量指标由小到大变化,注浆后强度增长率开始较大,并很快减小,而后趋于平缓；一般情况下,内聚力增长率约为摩擦系数增长率的2～5倍,单轴抗压强度增长率约为单轴抗拉强度增长率的2～3倍。

Theory of strength increment of grouting-reinforced bodies for broken rock mass based on BQ

Properly evaluating strength of grouting-reinforced broken rock mass is very important for rock engineering design. Based on the Mohr-Coulomb strength criterion, a theory of strength increment of broken rock mass before and after grouting is established. Equations for the relations among the growth rates of uniaxial compressive strength, uniaxial tensile strength, internal friction coefficient and cohesion (CTFC) are deduced. On the basis of the existing empirical formulas of cohesion and internal friction angle expressed by rock mass basic quality index (BQ), the equations for the growth rate of internal friction coefficient or growth rate of cohesion varying with the increment of rock mass basic quality index (ΔBQ) of broken rock mass before and after grouting are derived respectively. According to the existing empirical formula for the growth rate of uniaxial compressive strength of broken rock mass after grouting and the equations for the relations among the growth rates of CTFC, a nonlinear equation for the implicit variable ΔBQ is established. Using the numerical method of nonlinear equations, the value of ΔBQ can be calculated, thus the values of growth rates of CTFC can be easily obtained. The results show that the initial strength growth rates are larger, rapidly decrease and tend to be gentle with the rock mass quality index BQ from 200 to 350. Generally, the growth rate of cohesion is about 2 to 5 times that of friction coefficient, and the growth rate uniaxial compressive strength is about 2 to 3 times that of uniaxial tensile strength.