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.