Analytical solutions for the circular stress transducer embedded in rheological rock mass

Abstract

The rheological stress recovery (RSR) method was proposed to measure the in-situ stress of rock mass with time-dependent property by drilling a hole and embedding transducers into it. To solve the stress distribution on the transducer, a viscoelastic axisymmetric plane model was firstly built considering an arbitrary stress boundary condition. The analytical solution was developed by dividing the stress boundary conditions into axisymmetric and anti-axisymmetric combining with Laplace transformation technique. The explicit stress expressions on interfaces of rock–grout and grout–transducer was obtained using Burgers and Boltzmann viscoelastic models, respectively. Furthermore, the variations of transducer surface final stress, which is related to rheological time, geometric and mechanical properties of rock mass, grout parameter, and transducer materials, was proposed for calculating the measured stress by RSR method. For both of Burgers and Boltzmann viscoelastic model, final stress increases as elastic modulus ratio increases when elastic modulus ratio under 20, and the final stress could be ignored when diameter ratio is over 1.4. The rheological time increases with increasing of viscosity coefficient and the modulus ratio, but decreases as the shear modulus increases. The results in here provide a simple method for stress analyzing and have great value for understanding the relationship between the initial stress of rock mass and the measured stress for the RSR method.