Identification of the Elastic Modulus of Ground Rock based on Blasting Waves using the Adjoint Method

Abstract

The purpose of this research is to identify the elastic modulus of ground rock using an optimal control theory, which is the first order adjoint method. Elastic modulus is one of parameter to express geological condition. In order to perform safety constructions and reduce costs, it is important to know elastic modulus in advance. To identify the elastic modulus, the velocity of elastic waves are observed. The velocity of elastic waves are caused by the blasts with dynamite. The Optimal elastic modulus is identified using the first adjoint method so as to minimize the performance function, which is defined by the square sum of residual discrepancies of between the calculated and observed velocities. To calculate the state quantity in the ground, following basic equations are used in this research. As the basic equation, the equilibrium of stress equation, the strain-displacement equation and the stress-strain equation are used. The first order adjoint equation is used to calculate the gradient of the performance function. The weighted gradient method is applied to minimization technique. To solve the basic and adjoint equation, the finite element method and the Newmark β method are applied for the spatial and temporal discretizations, respectively. As the external force, borehole pressure is employed. The elastic modulus can be identified using these methods. For application to actual phenomenon, Ohyorogi-tunnel excavation site is adopted. It is located in Hiroshima prefecture, Japan.