Keywords: parameter identification, finite element method, elastic modulus, weighted gradient method, first order adjoint equation, performance function.

The purpose of the research presented in this paper is to identify the elastic modulus of ground rock using an optimal control theory, which is the first order adjoint method. The elastic modulus is one of the parameters to express geological condition. In order to perform safety constructions and reduce costs, it is important to know the elastic modulus in advance. To identify the elastic modulus, the velocity of elastic waves are observed. The velocity of elastic waves are caused by 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, 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 the minimization technique. To solve the basic and adjoint equation, the finite element method and the Newmark beta method are used. The borehole pressure is employed as the external force. The elastic modulus can be identified using these methods. For application to an actual phenomenon, the Ohyorogi-tunnel excavation site is adopted, located in Hiroshima prefecture, Japan.

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