SUMMARYThe purpose of this paper is to present a parameter identification method to determine the force of a blast and the elastic modulus of the ground using the measurements of a dynamic elastic wave, the adjoint equation method of optimal control theory, and the finite element method. Before the excavation of rocky ground, it is important to estimate the ground properties. In this paper, the elastic modulus is determined as the performance function is minimized using a technique based on the first-order adjoint method. The performance function is a square sum of the discrepancies between the computed and the observed values of the velocities. After the determination of the magnitude of the blasting force, we can determine the elastic modulus of the rock. As the basic equation to calculate the velocities of dynamic elastic body, elastic equilibrium equations with linear viscosity are employed. The adjoint equation method has been utilized in order to calculate the gradient of the performance function with respect to the parameters. The gradient of the performance function is calculated using the first-order adjoint equation. The weighted gradient method is applied for minimization. In order to solve the state equations in space and time, the finite element method and the Newmark 1 4 method are used. In this paper, we tested the practical application of our proposed method for determination of the elastic modulus of rock at the Ikawa tunnel located in the Tokushima prefecture, Japan.

SUMMARYThe purpose of this paper is to investigate the estimation of dynamic elastic behavior of the ground using the Kalman filter finite element method. In the present paper, as the state equation, the balance of stress equation, the strain-displacement equation and the stress-strain equation are used. For temporal discretization, the Newmark 1 4 method is employed, and for the spatial discretization the Galerkin method is applied. The Kalman filter finite element method is a combination of the Kalman filter and the finite element method. The present method is adaptable to estimations not only in time but also in space, as we have confirmed by its application to the Futatsuishi quarry site. The input data are the measured velocity, acceleration, etc., which may include mechanical noise. It has been shown in numerical studies that the estimated velocity, acceleration, etc., at any other spatial and temporal point can be obtained by removing the noise included in the observation.