Analysis of Dynamic in situ Backfill Property Tests. Report 2. An Improved Lagrangian Analysis for Stress and Particle Velocity Gage Arrays

摘要

An improved Lagrangian analysis method has been developed for analyzing stress records from gages embedded in soil during an explosive test. To employ this method, a series of stress (or particle velocity) histories are measured during the passage of a one-dimensional stress wave through a material. From the measured histories numerical approximations to the space and time derivatives of stress del sigma/del h and del sigma/del t are obtained (h is Lagrangian location). These values of the derivatives are used in the equations of conservation of momentum and mass to compute the particle velocity and strain at the gage locations. Thus stress-strain paths can be obtained in the material through which the stress wave has passed. The major improvement in the present analysis is the construction of a stress-time-distance surface from the stress histories. The surface is fitted in a least-squares sense to the set of histories. Then the space and time derivatives are obtained from the surface. Smoothness criteria are imposed on the surface to minimize the importance of oscillations in the data. The Lagrangian analysis is incorporated into a computer program called GUINSY. The surface fitting procedure and the integration of the equations of conservation are separated in the program to facilitate use of the fitting procedure with other types of data. This report includes derivations of the fitting, differentiation and integration procedures, the computer program, and sample problems.