Detecting structural collapse of structured natural clays using singular value decomposition of the strain response envelope

This paper introduces a systematic methodology to detect structural collapses by using the singular value decomposition of the strain response envelope. The singular value decomposition technique is a mathematical tool that enables us to investigate the strain response envelope in a quantitative way. Stress probe tests with various stress paths were conducted to obtain the stress-strain responses of structured and de-structured clay samples. For the structured clays, we used natural block samples obtained from an area near Chicago, IL. Reconstituted samples were used for the de-structured clays. The strain response envelope was constructed at a given stress input, and its evolution with increasing stress input was investigated by the singular value decomposition technique. The quantitative information, such as the translation, rotation, and expansion, elucidated the evolution of the strain response envelope. Based on this investigation, it was found that the structure plays a significant role in the stiffness degradation characteristics. The variation in the angles of the line connecting the origin and the center of the strain response envelope, α1, resulted mainly from the continuous generation of plastic flow as opposed to a specific structural collapse event during stress probing. However, the rotation angle of the major axis of the strain response envelope, α2, successfully detected abrupt structural collapses in the structured clays.