The Critical Indicator of Red-Bed Soft Rocks in Deterioration Process Induced by Water Basing on Renormalization Group Theory

Chang Xia,Zhen Liu,Guangjun Cui,Cuiying Zhou,Fengxian Zhu

doi:10.3390/app11177968

Abstract

The internal damage of red-bed soft rock induced by water is pervasive. The accumulation, growth, and localization of damage is a multi-scale process that can lead to significant strength loss in red-bed soft rock. Yet, research on the critical state of deterioration process considering multi-scale failure is limited due to high degree of system freedom. Renormalization group theory is an effective approach to find critical point of phase transition in a disordered system. To apply renormalization group theory in red-bed soft rocks, this article firstly analyzed their microstructures. Then, the granular unit model and stripy unit model are proposed to describe the self-similar characteristics of red-bed soft rocks. The calculation results based on renormalization group theory are consistent with the experimental results. The critical reductions of strength induced by water are 60% in light-yellow silty mudstone and 80% in grey silty mudstone. In addition, the critical state of damage propagation caused by stress is also studied and the analytical solution is derived. Results show that the renormalization group theory can effectively couple the micro damage and strength deterioration which provides guidance to the engineering.

Highlights

Red clastic rocks weathered in laterite from the Mesozoic–Cenozoic era is termed “red-bed” [1]
The Description of Red-Bed Soft Rock Deterioration Process Basing on Renormalization GrouWp hTehneoarydisordered system is self-similar in morphology or statistics, the renormalization group theory can be applied to analyze the critical point in phase transition process
According to renormalization group theory, the solution of Pn+1 = Pn is corresponding to the red bed soft rock critical state under failure process

Summary

Introduction

Red clastic rocks weathered in laterite from the Mesozoic–Cenozoic era is termed “red-bed” [1]. The water induced failure propagation in red-bed engineering is regarded as a multi-scale issue [10], including the dissolution and slide of clay minerals in meso-scale, the crack propagation and coalescence in meso-scale, and the strength deterioration in macro-scale Dealing with such a complex process, we need to find an applicable method. Sci. 2021, 11, 7968 the deterioration process in red-bed soft rock are limited either on meso-scale or on macroscale. TThhee rreedd--bbeedd ssoofftt rroocckk aanndd iittss pprrooppeerrttiieess iinn mmuullttii--ssccaallee. Escription of Red-Bed Soft Rock Deterioration Process Basing on Renormalization Group Theory 2.2. The Description of Red-Bed Soft Rock Deterioration Process Basing on Renormalization GrouWp hTehneoarydisordered system is self-similar in morphology or statistics, the renormalization group theory can be applied to analyze the critical point in phase transition process. TThhee sscchheemmaattiiccaall rreennoorrmmalization process of red-bed soft rock. Pce∗s=s, theorfe0d.6-buenddesrolfotnrgo-ctekrmwiwthatgerracnorurloasriomn.odel has a critical strength reduction coefficient of 0.6 under long-term water corrosion

Calculation Process of the Stripy Model

The Calculation for Critical State of Deterioration Induced by Stress

Experimental Schemes

The Meso-Structure Results of Red Bed Soft Rocks in SEM

The Strength Reduction Results of Water Immersion Experiments

Conclusions