Permeability-porosity relation during erosion-induced water inrush: Experimental and theoretical investigations

During the construction of tunnelling in soil ground, erosion-induced water inrush is one of the most serious geohazards, during which the migration of soil particles can substantially alter soil porosity and permeability. Understanding the permeability-porosity (k-φ) relation is crucial for predicting the rate of water inflow and the possibility of water inrush. The applicability of existing k-φ models in this problem has not been evaluated. In this study, the k-φ relation was investigated by a series of laboratory seepage-erosion tests on soil specimens with different Talbot indexes and initial porosities. Based on the experimental results, an evaluation was made on the performance of four popular k-φ models, including the Kozeny-Carman (K-C), Kruger, Ives-Pienvichitr (I-P), and Verma and Pruess (V-P) models. Two types of seepage-erosion processes were observed, including the common erosion and mutation erosion processes (CEP and MEP). CEP and MEP mean the processes with and without the occurrence of water inrush, respectively. During the CEP associated with low Talbot index and porosity, the permeability of soil was significantly overestimated by the V-P model and slightly underestimated by the other three models. During the MEP associated with high Talbot index and porosity, the erosion led to water inrush through three stages: slow and rapid evolution as well as stable stages. Significant underestimates of soil permeability were caused by all the models, thereby leading to high risk. None of these models was able to well capture the k-φ relation during different erosion-flow processes for both CEP and MEP. To address this problem, a power function with one adjustable exponent for the k-φ relation was proposed and verified.