Geofluids

Volume 2018, Article ID 7137601, 17 pages

https://doi.org/10.1155/2018/7137601

## Variation Characteristics of Mass-Loss Rate in Dynamic Seepage System of the Broken Rocks

^{1}Civil Engineering Department, Yancheng Institute of Technology, Yancheng, Jiangsu 224051, China^{2}School of Civil, Environmental & Mining Engineering, The University of Adelaide, Adelaide, SA 5005, Australia

Correspondence should be addressed to Hailing Kong; moc.621@gnokliah

Received 1 February 2018; Accepted 21 May 2018; Published 15 July 2018

Academic Editor: Paolo Fulignati

Copyright © 2018 Luzhen Wang and Hailing Kong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

When the collapse column and its adjacent rocks in complex geological structures are disturbed by mining, concomitant fine particle migration, mass loss, and porous structure variation during the water seepage process in broken rocks are the inherent causes for collapse column activation and water inrush. Studying the time-varying characteristics of the mass-loss rate in the dynamic seepage system of the broken rocks is of theoretical importance for the prevention of water inrush from the collapse columns. In this study, the seepage tests of the broken mudstone were carried out using the patented pumping station seepage method, and the time-varying function of the mass-loss rate was generalized. Then, the optimal coefficients in the function of mass-loss rate were computed using the genetic algorithm. At last, the mass-loss rate in the dynamic seepage system of the broken rocks with consideration of the acceleration factor was calculated using Lagrange discrete element method. The results showed that (1) the mass-loss rate was expressed as a time-dependent, exponential function with its coefficient related to the porosity, and its time-varying characteristics were affected by gradation; (2) the time-varying curves with Talbol power exponents less than 0.6 had a rapid change stage and a slow change stage, while the time-varying curves with Talbol power exponents greater than 0.6 had an initial gradual change stage, a rapid change stage and a slow change stage; (3) at the early seepage stage, the mass-loss rate decreased with Talbol power exponent increasing; and (4) after long time seepage, the mass-loss rate was close to zero and unrelated to Talbol power exponent, and the porous structure in broken rocks remained stable with its porosity close to a certain stable value.

#### 1. Introduction

At present, China is still a country with coal as its major energy source. With the gradual exhaustion of its shallow resources, deep excavation of coal resources has become the norm with the mining depth of individual coal mines of down to 1500 m [1]. However, deep coal seams are characteristic of a very complex geological structure, such as faults and collapse columns. Thus, their mining is often accompanied with severe water inrush, bringing serious threats to the safe production of coal mines [2, 3].

As a good underground water passageway, the collapse column is one of the main culprits for frequent water inrush in deep mine exploitation. Taking widely developed collapse columns in the North China coalfield as an example, they are broken rocks with variable porous and fracture structures formed by mixing various broken rock fragments of different sizes, cementing together through muddy and siliceous thin layers on their surfaces and compacting under the self-gravity of collapse columns or ground pressure [4]. Many collapse columns with their diameters of up to tens of meters often run through multiple strata. Due to mining disturbance, internal pores and fractures of rocks develop and expand, leading to changes in the stress field and the seepage field inside themselves and their adjacent rocks, subsequently, evident alteration of the network of cracks in the confined rocks and the porous structure of the broken rocks, and finally, the formation of water seepage passages.

Acted by groundwater pressure, their interior broken rocks undergo dissolution, erosion, and abrasion, and the resultant fine particles migrate and disappear under the entrainment of water seepage. When the migration and disappearance develops to a certain degree, the regional and connected pipe flow passages are formed inside the broken rocks and the confined underwater penetrates the roof and floor of coal seams through these passages, resulting in the occurrence of water inrush disasters.

Many related studies [4–15] have shown that during water inrush from the collapse column, coal mining makes the roof and floor strata of the coal seams generate a large number of fractures whose expansion and connection with the collapse column leads to water inrush, that is, indirect water inrush of the broken rocks. Clearly, these studies ignored the structural features of the collapse column itself. According to the on-site observation data, a small amount of mud and sand flows out before water inrush from the collapse column, and a large amount of rock fragments and coal debris pours out during water inrush [4]. Therefore, the migration and loss of internal fine particles during the seepage in the broken rocks is the intrinsic cause for collapse column activation and water inrush. This kind of phenomenon is frequently observed in the geotechnical field.

In recent years, many researchers have applied theoretical analysis, numerical simulation, and laboratory tests to study mass loss phenomena occurring in geotechnical engineering. Kenney and Lau [16] experimentally investigated the migration of mobile fine particles driven by seepage in the framework of pores and proposed the method for determining the mass loss of mobile fine particles using the particle gradating curve. Sterpi [17] established a finite difference model for these particles utilizing the continuity equation of mobile fine particles and the empirical formula of mass loss and pressure gradient of these particles. Cividini and Gioda [18] introduced the effect of seepage on the migration and mass loss of mobile fine particles and described the erosion and migration mechanism of mobile fine particles using the finite element method. Fox et al. [19] studied the erosion of groundwater on the riverbank and found that the erosion-induced mass loss of particles is related to the seepage velocity. Annamaria et al. [20] analyzed the various characteristics of the time-related fine particle density at various points in the effective seepage channel with coarse particles as the immobile framework using the finite element method. Fujisawa et al. [21] numerically simulated and reconstructed the piping phenomenon of soil grains due to erosion and framework migration and found that the amount of soil particles migrated was affected by the saturation of soil matrix and the distribution of particle sizes. Chang and Zhang [22] proposed well-graded soil and gap-graded soil to study the internal stability and found the ability of the coarse fraction of a soil to prevent the loss of its fine fraction due to seepage flow. Ke and Akihiro [23] conducted a series of seepage tests and pointed out that the hydraulic gradient would drop with the progress of suffusion and the eroded away fine particles insrease with the initial amount increasing. Chen et al. [24–26] through their experimental studies found that the variation of the postpiping sand outflow over time satisfies Boltzmann’s nonlinear relationship. Ma et al. [27] through the gas seepage properties of crushed coal specimens measurement found that (1) particle crushing during compaction was the main reason to increase small-size, indicating that gas seepage properties were strongly influenced by the particle size and axial displacement, and (2) the porosity decreased with the weight loss of larger particle size.

All of the above studies consistently showed that coarse particles served as the immobile framework while fine particles were the movable particles and could migrate and drain away along with seepage. These studies found that the migration and loss of mobile fine particles were affected by many factors, such as seepage type [16, 18, 24–26, 28], particle size graduation [19, 21–23, 27, 29–32], seepage velocity [20], and pore water pressure [17, 32–34]. However, they did not consider the porous structure inside the framework particles, the changes concurring with the migration and dissipation of fine particles, and the effect of time-varying porosity on fine particle loss. In essence, with the migration and loss of fine particles, the porosity of the framework structure changes over time. At the same time, the framework structure with time-varying porosity also affects the migration and dissipation of its internal fine particles. Therefore, the mass-loss rate of fine particles inside the framework of coarse particles has time-dependent, nonlinear characteristics, and it is a critical physical parameter in the seepage system. Studying the varying characteristics of the mass-loss rate is the basics to research the water-inrush incident in the collapsed column.

In this study, we explored the time-varying and nonlinear characteristics of the dynamic seepage system of broken rocks and examined the varying behavior of the mass-loss rate. Based on the results measured in the lab, we generalized a time-dependent, nonlinear function of the mass-loss rate and obtained the optimal coefficient values of the function using the genetic algorithm. We then introduced a time-related mass-loss rate function by reasonably selecting the acceleration factor to establish the actual collapse column model. At last, we applied the discrete element method to design the program of mass-loss rate response in the dynamic seepage system of broken rocks to compute and analyze the mass-loss rate and the spatiotemporal distribution of fine particles in the broken rocks of the actual collapse column.

In order to overcome the shortcomings that previous researchers often used, the pre-set discontinuous particle size gradation, which could not be acted as the variable in numerical and theoretical calculations, we first applied Talbol continuous grading formula to grade the broken rock samples and Talbol power exponent to describe the impact of particle size distribution on the mass-loss rate in the dynamic seepage system of broken rocks. In order to avoid blindly selecting the reference value of rational coefficient due to lack of experiences, we then adopted the genetic algorithm to calculate the optimal coefficients of the mass-loss rate function.

#### 2. Experiments

##### 2.1. Experimental Method and Principle

The patented pumping station seepage method was employed in our experiment on the mass-loss-concurring water seepage in broken rocks. Figure 1 shows the experiment apparatus and Figure 2 shows the structure of its core device: an open permeameter.