Characterization and Modeling Study on Softening and Seepage Behavior of Weakly Cemented Sandy Mudstone After Water Injection

Water injection induced rock softening and the associated water seepage characteristics are the common 9 and basic problems in hard roof pressure relief, underground reservoir construction and the prevention of mine 10 water disaster. In this paper, a series of laboratory studies was carried out to investigate these characteristics with 11 the weakly cemented sandy mudstone collected from Shendong Buertai coal mine, China. The characteristics of 12 water softening and the stress-seepage interactions in saturated weekly cemented sandy mudstone were directly 13 obtained. Then a modification method of the constitutive model for rock mass considering the softening effect and a stress-damage-driven model for permeability evolution were established. Research results show that water 15 saturation reduces the tensile strength, compressive strength and cohesion by 56%, and reduces the elastic modulus 16 by 28%. The hydraulic effect on Poisson’s ratio and internal friction angle is negligible. The relationship between 17 the permeability of weakly cemented sandy mudstone with complete compaction deformation is to be divided into 18 three stages of seepage shielding, seepage surge and seepage recovery. Rock permeability in each stage has a 19 negative exponential relationship with the effective stress. This research provides a theoretical basis for the 20 researches of hydro-mechanical couplings on weakly cemented sandy mudstone, which is insightful for rock 21 engineering practice.

Buertai coal mine 42108 longwall face was softened and fractured by water injection and fracturing. As a result, 33 the length and magnitude of periodic weighting reduced 18.9% ～ 70.6% and 13.7% ～ 19.4%, respectively 34 (Yang et al. 2020). On the other hand, it is critical to understand the dynamic stability of underground structure 35 under hydro-mechanical coupling effect. This is because protection of groundwater has the highest priority at 36 Shendong mining area (Selene et al. 2020). In addition, rock engineering associated with tunnels, water 37 conservancy and underground chambers in western China also encounter varying degrees of water softening and 38 seepage problems. Therefore, it is of great importance to study the hydraulic effects and seepage characteristics of 39 weakly cemented rocks in Shendong coal mining area. 40 The physical and mechanical properties of weakly cemented rocks in western China can change substantially 41 when saturated. A series of researchers has carried out experiments and mechanism studies on the water softening The collected rock cores are shaping into two kinds of geometries. The first type of rock samples was cut as 117 cylindrical samples with a diameter of about 50 mm and a height of 100 mm, which were used for compression 118 and permeability tests. The other type was prepared as disc samples with a diameter of about 50 mm and a height 119 7 of 25 mm that were suitable for the Brazilian test. The parallelism of the upper and lower ends and the flatness of 120 the faces were both less than 0.02. 121 Figure 3a shows a servo-controlled stress-seepage-temperature-chemical (MHTC) coupling system at China 122 University of Mining and Technology-Beijing, which was used to conduct triaxial compression tests and seepage 123 tests on natural and fully saturated rock samples. The experiments aims to study the deformation under various 124 confining pressure. During the test, both axial and confining pressures were displacement controlled at a rate of 125 0.001 mm/s. To investigate the influence of in-situ formation pressure on the water softening characteristics of 126 rock, the confining pressures were set as 0, 4, 6 and 8 MPa, respectively, corresponding to the depth that various 127 from 0 to 1000 m. A MTS Exceed E45 rock mechanics testing system from China University of Mining and 128 Technology-Beijing (see Fig. 3b) was used to carry out the Brazilian tests on natural and fully saturated rock 129 samples. The axial load is also controlled by changing the displacement at a speed of 0.001 mm/s. 130

Effect of water softening on compressive characteristics 131
The compressive properties of natural and saturated sandy mudstones were obtained from uniaxial 132 compressive and triaxial tests. Tests at each confining pressure were repeated three times. Figure 4 shows the 133 evolution of circumferential and axial strains with the deviatoric stress under different confining pressure. By 134 comparing the uniaxial and triaxial compressive stress-strain curves of natural and saturated sandy mudstones, one 135 can find that the compressive strength of fully saturated rock samples is significantly lower than that of natural 136 state rock samples. Thereby, the plastic compaction before the peak strength becomes more obvious for fully 137 saturated rock (A in the figure), whereas the stress failure after the post-peak slows down. In addition, Figure 4

Effect of water softening on tensile characteristics 147
The Brazilian test was implemented to estimate the tensile strength of the natural and saturated rock samples, 148 and four sets of tests were carried out under each state. Figure 5 shows the force-displacement curves obtained 149 from the Brazilian test. It can be seen from Fig. 5 that the failure strength (force) of the rock sample in the natural 150 state is substantially greater than that of the saturated rock sample. In the natural state, the force and deformation 151 of the sandy mudstone prior to the peak is almost elastic. At the same time, the force after the peak tensile strength 152 drops dramatically and the brittle fracturing of the rock is obvious. On the other hand, the force-displacement 9 curve and deformation characteristics of Brazilian test for the rock sample in fully saturated state are similar to that 154 of uniaxial and triaxial tests, especially the plastic behavior and fluctuated loading after the peak failure.  According to the Brazilian test, ultimate tensile strength ( t  ) of rock can be expressed as: where ti  is the tensile strength of one particular sample; i P means the failure load； i R represents the sample 160 radius; i t is the thickness of sample; n denotes the number of tests conducted.

161
Experimental results show that the tensile strengths at the natural state and fully saturated state are 4.03 MPa 162 and 1.38 MPa, respectively. Although the tensile strength drops 66% when the weakly cemented sandy mudstone 163 is saturated by water, the tensile strength keeps 1/10 of its uniaxial compressive strength at each state. 164

Comparison of mechanical properties between natural and fully saturated rock 165
Based on the aforementioned experiments, the mechanical properties of samples under natural and fully 166 saturated states are shown below in Table 1. 167  Confining pressure (MPa) 181

Model modification considering softening effect from water injection 218
Based on the theory of elasticoplastic strain, the total strain change of rock can be expressed as: 219 in which  represents the plastic factor,  is the internal friction angle and g is the plastic function.

228
Considering the water softening effect and the pore pressure effect on effective stress, e ij d can be modified 229 as: 230 where, p is pore pressure in the fractures,  means the Biot's coefficient.

232
Whereas, p ij d can be modified as: Furthermore, by implementing more experiments to obtain () E  , v and  , Eq.(7) can be further 250 simplified. Alternatively, numerical solution can be gathered by using existing numerical software, which will not 251 be described here. 252 4 Couplings among stress-damage-seepage and permeability model 253

Experimental design and procedures 254
For the fully saturated sandy mudstone samples, a full-process permeability test during the triaxial 255 compression was carried out to study the coupled stress-deformation-seepage interactions. The confining pressure 256 was applied to the rock sample at a loading rate of 1 MPa/min to a specified target of 3 MPa, and kept constant. 257 This confining pressure corresponds to a depth of about 400 m. The axial pressure was applied by displacement 258 control and stress servo loading method. The displacement rate was 0.02 mm/min. The water pressure at the inlet 259 of the rock sample was controlled at 1.1 MPa and the outlet was connected to atmosphere. After the seepage was 260 stabilized, the rock sample was tested for axial deformation and flow velocity under triaxial compression. The test 261 was repeated for twice under each axial pressure with a time interval of not less than 1 min. After the test under 262 one axial pressure was completed, the axial pressure was increased by 2-3 MPal. The measurement was performed 263 again until the rock sample was completely failed. 264 Figure 10 shows the co-evolution relationship of stress-strain and permeability of sandy mudstone in the 266 complete triaxial compression. It is clear that the permeability process of sandy mudstone under the triaxial 267 loading can be divided into three stages. The first stage is the seepage shielding stage. At this stage, the 268 permeability of the rock decreases with the increase of the stress level, from the initial value of 0.056 mD to 0.014 269 mD. The reason is that the effective stress closes the pre-existing fractures in the samples. By comparing the 270 stress-strain curve with the seepage evolution curve, it can be found that the seepage shielding stage corresponds to 271 the pre-peak compaction, elastic and initial plastic damage stages. The second stage is the seepage surge stage. As The permeability of the rock sample decreases and recovers with post-peak deformation. The fully saturated sandy 277 mudstone has weak cementation from the previous rock hydraulic effects. It can be seen from Fig. 10 that obvious 278 rheological behavior appears after rock failure. It results water filling in fractures, dislocation or further 279 compaction, which ultimately leads to a decrease in permeability. The seepage recovery stage corresponds to the 280 post-peak rheological stage in the triaxial test. The reality is obvious that the permeability of rock in the late stage 281 III could not keep dropping at a high rate, and the permeability will become stable with the increase of deformation 282 after failure. In Fig. 10, the seepage rate of the late stage III gradually decreases. In this test, the post-peak 283 permeability test data is limited and the process is not fully captured.

A coupled stress-damage-permeability model on sandy mudstone 287
Assuming the opening width of the fracture is b , the mean tortuosity is  , the crack length per unit area is where 0 means the initial values. that the rock permeability has an inverse exponential relationship with the effective stress. In particular, it should 306 be noted that the damage of rock can be further defined according to specific observation methods, such as the 307 using of extensive elastic modulus degradation, i.e.

Model validation 314
The permeability model proposed in this study is to validate by the sandy mudstone data and permeability test 315 results. Figure 11 shows the verification results of the coupled stress-damage-permeability model with the model 316 verification parameters in Table 2   In this paper, the hydraulic effect and seepage behavior of weakly cemented sandy mudstone in the Buertai 324 coal mine of Shendong mining area were systematically studied. Based on the experimental results, a modified 325 constitutive model considering softening effect of water injection and a stress-damage-driven model for 326 permeability evolution were proposed to incorporate stress-damage-seepage couplings. The following conclusions 327 can be drawn: 328 (1) Water softening on weakly cemented sandy mudstone is significant. After water saturation, the plasticity 329 of increases, the compressive strength decreases by 29%～57%. Thereby, the smaller the confining pressure, the 330 higher the softening effect on compressive strength. The modulus of elasticity decreases by 25%～30%. Although, 331