# Long-Term Bearing Deformation Characteristics of Caved Gangue in Gob under Different Moisture Conditions

Authors: Zhen Wang; Shanming Wei; Zhenhua Zhao; Liting Xing; Changsuo Li; Hailong Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In gob, the caved gangue is in a state of long-term bearing deformation with obvious time-dependent effect, even though the coal seam has been mined for a long time. As time goes on, because of the excessive deformation of caved gangue, the gob surrounding rock will easily aggravate the structural instability and cause dynamic disasters, such as mine water inrush and surface collapse. If the gob is filled with water, the bearing capacity of the caved gangue in waterlogged environment will be worse than that in dry environment, which will greatly increase the possibility of disasters. In order to study the bearing deformation characteristics of caved gangue under different moisture conditions, a testing system used for bearing deformation testing of caved gangue is developed. The typical caved gangue is chosen for samples. In view of the particle size distribution characteristics and stress state of caved gangue, the size distribution of caved gangue obeys the law of normal distribution and the load pattern is designed to step load. With the increase of axial load, the axial deformation of caved gangue increases gradually, the residual bulking coefficient decreases gradually, which are more obvious in load stage than in constant load stage. In the early constant load stage, the axial deformation of caved gangue grows rapidly, then tends to be slow and steady gradually; the relationship between strain and time meets the logarithmic relationship. In load stage, the D-value of axial strain decreases gradually along with the increase of axial load, whereas in constant load stage, it is opposite; the bearing deformation of caved gangue is consisted of two parts: instantaneous compression deformation and long-term deformation. For instantaneous compression deformation, the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. For long-term deformation, meanwhile, the water acting as the softening agent reduces the strength of the rock block and is conducive to the crushing of the rock block. The newborn rock blocks may slip and fill the gap between rock blocks, which also promotes the compressive strain of caved gangue specimen. The research results have important significance for forecasting and controlling the movement and deformation of overlying strata caused by mining.


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## Body

## 1. Introduction

There are three distinct zones (caved zone, fracture zone, and continuous deformation zone) of disturbance in overlying strata when the coal seam roof is controlled by caving method, based on the deformation and failure characteristics of overlying strata [1–7]. The caved zone is filled by the caved gangue composed of an immediate roof and part overlying strata [8, 9], as shown in Figure 1. The vertical height of the caved zone with a highly irregular shape and different granular caved gangue can reach 4–11 times the mining height [10, 11]. The caved gangue is gradually compressed by the overburden load resulting from mining disturbance, which supports the deformable upper rock strata [12, 13]. Therefore, the variable load compaction of caved gangue in gob directly determines the movement of the upper strata.Figure 1
Overlying strata failure mode after mining.The caved gangue in gob can be treated as a porous medium consisting of caved gangue blocks generated by caving, pilling, and recompressing [14]. Due to the nonuniform stress distribution in a gob, the degree of compaction of caved gangue mass varies with location and time, resulting in a variable load compaction. It is well known that the mining-induced gob stress profile near the working face region varies with the mining direction [15–17], as shown in Figure 2. Apparently, the gob close to the working face has a relatively low-stress situation due to the existence of hydraulic supports and the overburden hinge structure. Moving away from the working face towards the gob, the load carried by the caved gangue gradually increases, which results in a progressive compaction of the loosely packed rocks. The stress level of the caved zone far away from the working face almost recovers back to the original in-situ value and the gob was fully compacted. The caved gangue is in a state of long-term bearing deformation with obvious time-dependent effect, even though the coal seam has been mined for a long time. As time goes on, because of the excessive deformation of caved gangue in gob, the gob surrounding rock will easily aggravate the structural instability and cause dynamic disasters, such as mine water inrush and surface collapse [18–20]. If the gob is filled with water, the bearing capacity of the caved gangue in waterlogged environment will be worse than that in dry environment, which will greatly increase the possibility of disasters. Thus, it is essential to study the bearing deformation characteristics of caved gangue in gob under load, especially with different moisture contents. The results are difficult to obtain by field observation. Because of the concealment of underground excavation engineering, laboratory testing becomes an effective way to solve this problem [21–33].Figure 2
Stress distribution around gob.In the process of laboratory testing, the bearing deformation characteristics of caved gangue are mainly influenced by the own characteristics of specimens and the properties of experimental device. The own characteristics of specimen include compressive strength, particle size, particle size distribution, and moisture content. The properties of experimental device include the size of test vessel, load method, and measuring accuracy. Based on partial influencing factor, some scholars have carried out a series of studies on the caved gangue [34–39]. These studies significantly contribute to the understanding of bearing deformation characteristics of caved gangue. However, the small effective volume of the existing experimental devices is the common defect. With the increase of particle size of caved gangue, the problem of boundary effect will become more and more prominent. Moreover, the patterns of particle size distribution of caved gangue are varied, and the existing studies are mainly focused on single particle size distribution, uniform particle size distribution, and continuous particle size distribution. In this study, in order to study the bearing deformation characteristics of large-size caved gangue, a testing system used for bearing deformation testing of large-size caved gangue was developed. The typical sandstone from the roof was chosen for specimens. In view of the particle size distribution characteristics and stress state of caved gangue in caved zone, the size distribution of caved gangue obeyed the law of normal distribution, and the load method was designed to step load. The research results have important significance for forecasting and controlling the movement and deformation of overlying strata caused by mining.


## 2. Testing System and Scheme

### 2.1. Testing System

The testing system used for bearing deformation testing of large-size caved gangue is consisted of load support bracket, load head, testing chamber, servo control system of displacement and load, servo control system of water pressure and water yield, and operating deck, as shown in Figure3. (1) Load support bracket is consisted of base, frame, supporting structure of hydraulic cylinder, reaction frame, which plays the role of fixed, and supporting action. (2) Load head is connected to hydrocylinder by connecting rod. (3) Testing chamber is cylindric, the effective size are 400 mm diameter and 680 mm high. In order to facilitate the filling of caved gangue specimens, the testing chamber is composed of two compartments. (4) Servo control system of displacement and stress can control the load head by setting displacement or load. The meter full scale of displacement is 400 mm, and the accuracy is 0.01 mm. The maximum load is 600 KN, and the accuracy is 0.01 KN. (5) Servo control system of water pressure and water yield can fill the testing chamber with water by setting water pressure or water yield. The maximum water pressure is 2 MPa, the maximum water supply is 150 L/h, and the accuracy is 0.01 MPa. (6) Operating deck is fully automated, five basic parameters can be collected into a database in real time, such as time, displacement, load, water pressure, and water yield. The maximum sampling frequency is 10HZ.Figure 3
Testing system used for bearing deformation testing of large-size caved gangue.


### 2.2. Testing Scheme

#### 2.2.1. Particle Size Distribution

The rock specimens are sandstone from the gob of Daizhuang coal mine, which is located near Jining city, Shandong Province, China. Some basic parameters are shown in Table1. Considering the scale effect, the ratio between the diameter of caved gangue specimen and the maximum particle size of caved gangue should be greater than or equal to 5 [40–42]. Because the internal diameter of testing chamber is 400 mm, the maximum particle size of caved gangue could be tested is 80 mm. In order to minimize the influence of size effect on the testing results, the maximum particle size of the caved gangue selected in the test is determined to be 40 mm. The caved gangue is divided into 7 categories by the particle size, which are 5–10 mm, 10–15 mm, 15–20 mm, 20–25 mm, 25–30 mm, 30–35 mm, and 35∼40 mm, as shown in Figure 4. In this article, the size distribution of caved gangue specimens for testing obeys the law of normal distribution. In a complete caved gangue specimen, according to the particle size of caved gangue from small to large, the mass fraction of 7 categories is 5%, 10%, 20%, 30%, 20%, 10%, and 5%, respectively, as shown in Figure 5. For the caved gangue with a certain particle size, the relation between the mass fraction and particle size is as follows:(1)A=4.885+329.27910.761π/2e−2D−22/10.7612,where A is the mass fraction of the caved gangue with a certain particle size (%) and D is the minimum of the caved gangue in a certain particle size (mm).Table 1
Basic parameters of sandstone.
Moisture conditionUniaxial compressive strength (MPa)Tensile strength (MPa)Modulus of elasticity (GPa)Poisson's ratioDensity (kg/m3)Moisture content (%)Dry96.787.516.10.1992565.60Water saturated87.217.215.20.2092578.80.516Figure 4
Caved gangue with different particle sizes.Figure 5
Mass fraction of 7 categories of caved gangue.The actual height of caved gangue specimen is 655 mm, and the total mass is 110 kg. The initial bulking factor of caved gangue specimen is 1.901, and the voidage is 0.901. The assembled caved gangue specimen is shown in Figure6.Figure 6
Assembled caved gangue.The initial bulking factor of caved gangue (K) is given by(2)K=V1V0,where K is the initial bulking factor of caved gangue, V0 is the volume of complete rock, and V1 is the volume of caved gangue produced by complete rock in the state of natural accumulation.The initial voidage of caved gangue (P) is given by(3)P=V1−V0V0=K−1,where P is the initial voidage of caved gangue.The residual height of caved gangue specimen after the bearing deformation testing (h1) is given by(4)h1=h0−u,where h1 is the residual height of caved gangue specimen after the bearing deformation testing (mm), h0 is the initial height of caved gangue specimen (mm), and u is the deformation of caved gangue specimen (mm).The residual bulking factor of caved gangue specimen after the bearing deformation testing (K1) is given by(5)K1=h1⋅SV0,where K1 is the residual bulking factor of caved gangue specimen after the bearing deformation testing and S is the area of testing chamber, 125600 mm2.


#### 2.2.2. Load Method

The pressure acting on the caved gangue in gob is mainly from overlying strata. The pressure value is directly related to the height of the fractured overlying strata and increases with the increase in the height of the fractured overlying strata. In the time interval of two adjacent roof weightings, the pressure acting on the caved gangue in gob is basically unchanged, which is equal to the self-weight stress of total fractured overlying strata. During the roof weighting, the pressure acting on the caved gangue in gob will increase rapidly, and the increment is equal to the self-weight stress of generated fractured overlying strata. So the pressure acting on the caved gangue in gob is stair stepping, which provides evidence for designing the load method in the bearing deformation testing of caved gangue in gob. The load method is divided into 2 stages, namely, load stage and constant load stage. In load stage, the load speed is 0.5 kN/s. In constant load stage, the constant load is 100 kN, 200 kN, 300 kN, and 400 kN, respectively; the duration of each constant load is 4 hours. Before the formal testing, a preload of 20 kN is applied to the caved gangue in gob specimen until the deformation is constant, which needs about 15 minutes. The load method of a complete testing is shown as Figure7.Figure 7
Load method of a complete testing.


## 2.1. Testing System

The testing system used for bearing deformation testing of large-size caved gangue is consisted of load support bracket, load head, testing chamber, servo control system of displacement and load, servo control system of water pressure and water yield, and operating deck, as shown in Figure3. (1) Load support bracket is consisted of base, frame, supporting structure of hydraulic cylinder, reaction frame, which plays the role of fixed, and supporting action. (2) Load head is connected to hydrocylinder by connecting rod. (3) Testing chamber is cylindric, the effective size are 400 mm diameter and 680 mm high. In order to facilitate the filling of caved gangue specimens, the testing chamber is composed of two compartments. (4) Servo control system of displacement and stress can control the load head by setting displacement or load. The meter full scale of displacement is 400 mm, and the accuracy is 0.01 mm. The maximum load is 600 KN, and the accuracy is 0.01 KN. (5) Servo control system of water pressure and water yield can fill the testing chamber with water by setting water pressure or water yield. The maximum water pressure is 2 MPa, the maximum water supply is 150 L/h, and the accuracy is 0.01 MPa. (6) Operating deck is fully automated, five basic parameters can be collected into a database in real time, such as time, displacement, load, water pressure, and water yield. The maximum sampling frequency is 10HZ.Figure 3
Testing system used for bearing deformation testing of large-size caved gangue.


## 2.2. Testing Scheme

### 2.2.1. Particle Size Distribution

The rock specimens are sandstone from the gob of Daizhuang coal mine, which is located near Jining city, Shandong Province, China. Some basic parameters are shown in Table1. Considering the scale effect, the ratio between the diameter of caved gangue specimen and the maximum particle size of caved gangue should be greater than or equal to 5 [40–42]. Because the internal diameter of testing chamber is 400 mm, the maximum particle size of caved gangue could be tested is 80 mm. In order to minimize the influence of size effect on the testing results, the maximum particle size of the caved gangue selected in the test is determined to be 40 mm. The caved gangue is divided into 7 categories by the particle size, which are 5–10 mm, 10–15 mm, 15–20 mm, 20–25 mm, 25–30 mm, 30–35 mm, and 35∼40 mm, as shown in Figure 4. In this article, the size distribution of caved gangue specimens for testing obeys the law of normal distribution. In a complete caved gangue specimen, according to the particle size of caved gangue from small to large, the mass fraction of 7 categories is 5%, 10%, 20%, 30%, 20%, 10%, and 5%, respectively, as shown in Figure 5. For the caved gangue with a certain particle size, the relation between the mass fraction and particle size is as follows:(1)A=4.885+329.27910.761π/2e−2D−22/10.7612,where A is the mass fraction of the caved gangue with a certain particle size (%) and D is the minimum of the caved gangue in a certain particle size (mm).Table 1
Basic parameters of sandstone.
Moisture conditionUniaxial compressive strength (MPa)Tensile strength (MPa)Modulus of elasticity (GPa)Poisson's ratioDensity (kg/m3)Moisture content (%)Dry96.787.516.10.1992565.60Water saturated87.217.215.20.2092578.80.516Figure 4
Caved gangue with different particle sizes.Figure 5
Mass fraction of 7 categories of caved gangue.The actual height of caved gangue specimen is 655 mm, and the total mass is 110 kg. The initial bulking factor of caved gangue specimen is 1.901, and the voidage is 0.901. The assembled caved gangue specimen is shown in Figure6.Figure 6
Assembled caved gangue.The initial bulking factor of caved gangue (K) is given by(2)K=V1V0,where K is the initial bulking factor of caved gangue, V0 is the volume of complete rock, and V1 is the volume of caved gangue produced by complete rock in the state of natural accumulation.The initial voidage of caved gangue (P) is given by(3)P=V1−V0V0=K−1,where P is the initial voidage of caved gangue.The residual height of caved gangue specimen after the bearing deformation testing (h1) is given by(4)h1=h0−u,where h1 is the residual height of caved gangue specimen after the bearing deformation testing (mm), h0 is the initial height of caved gangue specimen (mm), and u is the deformation of caved gangue specimen (mm).The residual bulking factor of caved gangue specimen after the bearing deformation testing (K1) is given by(5)K1=h1⋅SV0,where K1 is the residual bulking factor of caved gangue specimen after the bearing deformation testing and S is the area of testing chamber, 125600 mm2.


### 2.2.2. Load Method

The pressure acting on the caved gangue in gob is mainly from overlying strata. The pressure value is directly related to the height of the fractured overlying strata and increases with the increase in the height of the fractured overlying strata. In the time interval of two adjacent roof weightings, the pressure acting on the caved gangue in gob is basically unchanged, which is equal to the self-weight stress of total fractured overlying strata. During the roof weighting, the pressure acting on the caved gangue in gob will increase rapidly, and the increment is equal to the self-weight stress of generated fractured overlying strata. So the pressure acting on the caved gangue in gob is stair stepping, which provides evidence for designing the load method in the bearing deformation testing of caved gangue in gob. The load method is divided into 2 stages, namely, load stage and constant load stage. In load stage, the load speed is 0.5 kN/s. In constant load stage, the constant load is 100 kN, 200 kN, 300 kN, and 400 kN, respectively; the duration of each constant load is 4 hours. Before the formal testing, a preload of 20 kN is applied to the caved gangue in gob specimen until the deformation is constant, which needs about 15 minutes. The load method of a complete testing is shown as Figure7.Figure 7
Load method of a complete testing.


## 2.2.1. Particle Size Distribution

The rock specimens are sandstone from the gob of Daizhuang coal mine, which is located near Jining city, Shandong Province, China. Some basic parameters are shown in Table1. Considering the scale effect, the ratio between the diameter of caved gangue specimen and the maximum particle size of caved gangue should be greater than or equal to 5 [40–42]. Because the internal diameter of testing chamber is 400 mm, the maximum particle size of caved gangue could be tested is 80 mm. In order to minimize the influence of size effect on the testing results, the maximum particle size of the caved gangue selected in the test is determined to be 40 mm. The caved gangue is divided into 7 categories by the particle size, which are 5–10 mm, 10–15 mm, 15–20 mm, 20–25 mm, 25–30 mm, 30–35 mm, and 35∼40 mm, as shown in Figure 4. In this article, the size distribution of caved gangue specimens for testing obeys the law of normal distribution. In a complete caved gangue specimen, according to the particle size of caved gangue from small to large, the mass fraction of 7 categories is 5%, 10%, 20%, 30%, 20%, 10%, and 5%, respectively, as shown in Figure 5. For the caved gangue with a certain particle size, the relation between the mass fraction and particle size is as follows:(1)A=4.885+329.27910.761π/2e−2D−22/10.7612,where A is the mass fraction of the caved gangue with a certain particle size (%) and D is the minimum of the caved gangue in a certain particle size (mm).Table 1
Basic parameters of sandstone.
Moisture conditionUniaxial compressive strength (MPa)Tensile strength (MPa)Modulus of elasticity (GPa)Poisson's ratioDensity (kg/m3)Moisture content (%)Dry96.787.516.10.1992565.60Water saturated87.217.215.20.2092578.80.516Figure 4
Caved gangue with different particle sizes.Figure 5
Mass fraction of 7 categories of caved gangue.The actual height of caved gangue specimen is 655 mm, and the total mass is 110 kg. The initial bulking factor of caved gangue specimen is 1.901, and the voidage is 0.901. The assembled caved gangue specimen is shown in Figure6.Figure 6
Assembled caved gangue.The initial bulking factor of caved gangue (K) is given by(2)K=V1V0,where K is the initial bulking factor of caved gangue, V0 is the volume of complete rock, and V1 is the volume of caved gangue produced by complete rock in the state of natural accumulation.The initial voidage of caved gangue (P) is given by(3)P=V1−V0V0=K−1,where P is the initial voidage of caved gangue.The residual height of caved gangue specimen after the bearing deformation testing (h1) is given by(4)h1=h0−u,where h1 is the residual height of caved gangue specimen after the bearing deformation testing (mm), h0 is the initial height of caved gangue specimen (mm), and u is the deformation of caved gangue specimen (mm).The residual bulking factor of caved gangue specimen after the bearing deformation testing (K1) is given by(5)K1=h1⋅SV0,where K1 is the residual bulking factor of caved gangue specimen after the bearing deformation testing and S is the area of testing chamber, 125600 mm2.


## 2.2.2. Load Method

The pressure acting on the caved gangue in gob is mainly from overlying strata. The pressure value is directly related to the height of the fractured overlying strata and increases with the increase in the height of the fractured overlying strata. In the time interval of two adjacent roof weightings, the pressure acting on the caved gangue in gob is basically unchanged, which is equal to the self-weight stress of total fractured overlying strata. During the roof weighting, the pressure acting on the caved gangue in gob will increase rapidly, and the increment is equal to the self-weight stress of generated fractured overlying strata. So the pressure acting on the caved gangue in gob is stair stepping, which provides evidence for designing the load method in the bearing deformation testing of caved gangue in gob. The load method is divided into 2 stages, namely, load stage and constant load stage. In load stage, the load speed is 0.5 kN/s. In constant load stage, the constant load is 100 kN, 200 kN, 300 kN, and 400 kN, respectively; the duration of each constant load is 4 hours. Before the formal testing, a preload of 20 kN is applied to the caved gangue in gob specimen until the deformation is constant, which needs about 15 minutes. The load method of a complete testing is shown as Figure7.Figure 7
Load method of a complete testing.


## 3. Testing Results and Analysis

### 3.1. Bulking and Deformation Characteristics

The parameters of caved gangue specimens during different testing stage are shown in Table2. With the increase of axial load, the axial deformation of caved gangue specimen increases gradually, as shown in Figure 8(a). The final deformation of caved gangue specimen under dry condition and water-saturated condition is 74.07 mm and 91.00 mm, respectively, and the corresponding strain value is 113.1×10–3 and 138.9×10–3, respectively. The residual bulking factor of caved gangue specimen under dry condition and water-saturated condition decreases gradually, which changes from 1.901 to 1.686 and from 1.901 to 1.637, respectively, as shown in Figure 8(b). The axial deformation in load stage is more obvious than that in constant load stage, which accounts for 77.8% of total deformation under dry condition and 67.6% of total deformation under water-saturated condition. The testing results indicate that the water promotes the compressive strain of caved gangue specimen obviously.Table 2
Parameters of caved gangue specimens during different testing stage.
Moisture conditionTesting stageDeformationStrainResidual bulking factorInitial value (mm)Final value (mm)D-value (mm)Accumulated strain/10−3Fitting formula of strain-timeR-squareInitial valueFinal valueDry20–100 kN load020.8220.8231.8——1.9011.840100 kN constant load20.8223.012.1935.1ε=33.77+0.25lnt0.9821.8401.834100–200 kN load23.0138.3815.3758.6——1.8341.789200 kN constant load38.3842.233.8564.5ε=59.72+0.85lnt0.9701.7891.778200–300 kN load42.2354.4712.2483.2——1.7781.743300 kN constant load54.4759.675.2091.1ε=86.37+0.91lnt0.9731.7431.727300–400 kN load59.6768.889.21105.2——1.7271.701400 kN constant load68.8874.075.19113.1ε=109.90+0.59lnt0.9411.7011.686Water Saturated20–100 kN load021.2721.2732.5——1.9011.839100 kN constant load21.2725.304.0338.6ε=34.24+0.80lnt0.9961.8391.827100–200 kN load25.3045.1019.8068.9——1.8271.770200 kN constant load45.1053.198.0981.2ε=71.64+1.75lnt0.9951.7701.746200–300 kN load53.1964.2611.0798.1——1.7461.714300 kN constant load64.2672.618.35110.9ε=101.66+1.69lnt0.9951.7141.690300–400 kN load72.6181.759.14124.8——1.6901.663400 kN constant load81.7591.009.25138.9ε=128.63+1.92lnt0.9941.6631.637Notes:ε is the accumulated strain of caved gangue specimen, ×10−3, t is the hold time in each constant load stage, min.Figure 8
Axial deformation-time curve and bulking factor-time curve of caved gangue specimens. (a) Axial deformation-time curve. (b) Bulking factor-time curve.
(a)(b)In order to show the change of the axial deformation of the caved gangue specimens in constant load stage intuitively, the axial strain-time curves are made, as shown in Figure9. The fitting formulas of strain-time curves in different constant load stages are shown in Table 2. The relationship between strain and time meets the logarithmic relationship. The R-square of each fitting formula is greater than 0.94. In the early stage, the axial strain increases rapidly, then becomes gently. In the late stage, the axial strain is unchanged basically.Figure 9
Strain-time curve of caved gangue specimens in constant load stage. (a) 100kN constant load (dry). (b) 200kN constant load (dry). (c) 300kN constant load (dry). (d) 400kN constant load (dry). (e) 100kN constant load (water saturated). (f) 200kN constant load (water -saturated). (g) 300kN constant load (water saturated). (h) 400kN constant load (water saturated).
(a)(b)(c)(d)(e)(f)(g)(h)The strain D-values of the caved gangue specimens in different stages are shown in Figure10.(1)
In load stage: From 20 kN to 100 kN, the axial strain D-value is 31.8×10−3and 32.5 × 10−3, respectively, under dry condition and water-saturated condition, which are equal basically and indicate that the water has no effect on the compressive strain of caved gangue specimen. From 100 kN to 200 kN, the axial strain D-value under water-saturated condition is 6.7 × 10−3 greater than that in dry condition, which indicates that the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. From 200 kN to 300 kN, the axial strain D-value under dry condition and water-saturated condition is 18.7 × 10−3 and 16.9 × 10−3, respectively; the latter is less than the former, which is because the previous accumulated strain under water-saturated condition is greater than that under dry condition, and is 81.2 × 10−3 and 64.5 × 10−3, respectively. From 300 kN to 400 kN, the axial strain D-value is 14.1×10−3and 14.0 × 10−3, respectively, under dry condition and water-saturated condition, which are equal basically.(2)
In constant load stage: In 4 constant load stages, the axial strain D-values under water-saturated condition are all greater than these under dry condition. According to the load from small to large, the increment of the axial strain D-values is 2.8 × 10−3, 6.5 × 10−3, 4.8 × 10−3 and 6.2 × 10−3, which indicates that the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. Meanwhile, the water acting as the softening agent reduces the strength of the rock block and is conducive to the crushing of the rock block. The newborn rock blocks may slip and fill the gap between rock blocks, which also promotes the compressive strain of caved gangue specimen. It is worth noting that the crushing of the rock blocks will appear only when the crushing stress is greater than the strength.Figure 10
Strain D-values of the caved gangue specimens in different stages. (a) Different load stages. (b) Different constant load stages.
(a)(b)


### 3.2. Particle Size Distribution Characteristics

After the testing, the caved gangue specimens under dry condition and water-saturated condition are screened and weighed again. The changes of mass fraction of caved gangue with different particle sizes are shown in Table3 and Figure 11. Under dry condition and water-saturated condition, the mass fraction of caved gangue with the particle size of 0-5 mm increases by 5.25% and 5.85%, respectively, while the particle size of 5–10 mm increases by 2.46% and 3.09%, respectively. The mass fraction of caved gangue blocks with the particle size of 10–20 mm is basically unchanged, so the particle size of 10–20 mm can be defined as the stable particle size. It does not mean that the load has no effect on the caved gangue blocks with the particle size of 10–20 mm because some caved gangue blocks have obvious new fracture marks after rescreening, which indicates that the mass fraction of caved gangue blocks with the particle size of 10–20 mm is dynamically stabilized, that is, the weight of newborn caved gangue blocks is basically equal to the weight of diminished caved gangue blocks. Under dry condition and water-saturated condition, the mass fraction of caved gangue with the particle size of 20–25 mm decreases by 3.19% and 3.32%, respectively, while the particle size of 25–30 mm decreases by 3.65% and 4.95%, respectively, and the particle size of 30–35 mm decreases by 0.98% and 1.14%, respectively. The mass fraction of caved gangue with the particle size of 35–40 mm is unchanged basically. The particle size distribution of caved gangue specimen provide a strong evidence that many rock blocks are broken into smaller blocks during testing.Table 3
Changes of mass fraction of caved gangue with different particle sizes before and after the testing.
Particle sizeMass fraction (%)DryWater-saturatedBefore testingAfter testingD-valueBefore testingAfter testingD-value0–505.255.2505.855.855–1057.462.4658.093.0910–151010.210.211010.430.4315–202020.080.082020.250.2520–253026.81-3.193026.68-3.3225–302016.35-3.652015.05-4.9530–35109.02-0.98108.86-1.1435–4054.82-0.1854.78-0.22Figure 11
Curves of mass fraction of caved gangue with different particle sizes before and after the testing.


### 3.3. Bearing Deformation Mechanism

During the bearing deformation testing of the caved gangue specimen, there will be a greater frictional force between the inner wall of testing chamber and the caved gangue specimen, which weakens the transfer of axial stress, so the pressure acting on these caved gangue blocks near the bottom of testing chamber is less than that near the top of testing chamber [43]. Because the diameter and height of the caved gangue specimen are 400 mm and 655 mm, respectively, the specimen is narrow and high. The distribution of compressive stress is shown in Figure 12.Figure 12
Compressive stress distribution of side wall and bottom of caved gangue specimen.The compressive stress of side wall of caved gangue specimen (σb) is given by(6)σb=ρgAμL1−1eμLn′h/A,where σb is the compressive stress of side wall of caved gangue specimen, ρ is the density of caved gangue, g is the gravitational acceleration, μ is the frictional factor between the inner wall of testing chamber and the caved gangue specimen, n′ is the specific value of lateral compressive stress and average vertical compressive stress, n′=σb/σcp, σcp is the average vertical compressive stress, A is the bottom area of caved gangue specimen, L is the perimeter of caved gangue specimen, and h is the height of caved gangue specimen.The vertical compressive stress of caved gangue specimen (σ) is given by(7)σ=σb1+2μ02+21+μ02μ02−μ24x2b2,where μ0 is the internal friction coefficient of caved gangue specimen μ0=tanφ, φ is the deflection angle of principal axis in the polar stress diagram near the side surface of caved gangue specimen, b is the diameter of caved gangue specimen, and x is the distance between the calculation point of vertical compressive stress value and the center of caved gangue specimen.Caved gangue in gob is noncohesive materials and their particles are generally of convex polyhedron shape. The contact between particles can be categorized as angle to face contact and angle to angle contact [44, 45]. A single rock block represented by letter “j” is taken as the object of study, assuming that there are n contacts between rock block “j” and other rock blocks in the caved gangue specimen. Under load, the force and contact area of the ith contact are Pi and δi, respectively (i = 1, 2, …, n). If there are m contacts on one contact surface labeled “A” of rock block “j”, then m ≤ n, as shown in Figure 13.Figure 13
Acting force on the certain contact surface A of rock block j.The normal stress (σA) and shear stress (τA) acting on the contact surface labeled “A” are given by(8)σA=∑i=1mσi==∑i=1mPiδicosαiτA=∑i=1mτi=∑i=1mPiδisinαi,where αi is the angle of intersection of normal of contact surface and acting force.As a whole, the total normal stress acting on the rock block manifests as compressive stress, which is less than the crushing strength (σs) of rock block in the general case; therefore, there will be no crushing between rock blocks. But for some weakness planes, the crushing strength (σsm) is less than the bearing stress (σim). Assuming that a total of K weakness planes will be crushed into smaller blocks.(9)σimk≥σsmkk=1,2…K.The total of strain (ε1) caused by crushing of weakness planes is given by(10)ε1=∑k=1K∫σimk−σsmkdζk,where ζk is equal to the ratio of strain to crushing stress.In addition, the shear stress will form the tangential stress (τk) on the surface of rock block “j”. But because the contact area is very small, the tangential stress is approximated as a uniform distribution. On the kth contact surface, the moment (Tk) about the barycenter of rock block “j” produced by tangential stress is given by(11)Tk=τk⋅rk⋅δk,where rk is the distance between the kth contact surface and the barycenter of rock block “j”.Around the barycenter of rock block “j”, a local coordinate (ξ-η plane) is created, the sum of tangential stress moment vector is given by(12)Tmξ=∑k=1KTkξk=∑k=1KPksinαkrkξkTmη=∑k=1KTkηk=∑k=1KPksinαkrkηk,where ξk and ηk are the projection coefficients of the local coordinate, which are equal to the ratio of projection value to original value of all shear stress, respectively.Under the action of moments, the newborn small rock blocks will slide and fill the gap between rock blocks, and the resulting strain (ε2) is given by(13)ε2=∑k=1K∫Tkξkdθξk+ηkdθηk,where θξ and θη are the compliance in shear, which are equal to the ratio of strain to shear stress.So, during the bearing deformation testing of the caved gangue specimen, the plastic deformation (ε) is given by(14)ε=ε1+ε2=∑k=1K∫σimk−σsmkdζk+∑k=1K∫Tkξkdθξk+ηkdθηk.It can be seen from the order of magnitude of the strain thatε2 is greater than ε1, so the deformation caused by slipping and filling the gap between rock blocks is greater than that caused by the crushing of weakness planes of rock blocks. That is, the major cause of bearing deformation of the caved gangue specimen is that the newborn small rock blocks slip and fill the gap between rock blocks.The bearing deformation of the caved gangue specimen can be divided into two stages: instantaneous compression deformation and long-term deformation. (1) Instantaneous compression deformation: As the increase of load, the caved gangue specimen becomes compacted gradually. The axial deformation in load stage is more obvious than that in constant load stage, which accounts for 77.8% of total deformation under dry condition, and 67.6% of total deformation under water-saturated condition, the time of load stage is short, the axial deformation will stop basically with the stop of load, but it is inadequate and only relatively stable. The contact between caved gangue blocks is brittle-elastic, the changes of caved gangue blocks mainly include crushing, slipping, and filling, which is more and more prominent with the increase of load. (2) Long-term deformation: In constant load stage, the impacted crushing of caved gangue is over, but the redistribution of stress between rock blocks will also lead to the crushing of weakness planes of rock blocks, causing the slipping and filling. Under dry condition, the axial deformation in constant load stage accounts for 22.2% of total deformation, and under water-saturated condition, the axial deformation in constant load stage accounts for 32.4% of total deformation. By comparison, the water promotes the compressive strain of caved gangue specimen obviously, especially in constant load stage. The bulk strain of the caved gangue mass is controlled by the rock particle rearrangement, including rotation and slipping between each rock block, and the bulk deformation of a single caved gangue block.


## 3.1. Bulking and Deformation Characteristics

The parameters of caved gangue specimens during different testing stage are shown in Table2. With the increase of axial load, the axial deformation of caved gangue specimen increases gradually, as shown in Figure 8(a). The final deformation of caved gangue specimen under dry condition and water-saturated condition is 74.07 mm and 91.00 mm, respectively, and the corresponding strain value is 113.1×10–3 and 138.9×10–3, respectively. The residual bulking factor of caved gangue specimen under dry condition and water-saturated condition decreases gradually, which changes from 1.901 to 1.686 and from 1.901 to 1.637, respectively, as shown in Figure 8(b). The axial deformation in load stage is more obvious than that in constant load stage, which accounts for 77.8% of total deformation under dry condition and 67.6% of total deformation under water-saturated condition. The testing results indicate that the water promotes the compressive strain of caved gangue specimen obviously.Table 2
Parameters of caved gangue specimens during different testing stage.
Moisture conditionTesting stageDeformationStrainResidual bulking factorInitial value (mm)Final value (mm)D-value (mm)Accumulated strain/10−3Fitting formula of strain-timeR-squareInitial valueFinal valueDry20–100 kN load020.8220.8231.8——1.9011.840100 kN constant load20.8223.012.1935.1ε=33.77+0.25lnt0.9821.8401.834100–200 kN load23.0138.3815.3758.6——1.8341.789200 kN constant load38.3842.233.8564.5ε=59.72+0.85lnt0.9701.7891.778200–300 kN load42.2354.4712.2483.2——1.7781.743300 kN constant load54.4759.675.2091.1ε=86.37+0.91lnt0.9731.7431.727300–400 kN load59.6768.889.21105.2——1.7271.701400 kN constant load68.8874.075.19113.1ε=109.90+0.59lnt0.9411.7011.686Water Saturated20–100 kN load021.2721.2732.5——1.9011.839100 kN constant load21.2725.304.0338.6ε=34.24+0.80lnt0.9961.8391.827100–200 kN load25.3045.1019.8068.9——1.8271.770200 kN constant load45.1053.198.0981.2ε=71.64+1.75lnt0.9951.7701.746200–300 kN load53.1964.2611.0798.1——1.7461.714300 kN constant load64.2672.618.35110.9ε=101.66+1.69lnt0.9951.7141.690300–400 kN load72.6181.759.14124.8——1.6901.663400 kN constant load81.7591.009.25138.9ε=128.63+1.92lnt0.9941.6631.637Notes:ε is the accumulated strain of caved gangue specimen, ×10−3, t is the hold time in each constant load stage, min.Figure 8
Axial deformation-time curve and bulking factor-time curve of caved gangue specimens. (a) Axial deformation-time curve. (b) Bulking factor-time curve.
(a)(b)In order to show the change of the axial deformation of the caved gangue specimens in constant load stage intuitively, the axial strain-time curves are made, as shown in Figure9. The fitting formulas of strain-time curves in different constant load stages are shown in Table 2. The relationship between strain and time meets the logarithmic relationship. The R-square of each fitting formula is greater than 0.94. In the early stage, the axial strain increases rapidly, then becomes gently. In the late stage, the axial strain is unchanged basically.Figure 9
Strain-time curve of caved gangue specimens in constant load stage. (a) 100kN constant load (dry). (b) 200kN constant load (dry). (c) 300kN constant load (dry). (d) 400kN constant load (dry). (e) 100kN constant load (water saturated). (f) 200kN constant load (water -saturated). (g) 300kN constant load (water saturated). (h) 400kN constant load (water saturated).
(a)(b)(c)(d)(e)(f)(g)(h)The strain D-values of the caved gangue specimens in different stages are shown in Figure10.(1)
In load stage: From 20 kN to 100 kN, the axial strain D-value is 31.8×10−3and 32.5 × 10−3, respectively, under dry condition and water-saturated condition, which are equal basically and indicate that the water has no effect on the compressive strain of caved gangue specimen. From 100 kN to 200 kN, the axial strain D-value under water-saturated condition is 6.7 × 10−3 greater than that in dry condition, which indicates that the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. From 200 kN to 300 kN, the axial strain D-value under dry condition and water-saturated condition is 18.7 × 10−3 and 16.9 × 10−3, respectively; the latter is less than the former, which is because the previous accumulated strain under water-saturated condition is greater than that under dry condition, and is 81.2 × 10−3 and 64.5 × 10−3, respectively. From 300 kN to 400 kN, the axial strain D-value is 14.1×10−3and 14.0 × 10−3, respectively, under dry condition and water-saturated condition, which are equal basically.(2)
In constant load stage: In 4 constant load stages, the axial strain D-values under water-saturated condition are all greater than these under dry condition. According to the load from small to large, the increment of the axial strain D-values is 2.8 × 10−3, 6.5 × 10−3, 4.8 × 10−3 and 6.2 × 10−3, which indicates that the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. Meanwhile, the water acting as the softening agent reduces the strength of the rock block and is conducive to the crushing of the rock block. The newborn rock blocks may slip and fill the gap between rock blocks, which also promotes the compressive strain of caved gangue specimen. It is worth noting that the crushing of the rock blocks will appear only when the crushing stress is greater than the strength.Figure 10
Strain D-values of the caved gangue specimens in different stages. (a) Different load stages. (b) Different constant load stages.
(a)(b)


## 3.2. Particle Size Distribution Characteristics

After the testing, the caved gangue specimens under dry condition and water-saturated condition are screened and weighed again. The changes of mass fraction of caved gangue with different particle sizes are shown in Table3 and Figure 11. Under dry condition and water-saturated condition, the mass fraction of caved gangue with the particle size of 0-5 mm increases by 5.25% and 5.85%, respectively, while the particle size of 5–10 mm increases by 2.46% and 3.09%, respectively. The mass fraction of caved gangue blocks with the particle size of 10–20 mm is basically unchanged, so the particle size of 10–20 mm can be defined as the stable particle size. It does not mean that the load has no effect on the caved gangue blocks with the particle size of 10–20 mm because some caved gangue blocks have obvious new fracture marks after rescreening, which indicates that the mass fraction of caved gangue blocks with the particle size of 10–20 mm is dynamically stabilized, that is, the weight of newborn caved gangue blocks is basically equal to the weight of diminished caved gangue blocks. Under dry condition and water-saturated condition, the mass fraction of caved gangue with the particle size of 20–25 mm decreases by 3.19% and 3.32%, respectively, while the particle size of 25–30 mm decreases by 3.65% and 4.95%, respectively, and the particle size of 30–35 mm decreases by 0.98% and 1.14%, respectively. The mass fraction of caved gangue with the particle size of 35–40 mm is unchanged basically. The particle size distribution of caved gangue specimen provide a strong evidence that many rock blocks are broken into smaller blocks during testing.Table 3
Changes of mass fraction of caved gangue with different particle sizes before and after the testing.
Particle sizeMass fraction (%)DryWater-saturatedBefore testingAfter testingD-valueBefore testingAfter testingD-value0–505.255.2505.855.855–1057.462.4658.093.0910–151010.210.211010.430.4315–202020.080.082020.250.2520–253026.81-3.193026.68-3.3225–302016.35-3.652015.05-4.9530–35109.02-0.98108.86-1.1435–4054.82-0.1854.78-0.22Figure 11
Curves of mass fraction of caved gangue with different particle sizes before and after the testing.


## 3.3. Bearing Deformation Mechanism

During the bearing deformation testing of the caved gangue specimen, there will be a greater frictional force between the inner wall of testing chamber and the caved gangue specimen, which weakens the transfer of axial stress, so the pressure acting on these caved gangue blocks near the bottom of testing chamber is less than that near the top of testing chamber [43]. Because the diameter and height of the caved gangue specimen are 400 mm and 655 mm, respectively, the specimen is narrow and high. The distribution of compressive stress is shown in Figure 12.Figure 12
Compressive stress distribution of side wall and bottom of caved gangue specimen.The compressive stress of side wall of caved gangue specimen (σb) is given by(6)σb=ρgAμL1−1eμLn′h/A,where σb is the compressive stress of side wall of caved gangue specimen, ρ is the density of caved gangue, g is the gravitational acceleration, μ is the frictional factor between the inner wall of testing chamber and the caved gangue specimen, n′ is the specific value of lateral compressive stress and average vertical compressive stress, n′=σb/σcp, σcp is the average vertical compressive stress, A is the bottom area of caved gangue specimen, L is the perimeter of caved gangue specimen, and h is the height of caved gangue specimen.The vertical compressive stress of caved gangue specimen (σ) is given by(7)σ=σb1+2μ02+21+μ02μ02−μ24x2b2,where μ0 is the internal friction coefficient of caved gangue specimen μ0=tanφ, φ is the deflection angle of principal axis in the polar stress diagram near the side surface of caved gangue specimen, b is the diameter of caved gangue specimen, and x is the distance between the calculation point of vertical compressive stress value and the center of caved gangue specimen.Caved gangue in gob is noncohesive materials and their particles are generally of convex polyhedron shape. The contact between particles can be categorized as angle to face contact and angle to angle contact [44, 45]. A single rock block represented by letter “j” is taken as the object of study, assuming that there are n contacts between rock block “j” and other rock blocks in the caved gangue specimen. Under load, the force and contact area of the ith contact are Pi and δi, respectively (i = 1, 2, …, n). If there are m contacts on one contact surface labeled “A” of rock block “j”, then m ≤ n, as shown in Figure 13.Figure 13
Acting force on the certain contact surface A of rock block j.The normal stress (σA) and shear stress (τA) acting on the contact surface labeled “A” are given by(8)σA=∑i=1mσi==∑i=1mPiδicosαiτA=∑i=1mτi=∑i=1mPiδisinαi,where αi is the angle of intersection of normal of contact surface and acting force.As a whole, the total normal stress acting on the rock block manifests as compressive stress, which is less than the crushing strength (σs) of rock block in the general case; therefore, there will be no crushing between rock blocks. But for some weakness planes, the crushing strength (σsm) is less than the bearing stress (σim). Assuming that a total of K weakness planes will be crushed into smaller blocks.(9)σimk≥σsmkk=1,2…K.The total of strain (ε1) caused by crushing of weakness planes is given by(10)ε1=∑k=1K∫σimk−σsmkdζk,where ζk is equal to the ratio of strain to crushing stress.In addition, the shear stress will form the tangential stress (τk) on the surface of rock block “j”. But because the contact area is very small, the tangential stress is approximated as a uniform distribution. On the kth contact surface, the moment (Tk) about the barycenter of rock block “j” produced by tangential stress is given by(11)Tk=τk⋅rk⋅δk,where rk is the distance between the kth contact surface and the barycenter of rock block “j”.Around the barycenter of rock block “j”, a local coordinate (ξ-η plane) is created, the sum of tangential stress moment vector is given by(12)Tmξ=∑k=1KTkξk=∑k=1KPksinαkrkξkTmη=∑k=1KTkηk=∑k=1KPksinαkrkηk,where ξk and ηk are the projection coefficients of the local coordinate, which are equal to the ratio of projection value to original value of all shear stress, respectively.Under the action of moments, the newborn small rock blocks will slide and fill the gap between rock blocks, and the resulting strain (ε2) is given by(13)ε2=∑k=1K∫Tkξkdθξk+ηkdθηk,where θξ and θη are the compliance in shear, which are equal to the ratio of strain to shear stress.So, during the bearing deformation testing of the caved gangue specimen, the plastic deformation (ε) is given by(14)ε=ε1+ε2=∑k=1K∫σimk−σsmkdζk+∑k=1K∫Tkξkdθξk+ηkdθηk.It can be seen from the order of magnitude of the strain thatε2 is greater than ε1, so the deformation caused by slipping and filling the gap between rock blocks is greater than that caused by the crushing of weakness planes of rock blocks. That is, the major cause of bearing deformation of the caved gangue specimen is that the newborn small rock blocks slip and fill the gap between rock blocks.The bearing deformation of the caved gangue specimen can be divided into two stages: instantaneous compression deformation and long-term deformation. (1) Instantaneous compression deformation: As the increase of load, the caved gangue specimen becomes compacted gradually. The axial deformation in load stage is more obvious than that in constant load stage, which accounts for 77.8% of total deformation under dry condition, and 67.6% of total deformation under water-saturated condition, the time of load stage is short, the axial deformation will stop basically with the stop of load, but it is inadequate and only relatively stable. The contact between caved gangue blocks is brittle-elastic, the changes of caved gangue blocks mainly include crushing, slipping, and filling, which is more and more prominent with the increase of load. (2) Long-term deformation: In constant load stage, the impacted crushing of caved gangue is over, but the redistribution of stress between rock blocks will also lead to the crushing of weakness planes of rock blocks, causing the slipping and filling. Under dry condition, the axial deformation in constant load stage accounts for 22.2% of total deformation, and under water-saturated condition, the axial deformation in constant load stage accounts for 32.4% of total deformation. By comparison, the water promotes the compressive strain of caved gangue specimen obviously, especially in constant load stage. The bulk strain of the caved gangue mass is controlled by the rock particle rearrangement, including rotation and slipping between each rock block, and the bulk deformation of a single caved gangue block.


## 4. Conclusion

(1)
The testing system used for bearing deformation testing of caved gangue is developed, which is consisted of load support bracket, load head, testing chamber, servo control system of displacement and load, servo control system of water pressure and water yield, and operating deck. In view of the particle size distribution characteristics and stress state of caved gangue, the size distribution of caved gangue obeys the law of normal distribution, and the load pattern is designed to step load.(2)
With the increase of axial load, the axial deformation of caved gangue increases gradually, the residual bulking coefficient decreases gradually, which are more obvious in load stage than in constant load stage. In the early constant load stage, the axial deformation of caved gangue grows rapidly, then tends to be slow and steady gradually; the relationship between strain and time meets the logarithmic relationship. In load stage, the D-value of axial strain decreases gradually along with the increase of axial load, and in constant load stage, which is opposite.(3)
The bearing deformation of caved gangue is consisted of two parts: instantaneous compression deformation and long-term deformation. For instantaneous compression deformation, the water acting as the lubricant promotes the compressive strain of caved gangue specimen and is conducive to rotation and slipping between each rock block. For long-term deformation, meanwhile, the water acting as the softening agent reduces the strength of the rock block and is conducive to the crushing of the rock block. The newborn rock blocks may slip and fill the gap between rock blocks, which also promotes the compressive strain of caved gangue specimen. The research results have important significance for forecasting and controlling the movement and deformation of overlying strata caused by mining.



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*Source: 6888916-2022-04-15.xml*