
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13617-1
10.1016/j.heliyon.2024.e37586
e37586
Research Article
Energy dissipation damage constitutive relation of CFRP passively confined coal sample
Li Qingwen tmxylqw2017@lnut.edu.cn
a⁎
Nie Fanfan a
Pan Chuangchuang a
Li Ling a
Zhong Yuqi a
Yu Mengmeng ab
Yang Hao a
a School of Civil and Architectural Engineering, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China
b School of Water Resources and Hydropower Engineering, North China Electric Power University, Beijing 102206, China
⁎ Corresponding author. tmxylqw2017@lnut.edu.cn
13 9 2024
30 9 2024
13 9 2024
10 18 e375864 6 2024
17 8 2024
5 9 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
In view of the stability problem of coal pillars left over during coal resource mining, (Carbon Fiber Reinforced Polymer) CFRP sheet is applied in coal pillar reinforcement. Uniaxial compression tests of CFRP passively confined coal samples are carried out to explore the mechanical response mechanism of passively confined coal samples under different layers, and the energy dissipation damage constitutive relationship of CFRP passively confined coal samples is established based on the energy dissipation principle. The conclusions are: As CFRP layers increased, the local damage of coal samples before the peak evolved from a 'cliff-like jagged' to a 'capillary jagged', with post-peak instability marked by a shift to more 'cliff-like' characteristics. The tests revealed improvements in peak strength and elastic modulus, with a defined functional relationship between these properties and CFRP layers. The energy storage capacity of passively confined coal samples improved with CFRP layers, requiring less axial deformation to achieve equivalent energy levels. The energy dissipation rate showed an initial decrease followed by an increase, with a minimum inflection point, the elastic energy consumption ratio tends to decrease slowly and then rapidly during post-peak instability. A damage constitutive relationship and evolution equation were developed, highlighting that the CFRP sheet significantly inhibits damage, with diminishing effectiveness beyond two layers. The study concludes that three-layer CFRP sheets provide optimal confinement, offering a novel strategy for the reinforcement of coal pillars and the prevention and control of rock burst, without considering the actual coal pillar dimensions and shape. To sum up, the use of CFRP sheet to strengthen coal pillar has considerable potential research value in strengthening coal pillar and improving the recovery rate of coal resources.

Keywords

Passive confinement
Coal
CFRP sheets
Energy dissipation damage
Constitutive relation
Uniaxial compression
Optimal layers
==== Body
pmc1 Introduction

To improve the recovery rate of coal resources in mines safely and efficiently, the technology of gob-side entry driving with small coal pillars has been widely promoted and applied to the support of underground engineering structures [1]. Coal pillars are underground engineering support structures commonly used in the underground mining of coal resources. Apart from carrying the load of the overlying rock strata, coal pillars were also eroded by the complex geological environment underground, which resulted in the instability of coal pillars and the redistribution of stresses in the overlying rock strata. If the coal pillar is not pre-stabilized, it will collapse similarly to the 'butterfly effect' once it is destabilized, resulting in serious mine disasters such as nonuniform settlement or rock burst [[2], [3], [4], [5], [6]].

The coal pillar is the only fundamental component of an underground engineering structure under a one-way stress state. At present, scholars have carried out substantial work and accumulated significant research results for its reinforcement problem. Zhang et al. [7] prepared φ50 mm × 100 mm standard specimens using sprayed concrete-wrapped coal samples to carry out uniaxial compression tests. It was found that the stress-strain curves showed bimodal characteristics and that the maximum bearing capacity was closely related to the radius ratio and the ratio of elasticity modulus; Wang et al. [8] performed uniaxial compression fine-scale simulations using standard specimens of paste-filled wrapped rocks and found that the peak strength increased with the increase in the diameter of the rock column; Yu et al. [9] carried out a uniaxial compression test on the standard specimen of an anchored inclined coal-rock combination and discussed the influence of bolt anchorage angle on the strength change of the coal-rock combination. Wang et al. [10] and Zhang et al. [11] carried out uniaxial compression tests for anchored sandstone and anchored fractured rock standard specimens, respectively, and found that the diameter of the anchor rod influenced the elasticity modulus and strength of brittle rock, yet the thicker the rod diameter, the better the anchoring effect, and established a linear relationship between the peak strength of the anchored fractured standard specimens; Wang et al. [12] developed uniaxial compression test through standard specimens of broken coal samples with different particle sizes, discovering that its compressive strength decreased and then increased with the increase of particle size, which was opposite to the correlation of water-cement ratio. Accordingly, drawing the experience of successful application of carbon fiber reinforced polymer (CFRP) sheets to reinforced engineering structures in the field of civil engineering, CFRP sheet has the advantages of being lightweight, high strength, corrosion resistant, easy to form any shape and simple construction [[13], [14], [15], [16], [17], [18]]. Das et al. [19] pioneered the use of CFRP sheet uniformly wrapped standard coal cylinder specimens to conduct uniaxial compression test, making full use of the passive lateral confining force provided by CFRP sheet to change from a unidirectional stress state to a three-way stress state, to achieve the effect of reinforcement. The results of the indoor test and numerical simulation indicated that the bearing efficiency and energy absorption level of CFRP sheet to coal is highly improved and exhibited some potential research value in reducing the size of the coal pillar, improving the recovery rate of the reserved coal pillar, and reinforcing coal pillar. Liu et al. [20], Li et al. [21,22], Xia et al. [23] and Shi et al. [24] have also carried out related research work on the standard specimen of small coal cylinder with uniformly wrapped of CFRP sheet. Most of them focus on the failure mode and mechanical properties of coal, while research on the constitutive relationship of energy dissipation damage is relatively rare.Nomenclature

Abbreviations	
	CFRP		Carbon fiber reinforced polymer	
	ISRM		International Society for Rock Mechanics and Rock Engineering	
	UCC		Unconfined coal samples	
	CFC		CFRP passively confined coal samples	
Variables	
	L		CFRP layers	
	εCFRP		the tensile strain of CFRP sheet, 10−2	
	σ1		the axial stress, MPa	
	ε1		the axial strain,10−3	
	σP		the peak strength, MPa	
	R2		fitting accuracy	
	δ		relative strength enhance ratio	
	E		the elastic modulus, GPa	
	ΔE		the elastic modulus increment, GPa	
	εh,p		the peak hoop strain, 10−3	
	U		the total energy, MJ·m−3	
	Ud		the dissipation energy, MJ·m−3	
	Ue		the elastic energy, MJ·m−3	
	εe		elastic strain in the axial stress direction	
	σ1i		the stress value at each point in the axial stress-strain curve, MPa	
	ε1i		the strain value at each point in the axial stress-strain curve, %	
	ηd		the variation of energy dissipation rate of	
	K		the elastic energy consumption ratio	
	σA		the axial stress at point A, MPa	
	εA		the axial strain at point A, %	
	D		the damage of CFRP passively confined coal samples	
	A		the nominal bearing area	
	A'		the effective bearing area	
	F		the loading on the passively confined coal samples	
	σ		the nominal stress	
	σ′		the effective stress	
	P		the probability density function of the micrometric damage	
	k		the scale parameters	
	m		the shape parameters	
	UAd		the dissipation energy corresponding to point A of the compaction section of the stress-strain curve in Fig. 6.	
	n		the number of microelement damages	
	N		the total microelements	
	ζL		the average damage rate	
	ΔζL		the increment of damage rate	

For that, the author will take the CFRP sheet layers as the variable, and develop the uniaxial compression test of CFRP sheet passively confined standard coal samples as the research object to analyze its mechanical properties. Based on the principle of energy dissipation, the energy dissipation damage constitutive relationship of coal samples confined by different CFRP layers was constructed to explore the influence of the CFRP layers on the energy dissipation damage evolution of coal samples. The research results can provide new ideas for the reinforcement of coal pillars with impact tendency.

2 Test summary

2.1 Preparation of coal samples

The coal samples used in the test were all taken from a working face of the Tashan Coal Mine of Tong Coal Group. According to the method recommended by the International Society for Rock Mechanics and Rock Engineering (ISRM), the larger coal blocks were processed into standard coal cylinders 50 mm in diameter and 100 mm in height. To ensure that the non-parallelism and non-perpendicularity of the two ends of the coal cylinder are lower than 0.02 mm, the coal samples are processed as vertically as possible in the bedding direction for core drilling. The prepared standard coal cylindrical specimens are shown in Fig. 1.Fig. 1 Standard coal samples.

Fig. 1

The KON-NM-4A non-metal ultrasonic detector of Beijing Konkorui has measured the p-wave velocity of the coal samples from 1600 m/s to 2800 m/s, with an average of 2214 m/s; the density of the coal samples ranges from 1.4 g/cm3 to 1.6 g/cm3, with an average value of 1.474 g/cm3. Aiming to decrease the influence of non-homogeneity of coal on the test results as much as possible, nine standard coal cylinders were finally selected as the test coal samples from the prepared coal samples with the principle of screening close to the average density and the average wave velocity (Fig. 2).Fig. 2 Screening of coal samples.

Fig. 2

2.2 CFRP fabric material properties

The fiber used in the test was Ruilix unidirectional carbon fiber, and the material properties were tested according to the test method for tensile properties of orientation fiber reinforced polymer matrix composite materials [25], produced seven CFRP strips with specifications of 250 mm × 25 mm × 0.167 mm (length × width × thickness), and tested the tensile

mechanical properties of the CFRP sheet using the WDW-300 microcomputer-controlled electronic universal testing machine, with the loading rate setting at 2 mm/min. The test results are presented in Fig. 3. It can be calculated that the average value of tensile strength of CFRP material is 918.07 MPa, the average value of tensile strain is 1.94 %, and the average value of elastic modulus is 47.54 GPa.Fig. 3 Tensile load-strain curves of CFRP coupons [21].

Fig. 3

2.3 Test scheme

Nine standard coal cylindrical specimens were divided into four groups, including one group of unconfined coal samples and three groups of fully confined coal samples with CFRP sheets considering the CFRP layers ranging from 1 layer to 3 layer. The specific test design scheme is given in Table 1. The coal sample number 'UCC' in Table 1 indicates the unconfined group, including three coal samples; 'CFC-2-C' indicates the fully confined group, the first three letters are the CFRP sheet confinement, followed by the first Arabian numeral is the layers, and the last letter is the coal sample. For example, “CFC-2-C″ is a 2-layer CFRP sheet fully confined coal sample.Table 1 Test scheme of CFRP-confined coal samples.

Table 1Coal sample number	CFRP layers L	Loading rate
/(mm·min−1)	Numbers	
UCC	0	0.12	3	
CFC-1-C	1	0.12	3	
CFC-2-C	2	0.12	3	
CFC-3-C	3	0.12	3	

Based on the test scheme in Table 1, the process of preparing CFRP confined coal samples is shown in Fig. 4, which borrows from Ref. [21], and its main procedures are as follows.(1) First, the height and length of the CFRP fabric were determined and trimmed for spare as shown in Fig. 4(a). The length of the CFRP sheet is taken according to the formula given in Ref. [21], and the width is the height of the coal sample H = 100 mm, namely, the length of the 1-layer CFRP sheet is 207.08 mm, the length of the 2-layer CFRP sheet is 364.16 mm, and the length of the 3-layer CFRP sheet is 521.24 mm. The lengths of the CFRP sheet include an overlap of 50 mm to ensure that the overlap zone of the CFRP-confined coal sample will not be damaged.

(2) Wipe and clean the surface of the coal sample with acetone and mark the starting point of the CFRP paste, as shown in Fig. 4 (b).

(3) Place the required small-size CFRP sheet in a flat position and apply an appropriate amount of impregnating adhesive uniformly on both sides of it, so that all of it is impregnated by the adhesive, as shown in Fig. 4(c).

(4) Align one end of the CFRP sheet with the marked starting point of adhesion, then slowly rotate the coal sample in the direction of wrapping, wrapping the CFRP sheet around the coal sample, and press firmly to make the glue between the coal sample and the CFRP sheets permeate out to ensure that the sidewall of the coal sample and the CFRP sheet have closely adhered to each other. In this process, the CFRP-wrapped coal sample was repeatedly scraped with a plastic scraper to remove the air bubbles, so that the two were sufficiently tightly adhered to each other, as shown in Fig. 4(d).

(5) The tightly wound CFRP sheet fully confined coal samples were placed in a ventilated place for resting, as shown in Fig. 4(e), and maintained in a laboratory environment for a 28d restoration period.

Fig. 4 The preparation of CFRP confined coal samples.

Fig. 4

2.4 Test setup

The test loading device adopts SAM-2000 microcomputer-controlled electro-hydraulic servo rock testing machine produced by Changchun Kexin Testing Machine Company. The axial stress and axial-radial deformation of the fully confined CFRP sheet are monitored by the pressure transducer and the extensometer of the machine. Considering the brittleness of coal sample destruction, Donghua Testing's DH3816 static strain tester (100Hz), 500 kN pressure transducer, and several strain gauges were employed to form a backup monitoring system to ensure the smooth implementation of the test. Drawing on [26], this test was conducted using displacement loading with a loading rate of 0.12 mm/min. Conventional uniaxial compression tests were conducted according to the established test scheme in Table 1, maintaining a constant loading rate until the destruction of the CFRP fully confined coal samples, and the test system and specimen assemblies are shown in Fig. 5.Fig. 5 Testing system and sample assembly.

Fig. 5

Fig. 6 Stress-strain curves and failure modes of typical coal samples under different CFRP layers.

Fig. 6

3 Test results and analysis

3.1 Stress-strain curves and test phenomenon

Through the comparison and collation, the typical specimens of each group of tests were selected, and the full-process stress-strain curves and the damage patterns of the corresponding CFRP passively confined coal samples were combined and plotted, as depicted in Fig. 6. The representative deformation and damage process of the CFRP confined coal samples under different layers can be divided into four stages: initial compression-density stage (0A), elasticity section (AB), yielding stage (BC), and post-peak damage section (CD). In the compaction stage (0A), the primary fractures existing inside the coal samples were gradually compressed, which made the coal samples develop higher strains under lower stresses. In the elastic stage (AB), the stress of each coal sample in the elastic section increased by 25.7 MPa, 37.5 MPa, 76.7 MPa, and 94.8 MPa, respectively, and the strain also increased by 1.5 ‰, 1.9 ‰, 3.6 ‰, and 3.8 ‰, respectively, which were directly correlated with the CFRP layers. It is mainly due to the passive confining effect of CFRP sheet that the bearing capacity of coal samples in the elastic section is enhanced, and the more layers of CFRP, the more obvious the improvement of the bearing efficiency of coal samples.

As the load increased continuously, the loading process of coal samples accompanied by the generation of a 'creaking' crisp sound, unconfined coal samples produced a large number of large-scale spattering of coal debris when the instability of the larger spattering area, yielding numerous diagonal cracks and poor integrity.; When the CFRP passively confined coal samples reached the bearing capacity maximum, accompanied by a loud bang, the CFRP sheet was partly broken in the middle or the end, and only a few small-scale coal chips were splashed out during the destabilization, and the radius of the splash was smaller, and the integrity of the coal samples was still intact and remained in the original state. When L = 0, the unconfined coal samples produced about four times localized yield damage phenomena similar to 'cliff-like jagged' in the yielding stage (BC) and about three times localized damage phenomena similar to 'cliff-like jagged' in the post-peak stage (CD), until gradually to the destruction at point D. This 'cliff-jagged' phenomenon before and after the peak is consistent with localized damage in the stress-strain curves of coal samples in Ref. [21]. When L = 1–3, growth of the CFRP

layers led to the stress-strain curves of the yield section from a similar “cliff-like jagged" gradually changed to 'capillary jagged'. The main reason for this phenomenon is that the lateral passive confinement provided by the CFRP sheet gradually increases, which effectively inhibits the development of cracks in the coal samples so that the local damage phenomenon is gradually reduced. In the post-peak stage (CD), the stress-strain curves of the passively confined coal samples gradually changed from a 'capillary jagged' to a 'cliff-like jagged' decline with the increase of the CFRP layers, generating a double peak phenomenon (L = 2–3), and the axial deformation increment decreased rapidly. The main reason is that the lateral passive confinement of the CFRP sheet improves the energy storage potential of the coal samples, enhances the randomness of the passive confinement of the coal samples' destabilization, restricts the efficiency of the internal fracture development of the coal samples, and can only expand the primary larger scale fracture, which ultimately leads to the smaller broken area of the passive confinement of the coal samples during the destabilization, and the smaller scale and splash range of the chips, which is in line with the damage patterns of the CFRP passive confined coal samples in Fig. 6.

3.2 The influence of the CFRP layers on the mechanical parameters of coal samples

3.2.1 Peak strength

The peak strengths of passively confined coal samples with different CFRP layers are presented in Fig. 7. The peak strength of the passively confined coal samples increases with the increase of the CFRP layers, but the growth rate varies in the range of 0 ≤ L ≤ 3. The peak strength of the passively confined coal samples firstly increases rapidly with a large slope of 1211.362 MPa·layer−1 and then decreases to a smooth growth with a slope of 40.781 MPa·layer−1 in a gradual transition. Based on the concept of enhancement ratio in Ref. [21], the concept of 'relative strength enchancement ratio δ' was proposed, which refers to the ratio of the strength of the latter layer to the strength of the former layer, and revealed that with the increase of the CFRP layers, the relative peak strength enhancement ratio of the passively confined coal samples showed a steep decrease with a slope of 1.068·layer−1, then a gentle decrease with a slope of 0.0433·layer−1, Within 0 ≤ L ≤ 3 layers, the relative enhancement ratio of coal samples at L = 1 is the largest, about 2.378. It is demonstrated that the load-bearing efficiency of standard coal samples could be significantly improved by wrapping CFRP sheets around them,Fig. 7 The variation of peak strength of coal samples under different CFRP layers.

Fig. 7

and the CFRP sheet provides reliable passive lateral confinement force, which changes the force state of the coal samples. However, with the increase of the CFRP layers, the relative enhancement ratio of the peak strength decreases, which indicates that there must be an optimal layer within a certain layer, taking into account the economic cost, construction simplicity, and the relative enhancement ratio, which is consistent with the conclusion of the [21].

According to the above analysis of the change rule of peak strength of passively confined coal samples under different.

CFRP layers, following the principle of high fitting accuracy, simple function, and few parameters, the model comparison function of nonlinear fitting of Origin software was used to filter the model, and the functional relationship that can characterize the evolution of the peak strength of passively confined coal samples under different CFRP layers was obtained as shown in Eq. (1):(1) σp=52.66+4.99L+0.91L3+66.11L0.5

Where σp is the peak strength of the coal sample, MPa.

3.2.2 Elastic modulus

The elastic modulus of passively confined coal samples with different CFRP layers is shown in Fig. 8. With the increase of the CFRP layers, the elastic modulus of the passively confined coal samples firstly grows rapidly with a slope of 1.706 GPa·layer−1 and then it progressively tends to grow steadily with a slope of 13.867 GPa·layer−1. Within the 0 ≤ L ≤ 3, the elastic modulus increment ΔE of the passively confined coal samples reaches a maximum value of about 3.73 GPa at L = 3 and achieves a minimum value of about 1.44 GPa at L = 2, followed by 2.01 GPa at L = 1. Evidently, the presence of CFRP sheet also improves the deformation characteristics of passively confined coal samples, and the improvement of the deformation capacity of passively confined coal samples is also verified from the axial peak strain in the stress-strain curves in Fig. 6. Based on the elastic modulus evolution law of passively confined coal samples under different CFRP layers, the screening process of Eq. (1) is referenced to obtain the functional relationship that can characterize the elastic modulus evolution law of passively confined coal samples under different CFRP layers, as shown in Eq. (2):(2) E=L−3.030.39−0.04L2+25.28

Where E is the elastic modulus of the coal sample, GPa.Fig. 8 The variation of elastic modulus of coal samples under different CFRP layers.

Fig. 8

3.2.3 Peak hoop strain

The peak hoop strains of passively confined coal samples with different CFRP layers are given in Fig. 9. The peak hoop strain is the average value of the hoop strain at the peak stress. From Fig. 9, compared with the unconfined coal samples, with the increase of the CFRP layers (1 ≤ L ≤ 3), the peak hoop strain of the passively confined coal samples decreases obviously, and the most obvious decrease is when L = 3 with about 73.43 %, the least obvious decrease is when L = 2 withFig. 9 The variation of peak hoop strain of coal samples under different CFRP layers.

Fig. 9

about 29.37 %, and the second decrease is when L = 1 with about 54.42 %. The main reason is that coal, as a nonhomogeneous material, inherently has numerous primary fractures, resulting in a slight float at L = 2. From this, the significant loop passive confinement force provided by the CFRP sheet changes the coal sample from a single axial force state to a three-way force state, limiting the loop deformation of the coal sample to realize the purpose of reinforcement. However, the lateral confinement force provided by the CFRP sheet is different from the conventional confinement force, the former varies with the loop deformation of the coal sample and belongs to the loop passive dynamic confinement force, while the latter belongs to the constant confinement force, which is fundamentally different from the conventional confinement force.

Based on the evolution law of peak cyclic strain of passively confined coal samples under different CFRP layers, the screening process of Eq. (1) is borrowed to obtain the functional relationship to characterize the evolution law of peak hoop strain of passively confined coal samples under different CFRP layers, as shown in Eq. (3):(3) εh,p=0.01557−0.02237L+0.01776L2−0.00386L3

Where εh,p is the peak hoop strain.

4 Energy dissipation damage constitutive relationship for CFRP passively confined coal samples

4.1 Energy calculation principle

For loaded passively confined coal samples, its deformation and destruction process is essentially a process of energy exchange between it and the outside world, accompanied by energy input, accumulation, dissipation, and release [[27], [28], [29]]. It is assumed that the passive coal sample does no heat exchange with the outside during deformation, and a portion of the energy input from the outside is collected inside the passive confined coal sample in the form of elastic strain energy, and released during unloading; the other portion dissipated by plastic deformation, fracture damage, and so on. According to the first law of thermodynamics [27,28]:(4) U=Ud+Ue

Where U is the total energy of the passively confined coal sample, MJ·m−3; Ud is the dissipated energy of the passively confined coal sample, MJ·m−3; and Ue is the elastic strain energy of the passively confined coal sample, MJ·m−3.

When the elastic energy accumulates to a certain extent, and the dissipation damage reaches a specific limit, the passively confined coal sample will be destabilized and release its internal energy. The correspondence between the elastic strain energy and dissipation energy of the passively confined coal sample is presented in Fig. 10.Fig. 10 Relation between elastic strain energy and dissipated energy in coal samples [27].

Fig. 10

As depicted in Fig. 10, the total energy of the passively confined coal sample cell can be identified by the definite integral of the area enclosed by its stress-strain curve and the coordinate axes:(5) U=∫0ε1σ1dε1=∑i=1n12(σ1i+σ1i+1)(ε1i+1−ε1i)

Where σ1i is the stress value at each point in the axial stress-strain curve, MPa; ε1i is the strain value at each point in the stress-strain curve, %. The elastic energy can be determined by integrating the area of the shaded part in the figure:(6) Ue=12σ1ε1e

According to Hooke's law, Eq. (6) can be rewritten as:(7) Ue=σ122E

Where E is the initial elastic modulus [28,29]. Therefore, the dissipation energy of passively confined coal samples during uniaxial compression tests is:(8) Ud=U−Ue

4.2 The influence of the CFRP layers on the energy evolution law of passively confined coal samples

According to Eqs. (5), (7), (8) in Section 4.1, combined with the stress-strain curve of each coal sample in Fig. 6, the total energy, elastic strain energy, and dissipation energy of the passively confined coal samples under different CFRP layers were calculated respectively, which are shown in Fig. 11.Fig. 11 Energy evolution law of coal samples under different CFRP layers.

Fig. 11

From Fig. 11(a), the energy storage potential of the passively confined coal samples increases significantly with the increase of CFRP layers, which is 5.79 times for L = 1, 7.93 times for L = 2, and 9.03 times for L = 3. This shows that the CFRP sheet can fully utilize its lightweight and high strength, and then reliably provide passive lateral confinement, which contributes to improving the energy absorption level of the coal samples. When ε1 ≤ 4 ‰, the energy storage level of passively confined coal samples under different CFRP layers differs little, but the energy storage capacity of L = 0 (unconfined) coal samples when ε1 ＜ 3.29 ‰ is always slightly higher than that of passively confined coal samples under L = 1–3 layers; when ε1 ≥ 3.29 ‰, the energy storage level of passively confined coal samples under CFRP layers of L = 3 is rapidly exceeding that of coal samples under unconfined and other conditions (L = 1–2); At ε1 ≤ 7 ‰, the energy storage level of the L = 1 layer CFRP passively confined coal samples is almost the same as that in the L = 2 layers case. It shows that the axial deformation required to achieve the same energy storage level with more layers is smaller. Fig. 11(b) shows that the elastic strain energy of coal samples is also greatly affected by the CFRP layers, and the trend of elastic strain energy of CFRP passively confined coal samples with different layers is similar to the stress-strain curves in Fig. 6, which verifies the conclusion from the composition of Eq. (7).

From Fig. 11(c), the dissipation energy is closely related to the friction of the closed fractures inside the passively confined coal samples, the initiation and expansion of the microfractures, as well as the macroscopic plastic deformation, and the existence of CFRP sheet promotes a greater degree of development of the primary fracture inside the coal samples, which strengthens the dissipation ability, and improves by about 5.75 times compared with that of unconfined coal samples at the L = 1 layer, and the increase level is the same at the L = 2–3 layers, which is about 6.885 times. The axial deformations of the coal samples at instability increased by 2.10–2.35 times, with similar working conditions for L = 2 and L = 3. At ε1 ≤ 7 ‰, the dissipated energy of L = 1–3 layers is perturbed approximately parallel to the strain axis, yet with different values, which are in the fracture compaction and linear elasticity segments (0A + AB) of the stress-strain curves in Fig. 6, and grows rapidly in the L = 1–3 layers once it enters into the yielding stage (BC). It can be seen that the dissipated energy is very sensitive to the development of internal cracks in the coal samples, and the passive lateral confinement provided by the CFRP sheets with different layers effectively inhibits the development of internal cracks in the coal samples, which leads to the overall destruction of the specimens when the coal samples are destabilized in the case of L = 0 condition, whereas the coal samples destabilized in the case of L = 1–3 condition are only locally destroyed and the original shape of the coal samples is still preserved, which is by the destruction pattern in Fig. 6.

ηd=Ud/U represents the variation of energy dissipation rate of coal samples with different CFRP layers [30];

K=Ud/Ue represents the elastic energy consumption ratio of coal samples to reflect the proportionality between energy storage and energy dissipation in the deformation process of passively confined coal samples [31,32], as shown in Fig. 12, and the 'purple underline' in Fig. 12(a) represents the peak strain corresponding to the peak stress. From Fig. 12(a), ηd of coal samples with different CFRP layers showed a tendency to decrease and then increase, and all of them existed at the minimum ηd inflection point in the pre-peak stage. Compared with unconfined coal samples, the effect of L = 1–3 layers of CFRP sheets on ηd is significant, where the axial strain at the minimum ηd inflection point increases with CFRP layers, and before the inflection point, the ηd curve shows an inverse Sigmoid function with a gentle decrease, while L = 0 shows an approximately straight-line decrease.Fig. 12 Variation in energy dissipation rate and elastic energy consumption ratio of coal samples with different CFRP layers.

Fig. 12

Coal samples have inherently numerous primary fractures, and fracture closure requires a certain amount of dissipated energy, so ηd is the largest in the initial section. With the increase of load, the completion of the fracture's gradual closure leads to the gradual decrease of the energy dissipation rate and reaches the minimum ηd inflection point, while the existence of CFRP raises the energy threshold of the coal fracture closure, and the closure efficiency decreases, causing an increase in the axial deformation at the inflection point. After the inflection point in the L = 0 condition, ηd increases rapidly, and the closed fractures inside the coal samples expand and converge rapidly, resulting in macroscopic fractures on the coal sample surfaces and large-scale spattering of coal debris and spattering distance; When L = 1–3, ηd before the peak strain after the inflection point increases slowly with the increase of CFRP layers, i.e., the rate of ηd decreases gradually, which indicates that the CFRP sheet effectively inhibits the expansion and convergence of the closed fractures inside the coal samples, and significantly improves the elastic energy storage level of the samples; there is a sudden increase of ηd in the post-peak stage, and the value of ηd decreases with the increase of the CFRP layers during the destabilization, and the scale and distance of the coal samples' debris are also reduced, which is consistent with the experimental phenomenon in subsection 2.1.

From Fig. 12(b), the K-value at the peak shows a gentle increase and then a gradual decrease with the CFRP layers, which is in the range of 0.54–0.81, and the proportion of the dissipation energy is less than that of the elastic energy in all cases at the peak. It shows that the coal samples in the pre-peak section are mainly for energy storage, and the elastic energy storage efficiency is improved by 1.30–1.38 times when L = 1–2 layers, but the elastic energy storage enhancement of the coal samples is no longer desirable with too many layers.

With the increase of the CFRP layers, the K-value at the time of damage first decreases gently and then declines rapidly, within the range of 1.27–2.76, indicating that the energy dissipation dominated in the post-peak period. The CFRP sheet effectively limited the lateral deformation of the coal samples and significantly increased the energy threshold for the coal samples' fractures development, while the energy dissipation for coal splinters splashing during destabilization at lower levels, which strengthens the load-bearing efficiency of the coal samples and further explains the reason for the increase in the peak strength of the passively confined coal samples in Fig. 7. Yet, K-value at the peak is lower than that at the destruction for all conditions, indicating that the total energy of coal samples in the pre-peak period is dominated by elastic energy and supplemented by dissipation energy, while the total energy in the post-peak stage is dominated by dissipation energy and supplemented by elastic energy, which also proves that the energy transformation of the coal samples from deformation to destabilization is a dynamic process. that is, it is manifested as a transformation and equilibrium between the input total energy, the releasable elastic energy, the dissipation energy, etc., For any moment in the deformation process, there is a particular energy state corresponding to it [31,32].

4.3 Construction of damage constitutive relationship for segmented CFRP passively confined coal samples

The stress-strain curves of CFRP passively confined coal samples under uniaxial compression have an obvious initial compaction stage (0A), which is combined with the principle of energy dissipation that the energy absorbed by the coal samples in the compaction stage is mainly used for the compaction of the original cracks without the sprouting and development of new cracks [33,34]. Therefore, assuming that no damage occurs in the passively confined coal samples at the compaction stage (0A), and continuous damage exists in the elastic, yield, and post-peak destabilization stages, the segmented energy dissipation damage constitutive relationship of the passively confined coal samples under different CFRP layers is constructed using point A as the boundary point.

Based on the previous research results of Li et al. [34], the constitutive relationship of the compact section of passively confined coal samples with different CFRP layers was proposed:(9) σ1=σA(ε1/εA)2

Where σA is the axial stress at point A, MPa; εA is the axial strain at point A, %.

Based on the statistical damage mechanics theory, the damage of passively confined coal samples can be defined as the ratio of the damaged area to the total bearing area [35], that is:(10) D=A−A′A=1−A′A

Where D is the damage of passively confined coal samples; A and A′ are the nominal bearing area and effective bearing area of coal samples, respectively, mm2. and the nominal stress and effective stress of coal samples satisfied the following relation equation [[34], [35], [36]]:(11) F=σ·A=σ′·A′

Where F is the loading on the passive confined coal sample, N; σ and σ′ are the nominal stress and effective stress of the uniaxially compressed coal sample, MPa, respectively.

It is obtained by the association of Eq. (10) and Eq. (11):(12) σ1=σ1′·(1−D)

According to the assumption of strain-coordinated deformation, the strains in the damaged and undamaged parts of the passively confined coal samples are consistent with the total strain. Assuming that the undamaged part of the passively confined coal sample still satisfies Hooke's law, and then substituting the relationship σ' = E · ε1 into Eq. (12), it can be obtained:(13) σ1=E·ε1·(1−D)

The segmental damage constitutive relationship of CFRP passively confined coal samples under uniaxial compression can be obtained by associating Eq. (9) with Eq. (13):(14) σ1={σA(ε1/εA)2(ε1<εA)E·ε1·(1−D)(ε1≥εA)

4.4 Derivation of energy dissipation damage variables

Based on the principle of statistical damage mechanics and energy dissipation [37,38], combined with section 3.2, it can be seen that the dissipation energy is very sensitive to passively confined coal samples' internal fractures development, so the dissipation energy is adopted to reflect the damage of passively confined coal samples. From the literature [34], the microunit damage of coal samples obeys the generalized Weibull distribution, and thus the microunit probability density and dissipation energy of the passively confined coal samples under uniaxial compression can be obtained to fulfill the relationship of Eq. (15):(15) P(Ud)=mk·(Ud−UAdk)m−1·exp[−(Ud−UAdk)]

Where P is the probability density function of the micrometric damage; k and m are the scale and shape parameters of the Weibull distribution to be determined: UAd is the dissipation energy corresponding to point A of the compaction section of the stress-strain curve in Fig. 6.

According to the principle of statistical damage mechanics, the damage variable D of passively confined coal samples is defined as the ratio of the number of microelement damages to that of total microelements:(16) D=n/N

With the increase of axial uniaxial compressive load, the number of microelement damages of passively confined coal samples can be calculated by the definite integral of Eq. (17) at any moment of deformation of loaded coal samples.(17) n=∫0UdN·P(x)dUd=N{1−exp[−(Ud−UAdk)m]}

The damage variable D of the passively confined coal sample can be obtained by solving Eq. (16) and Eq. (17) in conjunction with Eq. (18):(18) D=1−exp[−(Ud−UAdk)m]

4.5 Modification of energy dissipation damage constitutive relationship of passively confined coal samples with different CFRP layers

The elasticity modulus is corrected by transforming Eq. (2), Eq. (18), and Eq. (14) conjointly, which in turn leads to Eq. (19), a segmented energy dissipation damage constitutive relationship for passively confined coal samples with different CFRP layers.

Based on the full stress-strain curves in Fig. 6 and the dissipation energy curves in Fig. 11(c)–Eq. (19) is nonlinearly solved to calculate the scale and shape parameters k and m using the advantage of fast con-vergence of the genetic algorithm, which in turn yields the passively confined coal sample damage variable D. However, the D value is strongly affected by the CFRP layers at the moment, which is already con-firmed in the analysis of the energy dissipation in Fig. 11(c), and therefore, it is necessary to modify the CFRP layers about the shape parameters k and m. By referring to the layer correction of elastic modulus in Eq. (2), the evolution of parameters m, k can be obtained for the different CFRP layers as shown in.

Fig. 13, and the effect is significant (R2 = 0.99), and the relationship among the three can be expressed in Eq. (20).(19) σ1={σA(ε1/εA)2(ε1<εA)E·ε1·exp[−(Ud−UAdk)m](ε1≥εA)

(20) {m=1.829−0.468L2+0.121L3−0.851e−Lk=103.304+639.224L2−148.084L3+13.343L0.5

Fig. 13 The variation in Weibull distribution parameters under different CFRP layers.

Fig. 13

Converting Eq. (20) with Eq. (19) associatively, the energy dissipation damage ontological relationship Eq. (21) for passively confined coal samples under different CFRP layers is acquired eventually.(21) σ1={σA(ε1/εA)2(ε1<εA)(L−3.030.39−0.04L2+25.28)·ε1·exp[−(Ud−UAd103.304+639.224L2−148.084L3+13.343L0.5)1.829−0.468L2+0.121L3−0.851e−L](ε1≥εA)

4.6 Validation of the constitutive relationship

The test results of stress-strain curves of passively confined coal samples under different CFRP layers are compared with the theoretical values calculated by Eq. (21) constitutive model, as shown in Fig. 14. From Fig. 14, the theoretical model with two corrections has a good fit with the experimental results (R2 ≥ 0.94), particularly reflecting the 'jagged' phenomenon of the stress during the local instability, which is also an excellent point of this model to distinguish it from the conventional Weibull distribution continuum damage constitutive model in Ref. [39], Of course, the energy dissipation damage model also has some errors with the experimental results but still belongs to the reliable error range. The slope of post-peak damage of coal samples was observed to be the largest at L = 0, the smallest at L = 3, followed by L = 1 and L = 2 separately, indicating that the CFRP layers are inversely proportional to the growth rate of damage, and the more CFRP layers there are, the slower the growth rate of damage is, the less likely to produce damage, so the higher the load-bearing efficiency of passively confined coal samples is.Fig. 14 Comparison of experimental and theoretical curves.

Fig. 14

This shows that the CFRP sheet effectively inhibits and delays the generation and growth of coal sample damage, and the more layers of CFRP sheets with the same degree of damage, the greater the axial deformation of the passively confined coal samples; the more layers of CFRP sheets, the smaller the damaged area and size of the passively confined coal samples, which is consistent with the damage pattern in Fig. 6, and the destabilization of the passive samples in the case of L = 1–3 is only local damage, without forming full-height damage, which is in sharp contrast with the full height damage of the unconfined samples in the case of L = 0.

4.7 Influence of the CFRP layers on the energy dissipation damage evolution law

By associating Eq. (20) with Eq. (18), the damage evolution equations of passively confined coal samples under different CFRP layers can be transformed, as shown in Eq. (22).(22) D=1−exp[−(Ud−UAd103.304+639.224L2−148.084L3+13.343L0.5)1.829−0.468L2+0.121L3−0.851e−L]

The damage of passively confined coal samples with different CFRP layers is given in Fig. 15. The damage of passively confined coal samples increases gently with small fluctuations in the elastic section approximately parallel to and asymptotic to the strain axis until the yield stage when the damage starts to increase significantly with increased fluctuations and a sudden increase occurs at the peak strain.Fig. 15 Damage evolution law of CFRP confined coal samples.

Fig. 15

5 Discussion on the optimum layers of CFRP sheet

5.1 Damage

The damage loss rate values for passively confined coal samples with different CFRP layers given in Fig. 16 refer to the average damage rate obtained by linear regression of the marginal distribution on the damage curve of the fast-growth section denoted by 'ζL', as well as the increment of the damage rate denoted by "' Δ ζL'. From Fig. 16, under L = 0–3 layers, with the increase of the CFRP layers, the passively confined coal samples firstly decreased rapidly with a larger slope of 0.25395·layer−1 and then smoothed out gradually with a smaller slope of 0.00158·layer−1. It shows that the CFRP sheet is effective in slowing down the growth of coal damage, and the effect is significant, yet from the indicator, the value of a tends to 0 (Δ ζ3 = −0.00158) with the increase of the CFRP layers. Thus, the damage retardation effect is no longer significant with more layers of CFRP sheet, so from the damage point of view, 3 layers can be regarded as the optimal layers of CFRP sheet.Fig. 16 Variation in damage rate and its increment of coal samples under different CFRP layers.

Fig. 16

5.2 Project cost and construction difficulty

Based on the previous research background review section, it is known that the application of CFRP sheet in the field of civil engineering is very successful in reinforcing the engineering structure, mainly considering its advantages of lightweight, high strength, corrosion resistance, mouldability, and easy construction, etc., a reinforcement measure of applying CFRP sheet on the outer surface of small coal columns is proposed, which changes the force state of the columns and the measure has low requirements for the working environment of the construction, simple and fast construction, which is suitable for the limited environment of coal pillar reinforcement in the coal mining hollow area, and the fewer the layers of CFRP sheet are applied, the smaller the cost and the faster the construction is.

5.3 Load-bearing safety reserve

From the change rule of peak strength of coal samples under different CFRP layers in Fig. 7, the bearing capacity level of coal samples increases rapidly with the increase of CFRP layers while the relative strength enhancement ratio δ-value decreases rapidly and tends to be stable, δ2 = 1.31, δ3 = 1.27, which is a difference of 3.3 %. Hence, the enhancement effect of the load-bearing effectiveness slows down with the increase of the CFRP layers, and L = 3 layers are selected as the optimum layer considering the load-bearing safety reserve.

Considering the damage of coal samples, project cost, construction difficulty bearing safety reserve, etc., 3 layers were finally determined as the optimal layers of the CFRP sheet, which coincides with the conclusion of the literature [22], although the conclusion did not consider the size and shape effect of the coal pillars in the actual mining hollow area, it provides a new way of thinking for its reinforcement design and the prevention and control of the impact ground pressure, having a certain value of reference.

6 Conclusion

Under L = 0 condition, the unconfined coal samples were seriously damaged in the whole height range during destabilization, as well as the scale and splash radius of the splinters were large, and there were about 7 times 'cliff-like jagged' local damage phenomena before and after the peak. Under L = 1–3 conditions, with the increase of the CFRP layers, the passively confined coal samples were only partially broken and kept in the original state of instability, the scale and radius of the splash were small, and the local damage phenomenon before the peak gradually changed from 'cliff-like jagged' to 'capillary jagged'; after the peak, the local damage phenomenon gradually changed from 'capillary jagged' to 'cliff-like jagged' and the increment of axial deformation decreases rapidly and abruptly.

The peak strength and elastic modulus of passively confined coal samples both increase rapidly with the increase of the CFRP layers, while the relative enhancement ratio decreases gradually, but its value is not less than 1.2, as well as obtained the functional evolution relationship between the peak strength and elastic modulus under the different layers; while the annular peak strain shows a 'jagged' rapid decrease and the functional evolution relationship of annular peak strain under different layers was obtained.

With the increase of the CFRP layers, the energy storage capacity (total energy), elastic strain energy, and dissipation energy of the passively confined coal samples are all significantly enhanced, and the more the layers are, the smaller the axial deformation required to achieve the same level of energy storage, but when the layers are more than 2, the enhancement effect of the dissipation energy is no longer significant; the energy dissipation rate shows the characteristics of initially decreasing and then increasing trend, and there exists a minimum inflection point; the elastic energy ratio at the peak shows the trend of firstly slow increase and then slow decrease with the value of about 0.54–0.81; at the post-peak destabilization, the elastic energy ratio shows the trend of firstly slow decrease and then fast decrease with the value of about 1.27–2.76;

The energy dissipation damage constitutive relationship of passively confined coal samples with different CFRP layers was established, which overcame the 'jagged' phenomenon that the conventional Weibull distribution damage constitutive model was unable to reflect the stress in the coal samples during the pre-peak and post-peak local breakage, and the fitting accuracy was high and the effect was remarkable; The evolution equation of energy dissipation damage of coal samples considering the CFRP layers was derived, which found that the CFRP sheets effectively suppressed and delayed the growth of coal samples' damage, and the more the layers of the same damage, the larger the axial deformation, but the significance of the suppression and delay was gradually lost when the layers were not less than two.

Considering the damage of coal samples, project cost, construction difficulty, and load-bearing safety reserve, 3 layers are determined as the optimal wrapping layers, which does not take into account the effect of the actual coal pillar size and shape but provides a new way of thinking for the reinforcement of coal pillars with impact tendency.

Despite the significant advantages of CFRP sheets in reinforcing coal pillars, there are still many unresearched issues. For example, size effect, crack extension pattern, and soon. We believe that with the deepening of the research, these problems will be solved, and the technology of applying CFRP sheets to coal pillar reinforcement will become more mature and widespread.

Data availability

Data will be made available on request.

CRediT authorship contribution statement

Qingwen Li: Writing – original draft, Software, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. Fanfan Nie: Writing – review & editing, Writing – original draft, Software, Data curation. Chuangchuang Pan: Writing – review & editing. Ling Li: Writing – review & editing, Conceptualization. Yuqi Zhong: Writing – review & editing. Mengmeng Yu: Writing – review & editing. Hao Yang: Writing – review & editing, Investigation.

Declaration of competing interest

This manuscript has not been published or presented elsewhere in part or entirety and is not under consideration by another journal. We have read and understood your journal's policies, and we believe that neither the manuscript nor the study violates any of these. There are no conflicts of interest to declare.

Acknowledgements

This research was financially supported by the General Project of 10.13039/501100005047 Liaoning Provincial Natural Science Foundation (Grant No. 2023-MS-298), Liaoning Provincial Department of Education Basic Scientific Research Upper Level Project (Grant No. JYTMS20230866), Project of Liaoning Provincial Doctoral Research Start-up Fund (Grant No. 2019-BS-120) and Guiding Project of Liaoning province Natural Science Foundation (Grant No. 20180550297).
==== Refs
References

1 B. Zhang, P. Wang, S. Cui, et al. Mechanism and surrounding rock control of roadway driving along gob in shallow-buried, large mining height and small coal pillars by roof cutting. Journal of China Coal Society[J],46:2254-2267. (in Chinese).
2 Yang S. Wang Z. Jiang W. Advancing rate effect on rock and coal failure format in high-intensity mining face J. China Coal Soc. 41 3 2016 586 594 (in Chinese)
3 Yu Y. Bai J. Zhang S. Disaster mechanism of surrounding rock with double wing mining roadway group and its repair and reinforcement system Journal of Mining and Safety Engineering 37 6 2020 1133 1141 (in Chinese)
4 Zhu W. Chen L. Zhou Z. Failure propagation of pillars and roof in a room and pillar mine induced by longwall mining in the lower seam Rock Mech. Rock Eng. 52 4 2019 1193 1209
5 Yu D. Yi X. Lianget al Z. Research on strong ground pressure of multiple-seam caused by remnant room pillars undermining in shallow seams Energies 14 17 2021 5221
6 Dong H. Zhu W. Hou C. Load transfer behavior during cascading pillar failure: an experimental study Rock Mech. Rock Eng. 55 3 2022 1445 1460
7 Zhang C. Jin Z. Feng G. Double peaked stress–strain behavior and progressive failure mechanism of encased coal pillars under uniaxial compression Rock Mech. Rock Eng. 53 7 2020 3253 3266
8 Wang J. Fu J. Song Wei Particle flow simulation of mechanical properties and microcrack evolution characteristics rock-backfill combined model[J] J. China Inst. Min. Technol. 49 3 2020 453 462 (in Chinese)
9 Yu W. Wu G. Liu Z. Uniaxial compression test of coal-rock-bolt anchorage body and mechanical mechanisms of bolts Chin. J. Rock Mech. Eng. 39 1 2020 57 68 (in Chinese)
10 B. Wang, Y. Ning, T. Feng, et al. Experimental study on anchoring effect of brittle rock mass influenced by loading rates at low strain rate [J]. J. China Coal Soc., 2019, 44(9): 2691-2699. (in Chinese).
11 Zhang Y. Cui L. Hu J. Experimental study on the uniaxial compressive strength of anchorage body based on crack effect Journal of Mining & Safety Engineering 38 2 2021 253 259 (in Chinese)
12 Wang Q. Wang L. Liu B. Study of void characteristics and mechanical properties of fractured surrounding rock grout[J] J. China Inst. Min. Technol. 48 6 2019 1197 1205 (in Chinese)
13 Bai J. Wei Y. Zhang Y. Axial compression behavior of new seawater and sea sand concrete filled circular carbon fiber reinforced polymer-steel composite tube columns Acta Mater. Compos. Sin. 38 9 2021 3076 3085 (in Chinese)
14 Guo Y. Xiao S. Zeng J. Behavior of concrete-filled FRP tube columns internally reinforced with FRP-steel composite bars under axial compression Construct. Build. Mater. 315 2022 125714
15 Wang G. Wei Y. Miao K. Experimental study on axial compression performance of CFRP-steel composite tube filled circular seawater sea-sand coral concrete columns Acta Mater. Compos. Sin. 39 8 2022 3982 3993 (in Chinese)
16 Thamboo Julian Asad Tatheer Zahra Mohammad Monotonic and cyclic compression characteristics of CFRP confined masonry columns Compos. Struct. 272 2021 114257
17 Jiao C. Li S. Cui L. Axial compression behaviour of CFRP confined reactive power concrete filled steel tube stub columns Acta Mater. Compos. Sin. 38 2 2021 439 448 (in Chinese)
18 Zeng J. Liang S. Li Y. Compressive behavior of FRP-confined elliptical concrete-filled high-strength steel tube columns Compos. Struct. 266 2021 113808
19 Jyoti Das Arka Mandal Prabhat Kumar Chandra Nathghosh Extraction of locked-up coal by strengthening of rib pillars with FRP–A comparative study through numerical modelling Int. J. Min. Sci. Technol. 27 2 2017 261 267
20 Liu H. Zhao H. Chen H. Method of reinforcing residual coal pillars of room and pillar type coal face by prestressed fiber cloth[P]. China 4 2021 07-09.(in Chinese)
21 L Q. Hu L. Cao H. Axial compressive behavior of CFRP uniformly wrapped coal in circular columns [J/OL] Acta Materiae Compositae 39 2022 1 14 (in Chinese)
22 Li Q. Zeng X. Zhang X. Mesoscopic study on the effect of CFRP layers on the mechanical properties of coal circular-columns [J/OL] Coal Sci. Technol. 2022 1 13 (in Chinese)
23 Xia Z. Yao Q. Li X. Acoustic emission characteristics and energy mechanism of CFRP-jacketed coal specimens under uniaxial compression Construct. Build. Mater. 342 2022 127936
24 Shi X. Bai J. Feng G. Crack propagation law at the interface of FRP wrapped coal-backfilling composite structure Construct. Build. Mater. 344 2022 128229
25 The China National Standardization Man-agement Committee GB/T 3354-2014 Test Method for Tensile Properties of Orientation Fiber Reinforced Polymer Matrix Composite materials[S] 2014 Beijing: Standards Press of China (in Chinese)
26 Zhu C. Li S. Luo Y. Progressive damage process and failure characteristics of coal under uniaxial compression with different loading rates Shock Vib. 6 2021 1 12 2021
27 Li Z. Wang G. Huang T. Variation of energy and criteria for strength failure of shale under triaxial cyclic loading Chin. J. Rock Mech. Eng. 37 3 2018 662 670 (in Chinese)
28 Wang G. Zhang L. Xu M. Energy damage evolution mechanism of non-across jointed rock mass under uniaxial compression Chin. J. Geotech. Eng. 41 4 2019 639 647 (in Chinese)
29 Zhang L. Wang G. Ruide L.E.I. Energy damage evolution mechanism of single jointed rock mass with different lengths under uniaxial compression China J. Highw. Transp. 34 1 2021 24 34 (in Chinese)
30 Zhou J. Zhao Y. Gustavo Paneiro Loading rate and bedding plane coupled effect study on coal failure under uniaxial compression: acoustic emissions and energy dissipation analysis Geofluids 2022 2022 9028178
31 Li P. Cai M. Energy evolution mechanism and failure criteria of jointed surrounding rock under uniaxial compression J. Cent. S. Univ. 28 6 2021 1857 1874
32 Ma Q. Tan Y. Liu X. Experimental and numerical simulation of loading rate effects on failure and strain energy characteristics of coal-rock composite samples J. Cent. S. Univ. 28 10 2021 3207 3222
33 Hou Y. Yin S. Cao Y. Stress-strain relationship and damage constitutive model of cemented tailings backfill under uniaxial compression Materials Reports 36 16 2022 179 186 (in Chinese)
34 Li Q. Gao S. Hu L. Constitutive relation of energy dissipation damage of heterogeneous coal samples under different loading rates J. China Coal Soc. 47 S1 2022 609 620 (in Chinese)
35 Du F. Wang K. Zhang G. Damage characteristics of coal under different loading modes based on CT three-dimensional reconstruction Fuel 310 2022 122304
36 Zhang X. Cai J. Tang N. Experimental study on mechanical properties of deep sandstone and its constitutive model J. China Coal Soc. 44 7 2019 2087 2093 (in Chinese)
37 Du X. Xue J. Ma Q. Energy evolution characteristics of coal–rock composite bodies based on unidirectional load Nat. Resour. Res. 31 3 2022 1647 1663
38 Wang J. Li J. Shi Z. Deformation damage and acoustic emission characteristics of red sandstone under fatigue-creep interaction Theor. Appl. Fract. Mech. 117 2022 103192
39 Wang K. Jiang Y. Xu C. Mechanical properties and statistical damage model of coal with different moisture contents under uniaxial compression Chin. J. Rock Mech. Eng. 37 5 2018 1070 1079 (in Chinese)
