Gradient failure mechanism and control technology of deep roadways under the action of deviatoric stress field

Abstract

Deformation control of deep roadways is a major challenge for mine safety production. Taking a deep roadway with a burial depth of 965 m in a mine in North China as the engineering background, on-site investigation found that significant creep deformation occurred in the surrounding rock of the roadway. The original supporting U-shaped steel support failed due to insufficient supporting strength. The rock mass near the roadway experienced a transition from triaxial stress conditions to biaxial and even uniaxial stress states as a result of excavation and unloading, leading to a gradient stress distribution in the surrounding rock. From the perspective of the roadway's deviatoric stress field distribution, we investigated the gradient failure mechanism of the roadway and validated it through theoretical analysis and numerical simulations. The study found that the ratio of horizontal principal stress and vertical principal stress determines the distribution shape of the surrounding rock deviatoric stress field. The gradient distribution of the stress field in the roadway will cause time-related deformation of the roadway, which will lead to large deformation and failure of the roadway. Based on this, the control mechanism of roadway gradient failure was studied, and then a combined support technology of CFST supports with high bearing capacity was proposed.

Abbreviations

σ_r/MPa

Radial stress

σ_θ/MPa

Tangential stress

CFST

Concrete filled steel tube

τ/MPa

Shear stress

K

Lateral pressure coefficient

S₁/MPa

Maximum deviatoric stress

S₃/MPa

Minimum deviatoric stress

σ₁/MPa

Maximum principal stress

σ₂/MPa

Intermediate principal stress

σ₃/MPa

Minimum principal stress

R_p

Plastic zone radius

c

Cohesion

φ

Internal friction angle

r

The distance between any point and the center of the Roadway

θ

The angle between the line connecting any point and the center of the roadway and the horizontal direction

σ_ij/MPa

Stress state at a point

δ_ij

Kronecker symbol

q/MPa

Uniform load

σ₀/MPa

Mean stress

V

Surrounding rock creep coefficient

λ

Creep rate of surrounding rock

1. Introduction

In recent years, shallow underground resources have gradually depleted due to extensive extraction, leading to a shift towards deep-seated mining for resources like coal [1]. The excavation of deep roadways generates elevated in-situ stresses, non-linear substantial deformations, pronounced rheological behavior, frequent support component failures, and damage to surrounding rock [[2], [3], [4], [5]]. These challenges pose a formidable barrier to the safe and efficient extraction of underground resources. The imperative to investigate the destructive mechanisms of deep roadways and propose corresponding control technologies is evident [6,7].

Deep roadways are typically located within high-stress zones, and the surrounding rock typically undergoes a transition from elastic to plastic deformation, eventually reaching the point of fracture or even fragmentation after roadway excavation. The stress state and deformation characteristics of the surrounding rock at varying distances from the roadway center can vary significantly [8,9]. Consequently, effective control of deformation and failure in deep roadways necessitates a proper understanding of the deformation of the surrounding rock under different mechanical states and the mechanical mechanisms responsible for forming stable load-bearing structures under support conditions [10,11].

Scholars have conducted extensive research on the deformation mechanisms and control methods for deep roadways [[12], [13], [14]]. Dong were among the earliest to propose the theory of the loose zone in the surrounding rock, suggesting that roadway excavation and unloading can result in the formation of a certain range of damage zones [15]. Building on this, Zuo highlighted the significance of stress gradients as a crucial factor leading to rock mass failure [16]. They established a mechanical model for the gradient failure of deep roadways and investigated the influence of burial depth on stress gradients. Jing segmented deep soft-rock roadways from the roadway surface to deep within the surrounding rock into the plastic flow zone, strain-softening zone, plastic hardening zone, and elastic zone, deriving stress solutions for each zone [17]. Zhang employed three-dimensional modeling experiments to unveil the zonal failure phenomenon in deep roadways and established an elastic damage-softening model for zonal failure [18]. Zuo utilized numerical simulations to investigate the zonal failure in deep roadways. Their results indicated that, from the roadway surface to deep within the surrounding rock, the extent of microcracking in the failure zone gradually decreases [19]. Building upon the gradient failure mechanism of roadways, Zuo proposed the concept of a gradient support model and hierarchical control. Notably, they discovered that parameters such as fracture radius, support strength, and reinforcement thickness significantly impact gradient support [20].

Through field investigations, it has been observed that, based on zonal failure, the surrounding rock exhibits a gradient failure pattern in the radial direction of the roadway. Furthermore, an increase in roadway depth accentuates the gradient failure effect on the surrounding rock. The gradient failure phenomenon in deep roadways is particularly pronounced, as under the influence of unloading, the stress state of the surrounding rock transitions gradually from the remote triaxial virgin state to an approximately uniaxial stress state near the roadway edge [21,22]. The gradient failure of the surrounding rock results in substantial stress gradients within a defined range, gradual weakening of the mechanical properties of the rock mass, support component failures, and incidents of roadway instability and collapse.

According to the principles of elastoplastic mechanics, material deformation can be categorized into volumetric and shape deformations. Volumetric deformation in a material is induced by equal triaxial normal stresses, with the stress tensor governing the material's elastic deformation. Non-elastic deformation in materials primarily arises from shape deformations, with deviatoric stresses being a significant factor driving these shape changes. Consequently, deviatoric stress plays a pivotal role in understanding a material's non-elastic deformation. Deviator stress, considering the interaction between the magnitudes of principal stresses, provides a more comprehensive reflection of the stress state in rock masses under combined loading conditions. Fundamentally, it unveils the intrinsic nature of rock failure.

Extensive research has been conducted by scholars on the influence of deviator stress distribution on roadway surrounding rock. Wu investigating the impact of gently inclined close-distance coal seam mining on the deformation of transport roadways from the perspective of deviator stress distribution, it was observed that the asymmetric expansion of the roadway's plastic zone resulted from the combined effects of deviator stress distribution and the deflection of principal stresses [23]. The loading and unloading effects of roadway excavation alter the deviator stress distribution in surrounding rock, where an increase in deviator stress leads to tensional fracturing in shallow rock, shear sliding in the bearing zone, ultimately resulting in significant deformation of deep roadway surrounding rock. Chen investigating the deviator stress distribution patterns in roadway groups under varying coal pillar widths, a novel asymmetric reinforcement technique combining anchors, channel steel, and trusses was proposed [24]. Rui examining the influence of spherical stress components and deviator stress components on the stability of roadway surrounding rock, it was observed that, with a constant spherical stress component, an increase in deviator stress resulted in a wider plastic zone in the surrounding rock [25]. Similarly, with constant deviator stress, the plastic zone and the concentrated range of the difference in principal stresses increased with the augmentation of spherical stress. Experimental findings revealed that an increase in deviator stress further expanded the damage caused by unloading effects, leading to an accelerated rate of crack propagation within the surrounding rock [26]. Currently, research concerning the distribution patterns of deviatoric stress in roadways remains inadequate. Shan studied the asymmetric deformation mechanism by analyzing the deviatoric stress distribution of the surrounding rock of the near-fault roadway, and proposed corresponding support methods [[27], [28], [29]]. Zhao studied the evolution law of the deviatoric stress field of the lower coal seam roadway during the mining of the upper coal seam [30].

Field investigations have revealed that the damage to deep roadways often takes on a gradient destruction pattern. Currently employed support methods largely rely on empirical approaches, lacking in-depth research into the deformation mechanisms of roadways. The existing research primarily addresses the regularities in deviator stress distribution; however, there is a pressing need for more in-depth exploration of how deviator stress influences roadway deformation and the development of effective control technologies.

This article chooses the pump room roadway of a mine in North China as the engineering background, employs the principles of elastoplastic mechanics to analyze the mechanisms of gradient damage in deep roadway surrounding rock from the perspective of the deviator stress field distribution. In response to this failure mechanism, a joint control scheme for concrete-filled steel tube supports was proposed and successfully applied on site. This provides a certain reference for similar types of tunnel support in the future.

2. Project overview and roadway deformation and failure characteristics

2.1. Project overview

The background roadway is located in Handan City, Hebei Province, China. Its geological conditions are complex, faults are developed, and there are many collapse pillars. The burial depth is approximately 965 m, and the roadway layout is shown in Fig. 1. The rock types prevalent in the vicinity of the roadway primarily comprise sandy mudstone, along with coal seam 3. The cross-sectional shape of the roadway features a straight wall with a semi-circular arch, with a height of 3.2 m and a width of 4.2 m. The initial form of support employed was the U36 steel arch support, spaced at 800 mm intervals. After on-site investigation, it was found that significant creep deformation occurred in the surrounding rock of the roadway. The original supporting component, the U-shaped steel bracket, was greatly deformed due to the creep of the surrounding rock, seriously hampering the normal use of the roadway, as shown in Fig. 2.

Fig. 1.

Roadways layout [34].

Fig. 2.

Deformation characteristics of roadway.

2.2. Gradient deformation and failure characteristics of roadways

The excavation and unloading processes alter the stress state of the surrounding rock in roadways. The rock mass near the roadway experiences a transition from triaxial stress to biaxial and, ultimately, uniaxial stress states, depending on the distance from the roadway wall, as illustrated in Fig. 3. In the deep regions of the surrounding rock, unaffected by excavation disturbance, they remain in their virgin stress state. As the distance from the roadway decreases, the influence of excavation and unloading causes a gradual shift from triaxial to biaxial stress states. Within the biaxial stress state, the rock mass experiences minimal radial stress. However, as the zone of fracture in the roadway expands, an extreme stress condition emerges, where the lateral constraint forces on the rock mass near the roadway wall diminish to nearly zero. In this scenario, the rock mass is subjected to a uniaxial stress state, supported solely by gravity and the upward support from the roadway floor.

Fig. 3.

Schematic diagram of gradient failure of roadway caused by excavation.

To comprehensively assess the fragmentation and loosening patterns of the surrounding rock in the roadway, borehole inspections were conducted to observe the fractures and breakage in the rock mass beneath the original support. For this investigation, a mining-specific TS-C1201 borehole imaging instrument was employed. Boreholes were placed along the crown and sidewall sections of the test profile, with a borehole diameter of 32 mm, Fig. 4(a) and b are shown respectively.

Fig. 4.

Damage and destruction of surrounding rock in roadway.

Based on the observations of the surrounding rock in the roof, it is evident that within the 0–2.06 m range from the roadway wall, there are significant occurrences of both circumferential and radial fractures. These fractures exhibit considerable width and extensive distribution, frequently accompanied by hole collapse. At a depth of 1.92 m from the roof, abscission layer phenomena were noted. Within the 2.06–3.48 m range, circumferential fractures are densely distributed, while in the 3.48–4.54 m range, circumferential fractures appear intermittently. From 4.54 m to 6.95 m, circumferential fractures progressively diminish in size, with noticeably reduced fracture widths, often accompanied by inclined longitudinal fractures.

The observations of the surrounding rock in the sidewall revealed that within the 0–1.86 m range, the rock mass exhibits notable fragmentation, with multiple instances of fracture damage and a high density of circumferential cracks. In the 1.86–4.24 m range, there is a prevalent distribution of radial cracks, accompanied by occasional instances of circumferential fracture damage. As we descend to the 4.24–6.80 m range, there is a noticeable reduction in the density of radial cracks, coupled with narrower fracture widths. In this region, there is a substantial presence of inclined intersecting cracks and complex fractures.

In summary, the analysis reveals a gradient distribution of damage in the roadway's surrounding rock. The rock mass near the roadway wall experiences severe fragmentation, and as the depth of the boreholes increases, both the density and size of fractures follow a gradient reduction pattern. The stress state dictates the mode of rock mass failure. The stress state of the rock mass significantly varies from the roadway wall to deeper within the surrounding rock. Remote rock masses are less affected by excavation disturbances and remain closer to their virgin stress state. In contrast, the rock mass near the roadway undergoes unloading, with minimal or negligible radial stress. The stress state gradually transitions from triaxial to biaxial as the distance from the roadway wall increases. The rock mass at the roadway wall, as fragmentation progresses, experiences a diminishing lateral constraint, resulting in stress states approximating uniaxial stress.

3. Theoretical analysis of roadway surrounding rock stress

3.1. Analytical solution of stress in non-isobaric roadway

The complex stress field distribution within deep roadways, post-excavation, stands as a primary factor contributing to the deformation and failure of surrounding rock. With increasing burial depth, the ratio of the original rock stress to the secondary stresses relative to the rock mass strength escalates. Consequently, the surrounding rock undergoes extensive plastic deformation, predominantly taking the form of dilation deformation due to the influence of deviatoric stress fields. This dilation deformation is characterized by volume expansion resulting from the effect of deviatoric stress fields on the surrounding rock. This study approaches the mechanism of gradient failure in roadway surrounding rock from the perspective of deviatoric stress.

For simplification of calculations, this research focuses on circular roadways. Utilizing the principles of elastoplastic mechanics, roadway excavation is simplified into a plane strain circular opening problem, as illustrated in Fig. 5. It is assumed that the surrounding rock is an isotropic and homogeneous linear elastic body, and the load it receives is a uniform load [31,32]. The stress solution at any point in this mechanical model is as shown in Equation (1).

$$\begin{array}{c}{\sigma }_r\left(r,\theta \right)=\frac{1}{2}q\cdot \left(K+1\right)\cdot \left(1-\frac{a^2}{r^2}\right)+\frac{1}{2}q\cdot \left(K-1\right)\cdot \left(1-4\frac{a^2}{r^2}+3\frac{a^4}{r^4}\right)\cdot \cos 2\theta \\ {\sigma }_{\theta }\left(r,\theta \right)=\frac{1}{2}q\cdot \left(K+1\right)\cdot \left(1+\frac{a^2}{r^2}\right)-\frac{1}{2}q\cdot \left(K-1\right)\cdot \left(1+3\frac{a^4}{r^4}\right)\cdot \cos 2\theta \\ \tau \left(r,\theta \right)=\frac{1}{2}q\cdot \left(K-1\right)\cdot \left(1+2\frac{a^2}{r^2}-3\frac{a^4}{r^4}\right)\cdot \sin 2\theta \end{array}$$ (1)

In the above equation, q represents the vertical load borne by the roadway, a is the roadway radius, K denotes the ratio of horizontal stress to vertical stress, σ_r represents the roadway's radial stress, and σ_θ and τ respectively represent the circumferential stress and shear stress of the roadway.

Fig. 5.

Mechanical model of non-isobaric circular roadway (m).

Based on the principal stress calculation formula in the Cartesian coordinate system, a transformation from Cartesian coordinates to polar coordinates was performed. This resulted in the principal stress calculation formula for the roadway model in polar coordinates, as follows:

$$\begin{array}{c}{\sigma }_1=\frac{1}{2}({\sigma }_r+\sigma {}_{\theta })+\frac{1}{2}\sqrt{({\sigma }_r+\sigma {{}_{\theta })}^2+4{\tau }_{r\theta }^2}\\ {\sigma }_2=Kq\\ {\sigma }_3=\frac{1}{2}({\sigma }_r+\sigma {}_{\theta })-\frac{1}{2}\sqrt{({\sigma }_r+\sigma {{}_{\theta })}^2+4{\tau }_{r\theta }^2}\end{array}$$ (2)

3.2. Analytical solution of deviatoric stress in non-isobaric roadway

In the realm of elastoplastic mechanics, the stress state at a particular point is represented by a stress tensor, as shown in Equation (3). Based on the characteristics of deformation, this tensor is divided into the spherical stress tensor, which corresponds to volumetric deformations in the material, and the deviatoric stress tensor, which accounts for shape deformations. The former relates to changes in the material's volume, while the latter pertains to alterations in its shape.

$${\sigma }_{ij}=\left[\begin{array}{ccc}{\sigma }_1& 0& 0\\ 0& {\sigma }_2& 0\\ 0& 0& {\sigma }_3\end{array}\right]=\left[\begin{array}{ccc}{\sigma }_0& 0& 0\\ 0& {\sigma }_0& 0\\ 0& 0& {\sigma }_0\end{array}\right]+\left[\begin{array}{ccc}{\sigma }_1-{\sigma }_0& 0& 0\\ 0& {\sigma }_2-{\sigma }_0& 0\\ 0& 0& {\sigma }_3-{\sigma }_0\end{array}\right]$$ (3)

The deviatoric stress tensor governs the non-elastic deformation of materials. As per Equation (4), the deviatoric stress is a symmetric second-order tensor, and its three principal values, S₁, S₂ and S₃, correspond to the maximum, intermediate, and minimum deviatoric stresses, respectively. The calculation formula for these principal values is as follows:

$$s_{ij}=\left[\begin{array}{ccc}{\sigma }_1-{\sigma }_0& 0& 0\\ 0& {\sigma }_2-{\sigma }_0& 0\\ 0& 0& {\sigma }_3-{\sigma }_0\end{array}\right]=\left[\begin{array}{ccc}{s}_1& 0& 0\\ 0& s_2& 0\\ 0& 0& s_3\end{array}\right]$$ (4)

$${\sigma }_0=\frac{1}{3}\left({\sigma }_1+{\sigma }_2+{\sigma }_3\right)$$ (5)

$$S_i={\sigma }_i-{\sigma }_0\left(i=1,2,3\right)$$ (6)

$$\begin{array}{c}{S}_1={\sigma }_1-{\sigma }_0\\ S_3={\sigma }_3-{\sigma }_0\end{array}$$ (7)

According to Equation (7), S₁ and S₃ represent the deviation between the actual stress state of the surrounding rock and the average stress. The larger the value, the easier it is for the surrounding rock to be damaged. Substituting Equation (7) into Equation (2) gives Equation (8):

$$\begin{array}{c}{S}_1=\frac{1}{6}\left({\sigma }_r+{\sigma }_{\theta }\right)+\frac{1}{2}\sqrt{{\left({\sigma }_r-{\sigma }_{\theta }\right)}^2+4{\tau }^2}\\ S_3=\frac{1}{6}\left({\sigma }_r+{\sigma }_{\theta }\right)-\frac{1}{2}\sqrt{{\left({\sigma }_r-{\sigma }_{\theta }\right)}^2+4{\tau }^2}\end{array}$$ (8)

Substituting the above equation into Equation (1), the calculation formulas for the maximum and minimum deviator stress of the circular roadway can be obtained as follows:

$$S_1=\frac{1}{6}\left[\begin{array}{c}q\left(K+1\right)-\frac{2a^2\left(K-1\right)q\cos \left(2\theta \right)}{r^2}\\ +\frac{3}{2}\sqrt{\frac{q^2}{r^8}\left[\begin{array}{c}{\left[2a^2\left(K+1\right)r^2-2\left(K-1\right)\left(3a^4-2a^2{r}^2+r^4\right)\cos \left(2\theta \right)\right]}^2\\ +4{\left(K-1\right)}^2{\left(-3a^4+2a^2{r}^2+r^4\right)}^2{\sin }^2\left(2\theta \right)\end{array}\right]}\end{array}\right]$$ (9)

$$S_3=\frac{1}{6}\left[\begin{array}{c}q\left(K+1\right)-\frac{2a^2\left(K-1\right)q\cos \left(2\theta \right)}{r^2}\\ -\frac{3}{2}\sqrt{\frac{q^2}{r^8}\left[\begin{array}{c}{\left[2a^2\left(K+1\right)r^2-2\left(K-1\right)\left(3a^4-2a^2{r}^2+r^4\right)\cos \left(2\theta \right)\right]}^2\\ +4{\left(K-1\right)}^2{\left(-3a^4+2a^2{r}^2+r^4\right)}^2{\sin }^2\left(2\theta \right)\end{array}\right]}\end{array}\right]$$ (10)

In order to facilitate research, this paper uses the special value method to study the deviatoric stress distribution law of the roadway according to Equations (9), (10). Among them, the roadway radius a = 2 m and q = 20 MPa. Fig. 6 (a)～(j) shows the distribution rules of the maximum and minimum deviator stress when K is 0.5, 1.0 and 1.5 respectively.

Fig. 6.

Deflector stress distribution diagram of roadway.

Based on Fig. 6, it becomes apparent that concerning the maximum deviatoric stress, S₁, the closer the distance to the roadway center, the greater the magnitude of S₁. Conversely, the minimum deviatoric stress, S₃, increases with the distance from the roadway center. When K = 1, the distribution of S₁ and S₃ exhibits a circular and center-symmetric pattern. Their values depend solely on the radial distance and remain independent of the azimuthal angle. For K < 1, the deviatoric stresses near the roadway walls are more concentrated, with the roadway's roof and floor serving as regions for deviatoric stress release. Conversely, when K > 1, the distribution of S₁ is opposite to that when K < 1, with the roadway's roof and floor becoming regions of deviatoric stress concentration, while the roadway walls act as deviatoric stress release zones.

For K ≤ 1, the maximum value of S₁ decreases with an increase in the lateral confinement coefficient, while for K ≥ 1, the maximum value of S₁ increases with increasing lateral confinement. The relationship between S₁ and K exhibits a concave distribution pattern, with the minimum value attained at K = 1. As for S₃, when K ≤ 1, the minimum value increases with an increase in the lateral confinement coefficient, and when K ≥ 1, the maximum value of S₁ decreases with increasing K. The relationship between S₃ and K follows a convex distribution pattern, with the maximum value achieved at K = 1.

The distribution patterns of S₁ and S₃ indicate that the maximum deviatoric stress decreases radially along the roadway's radius from the roadway wall, while the minimum deviatoric stress increases radially from the roadway wall. According to elastoplastic mechanics, the magnitude of deviatoric stress indicates the difference between the actual stress state and the average stress state of the surrounding rock. Therefore, the magnitude and rate of change of deviatoric stress can better reflect the damage of surrounding rock. According to Fig. 6, it can be seen that the distribution of deviatoric stress also shows gradient distribution after excavation of the roadway, which is the main reason for the gradient damage of the surrounding rock.

3.3. Theoretical calculation of roadway plastic zone range

Assuming that the surrounding rock of the roadway undergoes continuous transition to an ideal plastic state, the Mohr-Coulomb strength envelope line, representing plastic deformation, is determined by c and φ and forms a straight line, as depicted in Fig. 7. Based on the Mohr's circle at the limit state, the rock mass exhibits the following plastic behavior:

$$\sin \phi =\frac{{\sigma }_1-{\sigma }_3}{{\sigma }_1+{\sigma }_3+2c\cot \phi }$$ (11)

Fig. 7.

Maximum shear stress strength criterion.

Substitute formula (1) and formula (7) into the above formula:

$$R_p=\sqrt{\frac{2a^{2}q\left(1-K\right)\sin \phi \cos 2\theta }{2c\cos \phi +q\left(1+K\right)\sin \phi -\left(S_1-S_3\right)}}$$ (12)

Equation (12) shows that the radius of the plastic zone of the roadway is closely related to the size of the deviatoric stress.

Substituting Equation (1) into Equation (11), the invisible equation of the boundary of the surrounding rock plastic zone with respect to r and θ can be obtained:

$$\begin{gathered} \begin{array}{c}f\left(r,\theta \right)={\left\{q\left(K+1\right)\frac{a^2}{r^2}-q\left(K-1\right)\cos 2\theta \left[1+3{\left(\frac{a^2}{r^2}\right)}^2-2\frac{a^2}{r^2}\right]\right\}}^2 \\ +{\left\{q\left(K-1\right)\sin 2\theta \left[1-3{\left(\frac{a^2}{r^2}\right)}^2+2\frac{a^2}{r^2}\right]\right\}}^2-\frac{\left(1-\cos 2\phi \right)}{2}\\ \begin{array}{c} \\ \times \left\{{\left[q\left(K+1\right)-2\cos 2\theta \cdot \frac{a^2}{r^2}q\left(K-1\right)\right]}^2-4c^2\right\}\\ -2c\sin 2\phi \left[q\left(K+1\right)-2\frac{a^2}{r^2}q\left(K-1\right)\cos 2\theta \right]-4c^2\end{array}\end{array} \end{gathered}$$ (13)

When f(r,θ) = 0, the dividing line equation between the elastic zone and the plastic zone of the surrounding rock can be obtained. Substituting q = 20 MPa, a = 2 m, c = 3 MPa, and φ = 30° into the above equation, the plastic zone boundaries were calculated when K was 0.25, 0.5, 1, and 1.5 respectively. Fig. 8 shows the radius of the plastic zone of the surrounding rock corresponding to different K values. When K = 1, the plastic zone of the roadway is circularly distributed, regardless of the azimuth angle θ. When K < 1 and as K decreases, the shape of the plastic zone gradually develops from a circle to a flat elliptical shape, and the plastic zone radius of the left and right sides is larger than the plastic zone radius of the top and bottom plates. As K continues to decrease, the plastic zone gradually exhibits a butterfly-shaped distribution pattern, the plastic zone range of the top, bottom plate and upper part decreases, and the plastic zone range of the shoulder expands significantly. When K > 1, the plastic zone of the surrounding rock transitions from circular to elliptical, with the long axis located in the vertical direction, showing a thin and tall distribution characteristic.

Fig. 8.

Plastic zone radius distribution of roadway.

4. Numerical simulation analysis of roadway deviator stress distribution

As mentioned earlier, the deviatoric stress distribution in the surrounding rock of a roadway exhibits a gradient pattern due to the excavation and unloading effect. The stress state of the surrounding rock gradually transitions from a triaxial stress state in the far end of the roadway to an approximate uniaxial stress state near the roadway walls. The distribution of deviatoric stress is a crucial factor in the occurrence of gradient failure in the surrounding rock. In this section, we utilize numerical simulations to investigate the post-excavation distribution characteristics of deviatoric stress.

Considering the geological conditions of the studied roadway, as shown in Table 1, we established a numerical computational model for the roadway, as depicted in Fig. 9. The dimensions of this model are Length × Width × Height = 50 × 3.2 × 36 m. The model comprises a total of 17,110 nodes and 13,312 elements. The roadway section adopts a straight wall semicircular arch design with dimensions Width × Height = 4.2 × 3.2 m. The mesh is divided through the Extrusion function. Through multiple trial calculations, the grid was continuously adjusted and improved until there was no grid distortion or stress concentration in the surrounding rock under the action of the initial in-situ stress field.

Table 1.

Physical and mechanical parameters of rock formations.

Rock formations	Modulus of elasticity	Density	Internal friction angle	Cohesion	Tensile strength
	(GPa)	(kg•m−3)	(°)	(MPa)	(MPa)
fine sandstone	14.8	2550	34	9.20	2.7
sandy mudstone	10.9	2400	32.4	7.52	2.1
3#coal	0.99	1600	26.5	0.82	1.9
mudstone	8.65	2450	30.5	6.54	1.9
siltstone	11.6	2500	36.8	7.15	2.5
4#coal	0.8	1600	28.6	0.85	1.5
limestone	15.7	2600	36	11.44	3.1

Fig. 9.

Numerical calculation model.

According to the measured results of on-site in-situ stress, uniform loads of 27.35 MPa and 28.3 MPa were applied to the model in the vertical and horizontal directions respectively, and the simulated burial depth was 965 m. The calculation uses a strain softening model and simulates excavation by assigning a null model to the model. The excavation step distance is 3.6 m. The X and Y directions respectively limit the horizontal displacement of the boundary, the Z direction limits the vertical displacement of the boundary, and the Y direction is the direction of roadway excavation. The physical parameters of the rock layers within the model are derived from laboratory test results, as presented in Table 1.

Based on the custom cloud chart function of Flac3D software, equations (5), (6), (7) are input into the model to obtain the deviatoric stress cloud chart of the surrounding rock of the roadway. This section calculates the distribution patterns of the maximum and minimum deviatoric stress in the surrounding rock after roadway excavation. Fig. 10(a)～(j) represents contour plots of the maximum and minimum deviatoric stresses in the surrounding rock for different values of the ratio K, which represents the ratio of horizontal principal stress to vertical principal stress. The K values considered are 0.5, 1, and 1.5.

Fig. 10.

Deviator stress distribution cloud diagram of roadway under different lateral pressure coefficients.

Based on Fig. 9, it is evident that the deviatoric stress distribution in the roadway exhibits a gradient pattern, and its shape varies with different K values. Regarding the maximum deviatoric stress, when K is less than 1, the maximum deviatoric stress decreases as K increases. Conversely, when K is greater than 1, the maximum deviatoric stress increases with increasing K, displaying a concave deformation trend. The minimum value of the maximum deviatoric stress is achieved when K = 1, at 23.6 MPa. In contrast, for the minimum deviatoric stress, it exhibits a convex shape with an upward trend as K increases. When K = 1, the maximum value is −6.05 MPa.

When K is less than 1, both the maximum and minimum deviatoric stresses are concentrated in the roadway's walls. On the other hand, when K is greater than 1, both the maximum and minimum deviatoric stresses are concentrated at the roadway's roof and floor positions. At K equals 1, both the maximum and minimum deviatoric stresses are evenly distributed along the roadway's edges and exhibit a radial gradient, spreading outward.

According to the results of 3.2 theoretical analysis, the magnitude of deviatoric stress indicates the difference between the actual stress state and the average stress state of the surrounding rock. The magnitude and rate of change of bias stress can better reflect the damage of surrounding rock. Therefore the roadway support should focus on these areas.

5. Control technology of high bearing capacity pressure equalizing support

5.1. Principles of control technology

It can be seen from the above that the greater the deviatoric stress of the surrounding rock, the greater the deviation between its actual stress state and the average stress state. I The area of concentration of deviatoric stresses in the surrounding rock is also characterized by a higher degree of gradient damage. In deep roadways, under the influence of gradient stress, the surrounding rock undergoes creep deformation towards the roadway's interior, eventually resulting in the failure of the support structure and roadway collapse. Therefore, it is necessary to consider roadway failure mechanisms, surrounding rock stress conditions, and surrounding rock creep deformation as an integrated study.

As shown in Fig. 11, assuming the roadway is circular and the surrounding rock is homogeneous, after a time interval of Δt, the creep deformation ε of the surrounding rock towards the roadway's interior can be calculated. The relationship between the creep rate of the surrounding rock and the radial stress gradient is expressed as follows:

$$V=\lambda \left({\sigma }_r-{\sigma }_{r0}\right)/\left(r-r_0\right)$$ (14)

In the equation above, V represents the creep rate of the surrounding rock, λ stands for the creep coefficient, which is related to the physical properties of the surrounding rock. A larger creep coefficient leads to a faster creep rate in the surrounding rock. σ_r represents the radial stress at a distance r from the center of the roadway. From the equation above, it's evident that the creep rate of the surrounding rock is directly proportional to the radial stress gradient in the roadway. The greater the radial stress gradient, the more pronounced the creep deformation in the roadway.

Fig. 11.

Stress distribution of surrounding rocks in deep roadways.

Based on Equation (14), there are two ways to reduce the stress gradient: Increase the support force at the roadway's edge to decrease the radial stress difference between the roadway's edge and the deep surrounding rock. When the support force at the roadway's wall is equal to the stress in the deep surrounding rock (σ_r = σ_r0,V = 0), V = 0, and, in this case, the surrounding rock doesn't undergo creep deformation. Select a reasonable method for loading and unloading pressure and control the unloading distance to shift the stress peak towards the deep surrounding rock. This doesn't change the radial stress difference but increases the difference between the distance from the stress peak to the roadway center (r) and the roadway radius (r₀). These strategies can help mitigate the risk of gradient deformation and failure in the surrounding rock of the roadway.

5.2. Full-scale comparison test of mechanical properties of support

• (1)Experimental program design

To further understand the mechanical properties of CFST supports, the research group designed a comparative test between CFST supports and U36 steel arch frames, as shown in Fig. 12(a) and (b) respectively [33]. The deformation characteristics, failure mode, and bearing capacity performance of the supports of the two structures under load are compared and analyzed. Choose a round seamless steel pipe with a size of φ194 × 8 mm, and choose C40 for the core concrete model. Each frame consists of 4 sections: the top arc section, the two side sections, and the bottom arc section. A sleeve connects each section with a size of φ219 × 8 mm. The overall size of the support is width × height = 4300mm × 3761 mm. At the same time, a U36 steel arch frame of the same size is designed as a comparison.

Fig. 12.

Indoor contrast test of steel tube concrete support and U36 steel arch frame [33].

Four pressure-bearing plates are arranged on the support's upper, lower, left, and right boundaries. The bearing plates are of the same interaction, material, and type as the supports, ensuring that the concentrated load of the jack is converted into a normal, uniform load. A 500t jack is set vertically, and two 200t jacks are set horizontally for loading. Among them, the loading in the vertical direction is controlled, and the loading in the horizontal direction is constrained, as shown in Fig. 12. According to theoretical estimates, the ultimate vertical load of CFST support is about 2000 kN, and the maximum vertical load of the U36 steel arch is about 600 kN. Static loading is adopted in stages and loaded in 30–50 stages. Vertical loads are carried out simultaneously with horizontal loads. For CFST, when the load increases to 1000 kN, the horizontal load remains unchanged, and the vertical load continues. The U36 steel arch frame does not improve after the horizontal load reaches 500 kN, and the vertical load continues to increase. To allow the specimen to deform fully, each load lasts about 2 min. Record the data after the deformation of the specimen is stable. The load-displacement curve recorded by the specimen is shown in Fig. 13.

• (2)Analysis of test results

Fig. 13.

Load-displacement curves of CFST Support and U36 steel arches.

According to the test curves, the load-displacement curves of the two supports are divided into four stages. They are the approximately elastic stage, the strengthening stage, the strength decreasing stage, and the unloading stage. The CFST support produces an almost elastic overall deformation at the initial loading phase. When the vertical load is 1597.8 kN, the top arc section of the support has obvious sinking deformation, and the sound of concrete being pulled and cracked in the steel pipe can be heard. When the load is 1709.5 kN, the top arc section is flattened, and the sleeves on both sides of the shoulder appear to have extrusion expansion deformation. When the load dropped to 1427.5 kN, inward concave deformation occurred on the top arc of the support, and the two sides also contracted inward.

The load-displacement curve of the U-shaped steel support is also divided into the above four stages. Its elastic limit is about 569.5 kN, and when the vertical load is 644.3 kN, the bearing capacity of the support decreases. During the test, the lapped section at the top of the U-shaped steel support was significantly deformed. At the end of the trial, it was found that due to the insufficient torsional rigidity of the section, the U-shaped steel support had a large twist deformation. Compared with the U-shaped steel support, the elastic limit of the steel tube concrete support is increased by 2.8 times, and the ultimate bearing capacity is increased by about 2.65 times. The bearing capacity of the steel tube concrete support is much higher than that of the U-shaped steel support, which can provide vital support resistance for the surrounding rock.

5.3. Combined support design

Based on on-site investigations, it was observed that the original U-shaped steel supports in the roadway experienced severe bending and even failure due to insufficient load-bearing capacity, as shown in Fig. 14. In response to this, we have designed a combined support system using CFST supports, as illustrated in Fig. 15. The steel-reinforced concrete supports feature a semi-circular arch with a width-height ratio of 4.2 m × 3.2 m, with each section spaced at 800 mm intervals. The support structure consists of three main components: the top arch section and the left and right side wall sections, which are interconnected with casing. The steel pipes have a diameter of 194 mm with an 8 mm wall thickness, while the casing has a diameter of 219 mm with an 8 mm wall thickness.

Fig. 14.

U-shaped steel support damage phenomenon.

Fig. 15.

CFST support design.

To enhance the physical mechanical properties of the surrounding rock and ensure better support-to-rock contact, we reinforced the roadway edge rock using a combination of post-grouting and shallow grouting. Grouting helps strengthen the surrounding rock and prevents stress concentration on the support structures. For shallow grouting of the surrounding rock, seven grout holes are arranged at each cross-section, with a hole depth of 3 m and grouting pressure of 4 MPa. Post-grouting includes five grout holes per cross-section, with a hole depth of 1 m and grouting pressure of 3 MPa. In the later stage of construction, in order to control the deformation of the two sides, additional anchor rods were installed on both sides to strengthen the support of the straight wall section of the roadway.

5.4. Support effect evaluation

This paper uses numerical simulation methods to establish numerical models of the roadway's original U36 steel arch support and CFST combined support. Detailed parameters used in the numerical models are provided in Section 4. In these numerical models, structural components are simulated using the structural units available in FLAC3D. The support system is represented using Beam elements, with specific parameters detailed in Table 2. For anchor rods, Cable elements are used for simulation, with an elastic modulus of 200 GPa and a yield strength of 500 MPa.

Table 2.

Mechanical parameters of scaffold structural units.

Support type	Cross sectional area (cm2)	Elastic modulus (GPa)	Poisson's ratio	Section moment of inertia
				Ix (cm4)	Iy (cm4)
U36	45.69	210	0.27	928.65	1244.75
Steel tube	46.75	206	0.30	2452.30	2452.30
Infill concrete	248.85	41	0.22	4497.25	4497.25

Fig. 16 (a)～(d) illustrates the displacement convergence of the roadway under two different support schemes. Under the U36 steel arch support, the maximum displacement at the roadway roof is 153.26 mm, whereas the employment of the CFST combined support scheme results in a maximum roof displacement of 57.7 mm, a reduction of 62.35 %. The maximum floor displacement under the original support is 161.33 mm, and this value is reduced to 80.897 mm with the combined support, marking a decrease of 49.86 %. The maximum horizontal displacement under the original support is 202.02 mm, and this is reduced to 77.61 mm with the optimized approach, signifying a 61.58 % reduction. It is evident that the application of the combined support scheme significantly improves the displacement convergence in various directions of the roadway.

Fig. 16.

Laneway displacement (m).

Fig. 17(a) and (b)illustrates the distribution of the plastic zone under both support schemes. The relatively low support resistance of the U36 steel arch results in a larger plastic zone in the roadway roof. In the original support scheme, with no reinforcement measures for the roadway sidewalls, the plastic zone extends significantly. CFST supports, with their higher support resistance, in conjunction with pre-stressed anchor rods in the sidewalls and shoulders, noticeably improve the overall plastic zone distribution in the roadway. The plastic zone radius significantly decreases, particularly in the roadway sidewalls to the roof arch region, demonstrating effective control over the surrounding rock deformation. Comparing the numerical simulation results of the two support schemes, it becomes evident that the new support scheme effectively mitigates roadway deformation and the expansion of the plastic zone.

Fig. 17.

Development of roadway plastic zone.

5.5. On-site monitoring

To accurately assess the stability of the roadway under CFST combined support, monitoring points were set up in the roadway during on-site investigations. The cross-point method was employed to monitor deformations in roadway displacement. Fig. 18 depicts the displacement monitoring curve for the roadway under CFST combined support. The graph reveals a three-stage deformation trend in the roadway over a monitoring period of 152 days. They are the early rapid deformation stage, the slow deformation stage and the stable deformation stage.

Fig. 18.

Roadway displacement monitoring under joint support.

In the initial stages of support installation, the roadway experienced rapid deformation. By the 15th day of monitoring, the roadway's roof and floor displacements had reached 101.87 mm and the sidewall convergence was 82.18 mm, accounting for 70.7 % and 64.2 % of the total deformation, respectively. This emphasizes that the bulk of roadway deformation occurred during the initial phase of rapid transformation. Around the 87th day of monitoring, the roadway's deformation rate stabilized, the deformation of the roadway enters the stable deformation stage. At this point, the roof and floor displacements were measured at 141.86 mm and 123.27 mm, respectively, contributing to 98.5 % and 96.3 % of the total deformation, showcasing a stable phase of deformation.

Fig. 19 shows the construction process of concrete-filled steel tube supports. Through on-site investigations and continuous monitoring, it was observed that for an extended period after implementing the combined support approach, the roadway's arch and sidewalls exhibited no significant deformations or damage. No major deformations in the supports or peeling of the sprayed concrete lining on the roadway surface were observed. Additionally, the surrounding rock at the roadway walls, having undergone reinforcement through combined support, maintained a favorable three-directional stress state, with no discernible signs of tension or shear cracks. This evidence underscores the positive effects of the new control technology in sustaining the long-term stability of the roadway, effectively mitigating deformation and damage trends in the surrounding rock.

Fig. 19.

Field application of CFST supports.

6. Conclusion

• (1)Investigation revealed that deep roadwaying in radial directions leads to a gradient failure phenomenon. The surrounding rock near the roadway undergoes triaxial stress states, biaxial stress states, and uniaxial stress states. Moving radially outward from the roadway's center, the surrounding rock transitions from uniaxial to biaxial and eventually triaxial stress states. This results in the formation of a gradient stress field in the surrounding rock, which consequently leads to gradient failure.
• (2)The formula for calculating the distribution law of deviatoric stress and the range of plastic zone of circular non-isobaric roadway is theoretically deduced. It is found that the deviatoric stress field of the surrounding rock after the roadway excavation shows the law of gradient distribution. The larger the surrounding rock deviatoric stress is, the larger the difference between its actual stress state and the average stress is, the more significant the stress gradient effect is formed, and the larger the degree of damage to the surrounding rock is. Numerical calculation results show that the ratio of horizontal stress to vertical stress K determines the distribution pattern of the tunnel deviatoric stress field and plastic zone. When K is less than 1, the deviatoric stress on the side of the roadway is concentrated, and when K is greater than 1, the deviatoric stress on the roof and floor of the roadway is concentrated.
• (3)Addressing the time-dependent failure characteristics of deep roadway surrounding rock, it was observed that increasing support reaction forces and reserving unloading space can mitigate stress gradients, thereby controlling the continuous deformation and failure of deep roadway surrounding rock. A combined support design of CFST support is proposed, and the numerical calculation results show that the deformation of the surrounding rock and the expansion of the plastic zone under the combined support scheme have been effectively controlled, and the field application has also achieved good results.

Data availability statement

Research-related data are not deposited into publicly available repositories.

Data will be made available on request.

CRediT authorship contribution statement

Hai long Wang: Writing – review & editing, Resources, Project administration. Dong Liu: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Conceptualization. Ren liang Shan: Writing – review & editing, Supervision, Resources. Yan Zhao: Investigation, Data curation. Zhao long Li: Software. Xiao Tong: Investigation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.