Numerical Simulation of Fracture Failure Propagation in Water-Saturated Sandstone with Pore Defects Under Non-Uniform Loading Effects

Abstract

The instability of mine roadways is significantly influenced by the coupled effects of groundwater seepage and non-uniform loading. These interactions often induce localized plastic deformation and progressive failure, particularly in the roof and sidewall regions. Seepage elevates pore water pressure and deteriorates the mechanical properties of the rock mass, while non-uniform loading leads to stress concentration. The combined effect facilitates the propagation of microcracks and the formation of shear zones, ultimately resulting in localized instability. This initial damage disrupts the mechanical equilibrium and can evolve into severe geohazards, including roof collapse, water inrush, and rockburst. Therefore, understanding the damage and failure mechanisms of mine roadways at the mesoscale, under the combined influence of stress heterogeneity and hydraulic weakening, is of critical importance based on laboratory experiments and numerical simulations. However, the large scale of in situ roadway structures imposes significant constraints on full-scale physical modeling due to limitations in laboratory space and loading capacity. To address these challenges, a straight-wall circular arch roadway was adopted as the geometric prototype, with a total height of 4 m (2 m for the straight wall and 2 m for the arch), a base width of 4 m, and an arch radius of 2 m. Scaled physical models were fabricated based on geometric similarity principles, using defect-bearing sandstone specimens with dimensions of 100 mm × 30 mm × 100 mm (length × width × height) and pore-type defects measuring 40 mm × 20 mm × 20 mm (base × wall height × arch radius), to replicate the stress distribution and deformation behavior of the prototype. Uniaxial compression tests on water-saturated sandstone specimens were performed using a TAW-2000 electro-hydraulic servo testing system. The failure process was continuously monitored through acoustic emission (AE) techniques and static strain acquisition systems. Concurrently, FLAC^3D 6.0 numerical simulations were employed to analyze the evolution of internal stress fields and the spatial distribution of plastic zones in saturated sandstone containing pore defects. Experimental results indicate that under non-uniform loading, the stress–strain curves of saturated sandstone with pore-type defects typically exhibit four distinct deformation stages. The extent of crack initiation, propagation, and coalescence is strongly correlated with the magnitude and heterogeneity of localized stress concentrations. AE parameters, including ringing counts and peak frequencies, reveal pronounced spatial partitioning. The internal stress field exhibits an overall banded pattern, with localized variations induced by stress anisotropy. Numerical simulation results further show that shear failure zones tend to cluster regionally, while tensile failure zones are more evenly distributed. Additionally, the stress field configuration at the specimen crown significantly influences the dispersion characteristics of the stress–strain response. These findings offer valuable theoretical insights and practical guidance for surrounding rock control, early warning systems, and reinforcement strategies in water-infiltrated mine roadways subjected to non-uniform loading conditions.

1. Introduction

In geotechnical engineering and underground space development, rock mass instability is a critical issue that poses a significant threat to engineering safety. Recent studies have demonstrated that rock mass failure often does not occur under uniform loading conditions; instead, it is triggered by the combined effects of non-uniform loading and multiple physical factors, such as groundwater and chemical processes [1,2,3]. In tunnel engineering, excavation disturbances or structural asymmetry can lead to substantial stress redistribution within the rock mass, resulting in localized zones of high-stress concentration. Concurrently, groundwater infiltrates through fractures, exacerbating the softening of joint surfaces, increasing pore water pressure, and degrading cementation structures. This ultimately promotes the degradation of rock mass strength and the propagation of fractures, potentially leading to sudden structural instability.

In practical geotechnical engineering applications such as tunnel excavation and underground mining, rock masses are frequently subjected to non-uniform loading conditions, which can induce localized stress concentrations, crack initiation, and progressive failure. Wang et al. and Yu et al. [4,5] investigated these phenomena by designing trapezoidal rock specimens and employing asymmetric loading devices to examine the failure characteristics of cavity-bearing rocks. Zhao and Ge et al. [6,7] further explored the coupled effects of eccentric external loading and internal voids, proposing damage constitutive models to characterize stress redistribution and fracture initiation mechanisms. These studies provide essential theoretical guidance for understanding rock failure behavior under complex loading paths and offer a solid basis for the experimental design and analysis of fracture evolution in saturated sandstone under non-uniform loading in this study.

The interaction between water and rock plays a crucial role in influencing the mechanical behavior of rock masses, particularly in groundwater-rich geological environments [8]. Li, Duan, Zhang, and Zhou et al. [9,10,11,12] systematically examined how variations in water content, pore pressure, and fracture network characteristics affect rock strength, energy dissipation, and crack propagation through uniaxial compression, direct shear tests, and infrared thermography. Thörn and Cardona et al. [13,14,15] focused on the nonlinear relationship between fracture aperture behavior and fluid flow, emphasizing that fracture permeability is highly sensitive to microstructural changes during closure and reopening cycles. He et al. [16] further demonstrated that water saturation and crack tip intersection angles significantly influence the mechanical response and fracture trajectories in sandstone. These findings deepen the understanding of hydro-mechanical coupling mechanisms and provide crucial support for this study’s investigation into water-induced damage and fracture behavior in saturated rock.

Geometric characteristics of rock masses, such as fracture inclination, cavity shape, and spatial configuration, are key factors governing fracture initiation and propagation. Luo and Chen [17,18] employed PFC2D with the parallel bond model to simulate the nonlinear effects of various fracture inclinations and loading rates on rock failure modes. Further research by Luo et al. [19] indicated that a fracture dip angle of 15° results in the most severe stress concentration at the crack tip and shows a strong nonlinear relationship between peak strength and loading rate. Tian [20] used fluid–structure coupling simulations to reveal a permeability “jump phenomenon” during crack propagation, supporting Cardona’s [14] model of abrupt hydraulic transitions in natural fracture systems. Zhang and Zhu [21,22] integrated acoustic emission monitoring with energy analysis to highlight the dominant role of fracture geometry in controlling damage evolution and failure mechanisms. These insights provide a solid theoretical foundation for this study’s focus on the influence of cavity geometry on stress localization and fracture development under coupled hydro-mechanical conditions.

In summary, substantial progress has been made in the study of non-uniform loading, hydro-mechanical coupling, and fracture geometry effects, which has laid a solid foundation for understanding the damage evolution behavior of rock masses. However, existing research often focuses on the influence of single factors, lacking a systematic understanding of the coupling mechanisms between non-uniform loading and saturated environments. In particular, under engineering scenarios such as roadway excavation and deep groundwater infiltration, the multidimensional interactions among crack propagation, stress distribution, fluid flow, and structural features remain to be fully clarified. Therefore, investigating the mechanical behavior and fracture evolution of saturated porous rock specimens under non-uniform loading conditions is essential to provide theoretical support for engineering stability assessment and disaster prevention (Figure 1).

2. Geological Control Factors of Mining Tunnel Stability Under Groundwater Erosion

In underground mining engineering, long-term groundwater seepage and erosion are among the principal factors governing the structural evolution and failure mechanisms of deep rock masses. The impact of groundwater on the stability of mining tunnels is comprehensively controlled by various geological conditions, including rock mass structure, lithological characteristics, the degree of weathering, and the spatial distribution of tectonic fracture zones. For instance, Bayat et al. [23] investigated the Nowsud Tunnel and reported that in karst regions, the coupling between fault zones and groundwater activity readily forms water inrush pathways, significantly compromising tunnel stability. Coli [24] highlighted that groundwater seepage through tectonic fracture zones often exhibits transient flow behavior, with hydraulic properties playing a critical role in the evolution of surrounding rock stress fields. Hack [25] emphasized that rock weathering not only reduces shear strength but also accelerates hydration and dissolution processes, which in turn hasten rock mass degradation. Moreover, Xing et al. [26], based on studies of an underground mine in the United States, demonstrated that stress concentration and seepage interaction in structurally complex zones are key mechanisms triggering instability and failure.

(1) The structural characteristics of the rock mass control the groundwater seepage path and the integrity of the surrounding rock structure. Discontinuous features such as joints, fractures, bedding planes, and faults are commonly present, forming high-permeability flow channels. These structural discontinuities not only reduce the overall strength of the rock mass but also provide active interfaces for water–rock interactions, significantly diminishing shear strength, which may result in structural displacements and slippage.

(2) Lithology and the physical–mechanical properties of the rock mass directly determine the response to water erosion. Weakly cemented and highly porous rocks, such as sandstone, mudstone, and shale, are highly susceptible to softening, swelling, and deterioration under the influence of water, leading to rapid loss of strength and stiffness. In contrast, dense and erosion-resistant rocks, such as granite and quartzite, exhibit greater stability under water exposure and retain superior mechanical properties.

(3) Both the degree of weathering and the intensity of tectonic fracturing are critical geological controls on the erosive impact of groundwater. Highly weathered zones are typically characterized by high porosity, low cementation, and a loose structural framework, making them highly susceptible to groundwater infiltration and associated deterioration. In contrast, tectonic fracture zones—marked by extensive rock fragmentation and enhanced permeability—often act as primary channels for groundwater accumulation and flow and are frequently correlated with increased risks of surrounding rock instability.

Although these geological factors provide pathways for groundwater seepage and weaken the mechanical properties of the surrounding rock, they are typically latent triggers. The primary cause of tunnel instability and failure is often the combined effect of groundwater erosion and a non-uniform stress field. Mining-induced disturbances alter the in situ stress distribution, creating localized zones of high-stress concentration. When these high-stress areas are further affected by water-induced softening, the surrounding rock undergoes dual degradation: structural weakening and loss of load-bearing capacity, which leads to the initiation of the failure process characterized by “stress release—crack propagation—structural collapse”. Therefore, the stress–water coupling effect not only integrates geological conditions but also serves as the primary driving mechanism for the transition of the surrounding rock from stable to unstable. Thus, studying the evolution of rock damage and failure under stress–water coupling is critical for improving our understanding of tunnel instability and failure modes under groundwater erosion.

3. Specimen Preparation and Testing Program Design

3.1. Specimen Preparation

Due to the large scale of underground tunnel engineering, complex geological conditions, and the significant safety risks associated with on-site testing, conducting comprehensive and systematic studies at the prototype scale presents substantial challenges. To more effectively simulate the mechanical response of mining tunnels in real-world engineering scenarios, this study focuses on a typical straight-wall circular arch tunnel as the research subject. The prototype tunnel structure has a total height of 4 m, consisting of a straight wall section of 2 m and an arch height of 2 m. The bottom width is 4 m, and the arch employs a semicircular design with an arch radius of 2 m. The prototype structure was scaled down proportionally using the principles of geometric similarity at a ratio of 1:100 to create small-scale specimens.

The specimens used in this study were prepared from natural sandstone parent rock [27], known for its excellent integrity. Prior to specimen preparation, the parent rock was manually selected to ensure the absence of significant fractures, joints, or weathering marks, thereby enhancing the representativeness of the specimens and the stability of the experimental data. Initially, a diamond saw cutting machine was used to make rough cuts in the parent rock, shaping it into rectangular blocks. Subsequently, precision cutting and grinding equipment was employed to refine these blocks into standard rectangular specimens with dimensions of 100 mm × 30 mm × 100 mm (length × width × height). Throughout the process, strict control over processing precision was maintained, with repeated measurements to ensure dimensional deviations remained within ±0.5 mm, significantly reducing experimental errors due to size discrepancies. After processing, all specimens were rechecked for dimensions using a vernier caliper to ensure consistency.

A standardized hole was designed and fabricated in the central region of each specimen to simulate the typical tunnel structure in underground engineering. This hole features a straight-wall circular arch geometry, with a rectangular base measuring 40 mm in length and 20 mm in width. The straight wall height is 20 mm, and the top is shaped as a semicircular arch with a radius of 20 mm. The hole structure was designed according to the principles of similarity theory and mechanical model similarity, ensuring that the structural characteristics of the prototype tunnel and the stress distribution pattern in the surrounding rock are preserved. This approach guarantees that the mechanical behavior of the prototype tunnel is accurately represented in the small-scale model specimens, providing a reliable engineering analog. Through this meticulous processing procedure, we ensured the consistency, reliability, and suitability of the specimens for experimental testing.

3.2. Experimental Scheme

The experimental setup for this study consists of five main components: the loading and control system, the acoustic emission (AE) signal acquisition system, the static strain acquisition system, a high-speed camera, and vacuum saturation equipment, as illustrated in Figure 2. The loading system is a TM-B-SW-2000 microcomputer-controlled electro-hydraulic servo testing machine (Jinli Testing Technology Co., Ltd., Changchun, China) provided by Harbin University of Science and Technology, which features high-precision displacement control. The axial displacement loading rate is set at 0.002 mm/s [28]. The accuracy of the loading force measurement is ±1% of full scale, and the displacement resolution is 0.01 mm. This system satisfies the technical requirements for loading precision and control stability in rock uniaxial compression tests. Specimen saturation is achieved using the ZKSB-II vacuum saturation machine, which is equipped with a vacuum pump and a constant-pressure water tank. The vacuum level is maintained at −0.098 MPa (±0.002 MPa), and the water pressure control accuracy is better than ±0.01 MPa. Each specimen is saturated for 24 h to ensure complete saturation. Acoustic emission signals are collected using the SH-II acoustic emission system, which operates concurrently with the loading process to monitor the initiation and propagation of fractures in real time. The deformation of the metal shim is monitored by the static strain acquisition system, which has a strain gauge sensitivity of 2.0 ± 1% mV/V and a sampling frequency of 1 kHz, allowing for precise analysis of localized stress concentrations. In addition, a high-speed camera with a resolution of 1920 × 1080 pixels and a frame rate of up to 1000 frames per second is used to capture the entire loading process, enabling synchronized analysis of both the images and the acoustic emission data. Considering the inherent randomness of sandstone failure behavior during uniaxial compression tests, five specimens were subjected to non-uniformly distributed loading tests within each group to ensure the reliability and representativeness of the experimental results. The findings are detailed in

Table 1. Basic information of the test group.

Serial Number	Specimen Type	Density (kg/m³)	Elastic Modulus (GPa)	Poisson’s Ratio (ν)	State of Affairs	Metal Gasket Arrangement Order	Specimen Height × Length × Width/mm
M-B-S	Water-saturated sandstone specimens with pore defects				Saturated with water
M-B-S-1		2620	11.0	0.27			100.14 × 100.24 × 20.11
M-B-S-2		2630	11.2	0.26			100.02 × 100.12 × 20.05
M-B-S-3		2620	11.1	0.27		SY-2, SY-3, SY-1	100.07 × 100.13 × 20.01
M-B-S-4		2630	11.3	0.26			100.12 × 100.04 × 20.03
M-B-S-5		2620	10.9	0.27			100.06 × 100.07 × 20.06
M-S-B
M-S-B-1		2630	11.2	0.26			100.09 × 100.13 × 20.12
M-S-B-2		2620	11.0	0.28			100.04 × 100.02 × 20.14
M-S-B-3		2630	11.3	0.27		SY-2, SY-1, SY-3	100.05 × 100.02 × 20.10
M-S-B-4		2630	11.1	0.27			100.07 × 100.02 × 20.10
M-S-B-5		2610	11.2	0.26			100.05 × 100.02 × 20.10
B-M-S
B-M-S-1		2620	11.1	0.28			100.03 × 100.16 × 20.13
B-M-S-2		2630	11.2	0.27			100.13 × 100.18 × 20.06
B-M-S-3		2610	11.0	0.27		SY-3, SY-2, SY-1	100.06 × 100.13 × 20.10
B-M-S-4		2610	11.3	0.26			100.05 × 100.03 × 20.05
B-M-S-5		2620	11.1	0.28			100.02 × 100.06 × 20.02

.

To investigate the evolution of damage in saturated sandstone under non-uniform loading conditions, this experiment is structured into three distinct experimental groups: M-B-S, M-S-B, and B-M-S. These groups aim to explore the fracture evolution of saturated sandstone under varying non-uniform loading distributions, as detailed in Table 1. Due to the uniform loading system employed in the experiment, direct non-uniform loading tests cannot be conducted. To overcome this limitation, three types of metal shims with different elastic moduli are utilized and arranged in three distinct configurations at the top of the specimens. In the M-B-S group, the metal shims are arranged from left to right as SY-3, SY-1, and SY-2; in the M-S-B group, the arrangement is SY-2, SY-1, and SY-3; and in the B-M-S group, the order is SY-3, SY-2, and SY-1. By applying material mechanics stress calculation formulas, the stress values in the various loading zones at the upper part of the specimen can be determined based on the relationship between elastic modulus and strain. Although the testing machine applies a uniform load to the specimen, the differing elastic moduli of the metal shims result in varying strain responses, leading to different stress transmission through the shims to the upper part of the specimen. This creates non-uniform loading regions at the top. Consequently, three distinct loading zones are formed in the upper portion of the specimen, as illustrated in Figure 3.

4. Experimental Results and Analysis

4.1. Non-Uniform Loading Zone

During the loading process, strain data for the metal shims were collected using a static strain acquisition system, and stress–strain curves for the metal shims were subsequently plotted. As shown in Figure 4, the stress–strain curves for the metal shims in the M-B-S, M-S-B, and B-M-S groups are compared. In the M-B-S group, the stress–strain curves of all three types of metal shims exhibit an elastic phase, with peak stress values of 34.6 MPa, 46.8 MPa, and 78 MPa, respectively, at the initiation of plastic failure. Similarly, in the M-S-B group, the stress–strain curves display an elastic phase, with the peak stress values for SY-1, SY-2, and SY-3 reaching 44.1 MPa, 64.6 MPa, and 95 MPa, respectively, at the onset of plastic failure. In the B-M-S group, the stress–strain curves for the three types of metal shims also show an elastic phase, with peak stress values of 37.5 MPa, 52.8 MPa, and 79.5 MPa, respectively, at the transition to plastic failure. Comparative analysis reveals that the stress experienced by the metal shims in the M-B-S and B-M-S groups is quite similar, whereas the metal shims in the M-S-B group experience higher stress levels than those in both the M-B-S and B-M-S groups.

By monitoring the strain in the stress-transmitting medium, the distribution of the non-uniform stress field at the upper end of the specimen can be determined. As shown in Figure 5, the trends in stress distribution at the upper end of the three specimen groups are presented. Under the influence of the metal shims, which act as the stress-transmitting medium, the upper part of the specimen exhibits regions with low-, medium-, and high-stress levels. In the M-B-S group, the non-uniform stress distribution at the specimen’s upper end, from left to right, is characterized by a low-stress region, a high-stress region, and a medium-stress region. The stress curve at the specimen’s top shows a convex shape. In the M-S-B group, the non-uniform stress distribution at the upper end, from left to right, is marked by a medium-stress region, a low-stress region, and a high-stress region, resulting in a concave stress curve. In the B-M-S group, the non-uniform stress distribution at the specimen’s upper end, from left to right, is characterized by a high-stress region, a medium-stress region, and a low-stress region, with the stress curve exhibiting a decreasing trend from left to right.

4.2. Stress–Strain Curve of Saturated Sandstone with Pore Defects

As illustrated in Figure 6, the peak stress strengths of the specimens vary depending on the combinations of metal shims used. The relationship between the peak stress strengths for each group is as follows: M-S-B group > M-B-S group > B-M-S group. The peak stress values for the M-B-S, M-S-B, and B-M-S groups are 78 MPa, 95 MPa, and 70.7 MPa, respectively. The figure clearly demonstrates that, under the combined effects of non-uniform loading and water, the stress–strain curves of the three groups of specimens exhibit a staged phenomenon during the rock loading process. This phenomenon includes the initial compaction phase, the elastic phase, the plastic yield phase, and the plastic failure phase.

As illustrated, during the initial compaction phase, the stress–strain curves of all three groups exhibit a concave trend. At this stage, the internal particle gaps and primary fractures of the sandstone specimens are progressively compressed and compacted due to non-uniform loading, resulting in a reduction in fractures. Once the specimens enter the elastic phase, as the load gradually increases, the stress–strain curves of all three groups demonstrate a linear relationship. In this phase, the stress on the specimens remains below their elastic limit, allowing them to exhibit elastic behavior. When the load is released during this stage, the specimens return to their original state.

During the plastic yield phase, the stress–strain curves of all three groups exhibit a convex trend. At this stage, the stress on the specimens reaches their yield strength, resulting in plastic deformation. Irreversible crack propagation occurs within the specimens, and upon removal of the external force, the specimens cannot return to their original shape. After the specimens reach their peak stress and transition into the plastic failure phase, significant damage and rupture ensue. In this phase, the specimens display pronounced crack propagation on the surface while internal cracks and fractures fully develop, interconnecting to form extensive fracture surfaces. The overall structure of the specimen is compromised, which is represented in the stress–strain curve by a rapid decline.

4.3. Analysis of Crack Propagation and Evolution in Saturated Sandstone with Void Defects

Fracture Characteristics of Saturated Sandstone with Void Defects

To investigate the crack evolution behavior of specimens with void defects under the combined effects of water saturation and non-uniform loading, the fracture evolution processes and morphologies of three specimen groups—M-B-S, M-S-B, and B-M-S—were recorded using a high-speed camera.

As shown in Figure 7, under non-uniform loading conditions, the saturated sandstone specimen in the M-B-S group is divided from left to right into medium-stress, high-stress, and low-stress zones. Figure 7a presents a physical image of crack propagation in the M-B-S specimen. To facilitate a clearer analysis of the crack propagation process and fracture morphology, a schematic diagram depicting the crack evolution and fracture pattern for the M-B-S group is shown in Figure 7b. The M-B-S specimen exhibits a tensile-shear mixed-mode failure pattern. The crack configuration is primarily characterized by a dominant through-going main crack, accompanied by secondary cracks with irregular propagation paths, as well as localized spalling zones at the crack tips. The crack propagation sequence in the M-B-S specimen begins with the initiation of tensile crack 1a in the high-stress zone. This crack propagates nearly vertically through the high-stress region, extending in the direction of maximum principal stress. It exhibits linear geometry with clean edges and a relatively stable width, indicating that tensile forces dominate the initial stage of crack growth. Subsequently, under the influence of non-uniform forces acting at the top of the specimen, tensile crack 1^a extends toward the low-stress region in the later stages of its development, triggering the formation of shear crack 2^a. Crack 2^a exhibits bending and sliding characteristics, with irregular edges and rough surfaces typical of shear slip behavior. This behavior reflects the features of stress concentration and slip, which are characteristic of shear failure modes. Subsequently, under the combined influence of tensile shear stress disturbances from cracks 1^a and 2^a, as well as stress concentration around the void defect, rock spalling occurs at the interface between the high- and low-stress zones, leading to the formation of an irregularly contoured spalling zone 3^a. Stress relief in zone 3^a causes a redistribution of the stress field around the arched void, resulting in stress concentration along the left wall of the void and the development of shear crack 4^a. During the propagation of crack 4^a, secondary microcracks with irregular morphologies form due to shear slip, acting as bypass paths that accelerate local instability and failure. Moreover, the specimen’s saturated condition further weakens the rock matrix and lowers the threshold for crack propagation, increasing the susceptibility of weak planes to spalling. In the later stages of crack 4^a propagation, under the combined effects of water and shear stress, another spalling zone 5^a forms at the boundary of the low-stress region. Subsequently, a new shear crack 6^a initiates at the tip of spalling zone 3^a, propagating toward the specimen boundary and ultimately leading to the formation of a laminated spalling zone 7^a in the lower right corner.

In summary, the non-uniform loading conditions provide a dominant stress-driven pathway for specimen instability and failure, while the saturated water environment promotes crack activation. Under their combined influence, the M-B-S group demonstrates a progressive failure mode characterized by a chain-reaction process involving stress transmission, crack initiation, and rock block spalling. This process transitions from tensile fracturing to shear failure, ultimately leading to localized rock block instability and spalling.

As illustrated in Figure 8, under non-uniform loading conditions, the saturated sandstone specimen in the M-S-B group is divided from left to right into medium-stress, low-stress, and high-stress regions. Figure 8a shows the physical process of crack propagation in the saturated specimen, while Figure 8b provides a schematic diagram that illustrates the crack propagation path and fracture morphology, offering enhanced clarity for analysis.

At the initial stage of loading, the upper portion of the high-stress region experiences the greatest concentration of tensile stress, leading to the initiation of the primary tensile crack, denoted as crack1^b. This crack propagates in a straight trajectory, exhibiting typical tensile-dominated failure behavior. The infiltration of saturated water at the crack tip, combined with the accumulation of pore water pressure, further reduces the tensile strength of the local rock matrix, facilitating rapid crack propagation. The subsequent localized spalling phenomenon indicates that crack 1^b not only represents the point of initial tensile failure but also significantly weakens the surrounding structure, with water-induced softening contributing to more brittle spalling characteristics. The development of crack 1^b leads to the release of local stress fields, inducing stress transmission downward and resulting in the formation of a bending–shear tensile composite crack 2^b on the right wall of the void. The crack path is significantly influenced by the geometric disturbances of the void, and the presence of pore water further promotes crack extension along weak planes, thereby exhibiting a shear–tensile coupled failure mechanism. As failure in the high-stress region propagates, the medium-stress region gradually becomes the primary load-bearing zone. In the upper-left corner, compressive failure limits are reached, leading to the formation of spalling zone 3^b. This region exhibits overall block detachment at the edges, showing rapid instability under the triggering effect of pore water pressure, characteristic of brittle spalling failure controlled by compressive–shear interactions. Next, a primary tensile crack, labeled 4^b, forms along the existing weak plane in the high-stress region. The crack extends from crack 1^b and, under the weakening influence of saturated water, rapidly propagates through the material, exhibiting typical tensile–through failure. The bearing capacity of the medium-stress region gradually decreases, leading to the formation of a tortuous shear crack, designated 5^b, while a spalling zone, referred to as 6^b, emerges in the central-left region. This area represents a localized instability zone following stress redistribution, where pore water further accelerates rock deterioration, exacerbating the development of tensile–spalling coupled failure. As shear crack 5^b extends and spalling zone 6^b experiences localized instability, stress continues to concentrate in the lower-left region of the specimen. The weakening and lubricating effects of pore water contribute to the formation of shear–slip crack 7^b. The crack path is irregular, exhibiting bending and sliding features on its surface, reflecting structural slip failure under compressive–shear interactions. This process is accompanied by the activation of weak planes within the rock, with water infiltration facilitating crack propagation along these planes and reducing friction. Ultimately, based on crack 7^b, a final spalling zone, 8^b, develops in the lower-left corner. This area undergoes block-like spalling due to long-term stress accumulation and the combined weakening effects of pore water. The well-defined boundary indicates that the rock has lost its residual bearing capacity and is undergoing complete instability. The overall failure progresses into its final stage, characterized by a late-stage coupling failure mode that transitions from shear slip to localized spalling.

In summary, under non-uniform loading conditions, the fracture process in the M-S-B group saturated sandstone specimen is initiated by a tensile crack in the high-stress region. This crack progressively evolves into a composite failure involving shear, slip, and spalling. The continuous influence of pore water facilitates crack propagation, amplifies failure intensity, and accelerates rock deterioration. Ultimately, the crack system becomes fully interconnected due to the combined effects of pore water softening and stress accumulation, leading to overall rock instability and failure.

As illustrated in Figure 9, under non-uniform loading conditions, the saturated sandstone specimen in the B-M-S group is segmented from left to right into high-stress, medium-stress, and low-stress regions. The effects of non-uniform loading cause the specimen to display distinct sequential crack evolution characteristics across these varying stress regions. The cracks primarily observed include through-going tensile cracks, secondary tensile cracks, and spalling cracks, all of which are significantly influenced by the weakening effect of saturated water infiltration.

Initially, during the early stages of loading, the primary crack, designated as crack 1^c, forms at the upper portion of the high-stress region. This crack is a typical through-going tensile crack characterized by a straight propagation path and rapid extension, reflecting brittle failure under localized tensile stress concentration. Under saturated conditions, pore water infiltrates the crack tip, leading to an increase in pore pressure, which further reduces the tensile strength of the local rock matrix, facilitating rapid crack propagation. This process also induces the simultaneous initiation of several secondary tensile cracks around crack 1^c. These secondary cracks exhibit a radial expansion pattern centered around crack 1^c, indicating a significant water–stress coupling acceleration effect in this region. As crack 1^c continues to propagate, it compromises the integrity of the rock mass in the high-stress region, ultimately leading to the formation of a block-like spalling zone, 4^c, which is a typical tensile–spalling composite crack. The boundaries of this spalling zone are well-defined, and the spalling failure occurs rapidly, reflecting the combined effects of water pressure accumulation at the crack tip and the interconnection of microcracks. In the medium-stress region, due to the redistribution of the stress field, tensile cracks 2^c and 3^c initiate sequentially. Crack 2^c extends toward the upper-left portion of the arched void, while crack 3^c propagates toward the right wall of the void. During the later stages of crack 3^c, it reaches the weak plane at the lower-right corner, further inducing the formation of spalling zone 5^c, which is characterized by local stress concentration and structural weakening due to the combined influence of saturated water infiltration. Finally, in the low-stress region, crack 6^c initiates during the mid-to-late loading phase. This crack has a short propagation path and extends slowly, making it a typical delayed tensile crack. The formation of crack 6^c is primarily influenced by long-term pore pressure accumulation and the degradation of rock strength, indicating that under low-stress conditions, the delayed activation of cracks due to water is more pronounced.

In summary, the B-M-S group saturated sandstone specimen subjected to non-uniform loading demonstrates a composite failure mode characterized by tensile stretching, multi-crack evolution, and localized spalling instability. The formation of cracks is influenced by variations in stress distribution and the combined effects of saturated water. Pore water significantly contributes to the instability and failure of the saturated specimen by reducing rock strength, enhancing the connectivity of microcracks, and activating weak planes.

Through the analysis of crack propagation results in saturated sandstone specimens from various groups, similarities in crack development are evident. Specifically, within the different stress regions of the specimens, the degree of crack development and propagation varies. Based on the extent of crack development, the specimens can be classified into the following stages: high-stress region—intense zone, medium-stress region—active zone, and low-stress region—quiescent phase.

4.4. Acoustic Emission Characteristics of Saturated Sandstone with Void Defects

During the instability and damage process of rocks, primary microcracks continuously expand and develop. The microscopic vibrations generated by these crack formations are transmitted as elastic waves to the surrounding environment [29,30,31]. Therefore, in laboratory experiments, acoustic emission (AE) monitoring equipment is used to capture the elastic wave signals emitted by rocks during the damage and instability process. By analyzing the characteristics of these signals, the failure and instability of rocks can be predicted. This method is widely used in rock mechanics.

Due to the varying stress field distributions in three groups of non-uniformly loaded sandstone specimens, this study utilizes acoustic emission signal monitoring to investigate the acoustic instability and failure characteristics of saturated sandstone under non-uniform loading conditions. The findings are expected to provide valuable insights for monitoring instability and failure in actual underground tunnels subjected to non-uniform loading.

For the uniaxial compression tests of saturated sandstone conducted under three different non-uniform loading conditions with varying stress magnitudes, the characteristics of the acoustic emission (AE) ring count signals exhibit a distinct trend. This allows the sandstone to be categorized into four stages: quiet stage (I), active stage (II), intense stage (III), and peak stage (IV). As shown in Figure 10a, this represents the stress-ring count trend curve for the M-B-S group of saturated sandstone under uniaxial compression. At the initial stage of acoustic emission (AE) monitoring, the applied load is relatively low, and the microcracks within the sandstone are in a gradual closure phase. During this period, the AE signal values remain low. To facilitate a more detailed analysis of the signal characteristics generated by the sandstone during the early loading process, the AE signal characteristics are magnified. Within the first 450 s of the uniaxial compression process, the AE ring count signals are predominantly concentrated below 500 counts. As the load gradually increases, fluctuations in the ring count signal become evident, and the overall trend of the ring count signal shows an upward trajectory, as indicated by the red arrows. When the uniaxial loading reaches 232 s, the ring count signal exhibits a local single-peak phenomenon, with the peak count reaching 500, and the stress curve shows a slight inflection. At this point, microcracks in the high-stress region of the sandstone close, and the accumulation of microcracks reaches a critical point, generating a large number of elastic waves. Due to the varying stress levels in different regions of the sandstone, the medium-stress and low-stress regions remain in the quiet stage (I). Therefore, this point is recognized as a warning characteristic, marking the sandstone’s entry into the active stage. At this stage, part of the sandstone enters the active phase (II), as the overall trend of the ring count signal shows an upward trajectory, with the ring count signal being higher than in the quiet phase. However, due to the non-uniform loading in the experiment, different stress regions of the sandstone are in varying stages. As a result, compared to the quiet phase (I), the early active phase does not show a significant increase in the ring count signal. As loading progresses to the later stages of the active phase, the sandstone fully transitions into this phase, resulting in a sharp increase in the acoustic emission (AE) signal. When the loading reaches 445 s, surface spalling occurs at the arch defect in the high-stress load region of the sandstone, which corresponds to a significant inflection point in the stress curve. The propagation of cracks and surface spalling generates a substantial number of elastic waves, leading to a sharp rise in the AE ring count signal. The local peak value reaches 25,044 counts, and this peak is identified as a critical warning characteristic point. Once the surface spalling is complete, the acoustic emission (AE) ring count signal stabilizes at approximately 11,000 counts. Subsequently, surface spalling occurs at the arched defect in the medium-stress region of the sandstone, accompanied by noticeable fluctuations in the stress curve. The AE ring count signal increases again, reaching a local peak of 25,781 counts. After the spalling process concludes, the ring count signal decreases and stabilizes around 6000 counts. The sandstone then enters the peak stage (IV), during which its load-bearing capacity declines rapidly. The AE ring count signal exhibits a sharp upward trend as surface cracks extend significantly, the main crack propagates, and the sandstone approaches its ultimate compressive strength, leading to instability and failure. At this point, the AE ring count signal peaks at 28,946 counts. Observation of the M-B-S group throughout the entire process reveals that the ring count signal exhibits a stepwise pattern. During the quiet (I) and active (II) stages, as the sandstone undergoes early- and middle-stage loading, internal crack development is slow, and no significant surface cracks form, resulting in fewer acoustic emission (AE) signals. As non-uniform loading progresses, the sandstone transitions into the intense (III) and peak (IV) stages, where primary cracks initiate and propagate, leading to intensified internal crack development. The substantial number of elastic waves generated during this phase is collected, resulting in a sharp increase in the ring count signal, which peaks at the ultimate compressive failure point. The total ring count for the M-B-S group of saturated sandstone throughout the entire test is 1,321,425 counts.

As illustrated in Figure 10b, this graph depicts the stress–ring count trend for the M-S-B group of saturated sandstone during uniaxial compression. In the initial loading phase, the acoustic emission (AE) ring count signals predominantly cluster around 100 counts, exhibiting minimal fluctuations. However, when the loading duration reaches 233 s, a sharp increase in the ring count signal is observed, peaking at 869 counts. This surge indicates that the natural microcracks within the sandstone have been compacted, resulting in slight vibrations. At this juncture, the quiet phase of the sandstone concludes, marking this point as a significant warning characteristic that signifies the transition from the quiet stage (I) to the active stage (II).

As observed in the amplified figure, the characteristics of the acoustic emission (AE) signals exhibit a significant change after the warning characteristic point. Following this point, the sandstone enters the active stage (II), during which the AE ring count signals begin to display considerable fluctuations and an upward trend, as indicated by the red arrows in the figure. Similar to Figure 10a, when the loading reaches 508 s, the stress curve shows an inflection point, and microcracks start to form on the surface of the sandstone, generating a substantial number of AE signals. This results in another sharp increase in the AE ring count signal, reaching a local peak of 28,380 counts. This point is identified as the warning characteristic of the intense stage (III). Subsequently, the AE signals enter a period of stabilization. At the conclusion of the intense stage (III), approximately 575 s in, a significant increase in the AE ring count signal is observed, peaking at 29,423 counts. This indicates the end of the warning period for the intense stage (III). Subsequently, the AE signals stabilize, and a bimodal feature emerges in the AE ring count signals during this stage. Compared to Figure 10a, the acoustic emission (AE) ring count trend for the M-S-B group of saturated sandstone in the active stage (II) exhibits a higher total count than that of the M-B-S group. This indicates that crack development in the M-S-B group is more pronounced during this stage. Furthermore, the total AE ring count for the M-S-B group across all stages reaches 1,410,136 counts.

As shown in Figure 10c, this is the stress–ring count trend curve for the B-M-S group of saturated sandstone during uniaxial compression. During the initial and mid-loading stages, the acoustic emission (AE) ring count signals are mainly concentrated around 50 counts, with fluctuation peaks reaching up to 100 counts. This behavior is attributed to the sandstone being in a saturated state, where the water fills the microcracks within the sandstone and inhibits the crack propagation, reducing the generation of fracture-related AE signals. Particularly during the quiet phase, the microcracks expand slowly due to the hydration effect, leading to a reduction in AE signals. As compressive stress increases, the pore water pressure within the saturated sandstone gradually increases, causing microcracks to propagate along the water channels. As microcracks and localized damage accumulate, a critical point in microcrack propagation is reached at 200 s, leading to a sharp increase in AE ring count signals and the formation of a local peak at 448 counts. Due to the non-uniform loading conditions, the loads applied to different regions of the sandstone vary, causing microcracks in different areas to be at different stages of development. At this point, the sharp increase in AE signals marks the transition of cracks in some regions into the active stage (II); thus, this point is identified as a warning characteristic. When the loading reaches 400 s, the AE ring count signal exhibits a warning characteristic, with a local peak value of 18,610 counts, indicating that the sandstone has entered the intense stage (III). Due to the non-uniform stress distribution, with high stress in the left region, medium stress in the center, and low stress in the right region, significant stress concentrations occur in the left and middle regions of the saturated sandstone. Additionally, under the influence of water infiltration, cracks rapidly propagate in these regions over a short period of time, causing the sandstone to transition quickly from the intense stage (III) to the peak stage (IV). Therefore, the intense stage (III) for this group of saturated sandstone is relatively short, and the characteristic end point of the intense stage is reached rapidly, with the AE ring count reaching 18,720 counts. Similar to the M-B-S and M-S-B groups of saturated sandstone during the intense stage (III), the AE ring count signals exhibit a bimodal cyclic characteristic. Subsequently, the sandstone enters the peak stage (IV), where the AE ring count signal reaches the overall peak value of 32,294 counts. Compared to the other two groups, the total AE ring count for the B-M-S group of saturated sandstone throughout the entire process reaches 925,572 counts.

By analyzing the acoustic emission (AE) characteristics of sandstone under non-uniform loading with three different stress configurations, the AE ring count signals for the three groups of sandstone show a consistent upward trend during both the quiet stage (I) and the active stage (II), though with varying curvatures. A comparative analysis reveals the following trend: B-M-S group > M-S-B group > S-B-M group. In the intense stage (III), the AE ring count signals for all three groups of saturated sandstone exhibit a cyclic pattern. Each cycle is marked by a sharp increase in the signal, forming a single peak, followed by a decline to a stable region. During the intense stage (III), the signal characteristics cycle twice, ultimately forming a distinct bimodal pattern in the AE ring count signals throughout this phase. Upon entering the peak stage (IV), all three groups of saturated sandstone undergo instability and failure, resulting in a substantial increase in AE signals. The AE ring count signal reaches its peak during this phase. However, the total AE ring count signal varies in magnitude, following this trend: M-S-B group > M-B-S group > B-M-S group.

According to previous studies [32,33,34], the variation in acoustic emission (AE) peak frequency of sandstone samples under uniaxial compression with uniform loading exhibits distinct zonal characteristics. Building on this foundation, the present study investigates the AE peak frequency behavior of sandstone subjected to non-uniform loading conditions, using the uniform loading scenario as a baseline. As illustrated in the corresponding figure, the AE peak frequency signals from different sandstone groups are categorized into four distinct regions: low-frequency (I), medium-frequency (II), high-frequency (III), and ultra-high-frequency (IV). In Region I, the M-B-S group shows a lower proportion of peak frequency signals during the early loading stage, which increases significantly in the later stages. The M-S-B group demonstrates a high proportion of signals in both early and late stages, with a noticeable reduction during the intermediate phase. In contrast, the B-M-S group maintains a consistently high level of low-frequency signals throughout the entire loading process. In Region II, the M-B-S group’s AE peak frequency signals are concentrated in the 125–150 KHz range, forming a narrow band that persists through all loading phases. The M-S-B group initially exhibits a broader band centered around 100–150 KHz, which progressively narrows during the mid-to-late stages and transitions into a narrower band around 125–150 KHz. The B-M-S group displays early-stage fluctuations around 125–150 KHz, followed by increased signal activity in the mid-to-late stages, dispersing across the entire medium-frequency region. In Region III, the M-B-S group’s signals are predominantly distributed between 200–250 KHz and 260–290 KHz, with a signal void in the 250–260 KHz range. The M-S-B group, by contrast, exhibits no such void and presents the most active and densely distributed high-frequency signals among the three groups. The B-M-S group shows the lowest signal density in this region, with activity mainly confined to 200–225 KHz and 250–275 KHz, leaving a blank interval between 225 and 250 KHz. In Region IV, both the M-B-S and M-S-B groups exhibit similar characteristics, with high AE signal activity sustained within the 300–350 KHz range across the entire test duration. The B-M-S group presents an early-stage concentration of signals, followed by a sharp increase in mid-to-late stages, where the signals expand from 300 to 325 KHz to a broader 300 to 375 KHz range, peaking in the plastic failure phase. Figure 11b,c further reveal that the M-S-B group demonstrates extremely high signal intensities in the later loading stages, surpassing those observed in the M-B-S and B-M-S groups, whereas the B-M-S group shows a complete signal void during the early and middle phases. Compared to the uniform loading scenario, sandstone subjected to non-uniform loading exhibits more prominent AE peak frequency transition phenomena across all four frequency regions. Notably, the B-M-S group displays the most pronounced transitions, particularly between Regions I and II and between Regions II and III. This behavior can be attributed to the differential stress distributions induced by non-uniform loading, which cause coexisting states across different regions of the sample during the same time interval, thereby enhancing the signal transition effects in AE peak frequency behavior.

4.5. Numerical Simulation Results and Analysis

4.5.1. Numerical Modeling

FLAC^3D is a three-dimensional numerical simulation software based on the Lagrangian algorithm, extensively used for analyzing mechanical problems in geotechnical engineering. It is capable of handling complex geometries and nonlinear material behavior, enabling the simulation of rock deformation, stress distribution, and other mechanical responses under various loading conditions. FLAC^3D is particularly effective in identifying plastic zones, crack evolution, and failure mechanisms in rock masses subjected to loading [35,36]. In this study, FLAC^3D is utilized to simulate the failure process of sandstone specimens under uniaxial compression. A three-dimensional numerical model, with dimensions identical to those of the physical sandstone sample, is first constructed to generate a heterogeneous representation that closely reflects the actual material characteristics [37]. Following model construction and material property assignment, boundary conditions are applied. Given the uniaxial loading scenario, confining pressure is not considered; velocity constraints are applied solely at the base of the model, while the lateral boundaries remain free. The FISH programming language is employed to define the non-uniform loading stress distribution at the top surface of the model. A servo control mechanism is implemented to replicate the real-time loading process, as illustrated in Figure 12.

Prior to performing the simulation experiments, it is essential to calibrate the parameters of the numerical model. This calibration is carried out by establishing a simulation environment that closely replicates the actual laboratory testing conditions. A trial-and-error approach [38] is employed to iteratively adjust the model parameters until the numerical results converge with the experimental data obtained from physical tests. The calibrated mechanical parameters are listed in

Table 2. Simulation parameters related to sandstone specimens.

Designation	Bulk Modulus/Pa	Shear Modulus/Pa	Densities kg/m3	Cohesion/Pa	Angle of Internal Friction/°	Tensile Strength/Pa
sandstone	12 × 109	6 × 109	2600	4 × 106	35	2 × 106

. To monitor the evolution of the stress field across different loading zones, three sets of stress monitoring points are strategically placed within the non-uniform loading region at the top of the numerical model. To validate the mechanical parameters presented in Table 2, the simulation results of the M-S-B group specimen are compared with the corresponding laboratory measurements, as illustrated in Figure 13. The numerical simulation yields a uniaxial compressive strength of 95.1 MPa and a peak strain of 1.4%, while the laboratory test reports a uniaxial compressive strength of 95 MPa and a peak strain of 1.33%. The close agreement in both peak strength and strain confirms the reliability of the parameter calibration. Moreover, the damage distribution pattern observed in the simulation closely aligns with the macroscopic failure morphology obtained from the physical test, demonstrating that FLAC^3D is a valid and reliable tool for investigating the mechanical behavior of fractured rock masses.

4.5.2. Distribution Law of Saturated Non-Uniform Stress Field of Defects Containing Holes

The application of non-uniform loading during the uniaxial compression of the sandstone model results in a distinct non-uniform stress distribution in the upper region of the specimen. As loading progresses and internal stress concentrations develop within the sandstone, various stress zones exhibit phenomena of either stress transfer or contraction. However, the overall stress distribution of the sandstone specimen follows a banded pattern that corresponds to the identified stress zones.

In the high-stress region, the stress field distribution varies depending on its location. In the BMS and MSB groups, the high-stress regions are located on the left and right sides of the sandstone model, respectively. Both groups share a common feature: stress penetration occurs within these high-stress areas, leading to stress expansion. In contrast, the high-stress region in the MBS group is located at the center of the model. Due to the arched defect in the center of the saturated sandstone model, no stress penetration occurs. Instead, stress is transferred from the high-stress region to the low- and medium-stress regions.

In the medium-stress region, the behaviors of the different groups exhibit distinct characteristics. In the MBS group, the medium-stress area is “cut off” due to stress transfer from the high-stress zone, preventing stress penetration. In the MSB group, the medium-stress region not only shows stress penetration but also exhibits an expanding trend. In the BMS group, the medium-stress area is located in the central part of the model, where stress penetration does not occur; however, a trend of stress transfer is observed.

In the low-stress region, all three saturated sandstone groups demonstrate similar behavior, regardless of the location of the stress zones. In each case, the low-stress regions show a contraction trend. Furthermore, as shown in the figure, stress concentrations are evident on both sides of the arched defect at the center of the sandstone model.

From the analysis of the figure, it is clear that the three groups of saturated sandstone do not exhibit distinct separation at the boundaries of the stress zones. Rather, a transitional pattern is observed: the high-stress regions consistently exhibit an expanding trend, while the low-stress regions show a contraction trend. The behavior of the medium-stress regions is influenced by their position, leading to either expansion or contraction. Specifically, as shown in Figure 14a, when the medium-stress region is located on the right side, it is influenced by stress transfer from the high-stress region in the center, resulting in stress contraction in the medium-stress area. In Figure 14b, when the medium-stress region is on the left side and the central region is in the low-stress zone, the medium-stress region exhibits stress transfer behavior. In Figure 14c, when the medium-stress region is centrally located, it is influenced by both stress transfer from the high-stress region on the left and stress contraction from the low-stress region on the right. Consequently, the medium-stress region displays a coexistence of stress expansion and contraction. The arched defect at the center of the saturated sandstone model shows stress concentration on both sides, unaffected by the non-uniform loading stress zones.

Plastic zones in three groups of saturated sandstone specimens (M-B-S, M-S-B, and B-M-S) under non-uniform loading conditions at ultimate bearing capacity, as illustrated in Figure 15. The results indicate that plastic failure in all three specimen groups is primarily concentrated in the high-stress regions, where the density of shear failure zones is highest, followed by the medium-stress regions, and lowest in the low-stress regions. This demonstrates pronounced stress sensitivity.

In the high-stress regions, both the M-S-B and B-M-S groups form continuous shear failure bands, exhibiting strong localization and connectivity. In contrast, the M-B-S group shows a deviation in the shear failure path due to geometric disturbances caused by the arched cavity within the high-stress zone. This prevents the formation of a fully connected shear band and leads to the expansion of plastic zones into the medium- and low-stress regions. In the medium-stress zones, the M-B-S and M-S-B groups exhibit widely distributed shear failure elements, whereas in the B-M-S group, these elements are mainly concentrated on both sides of the cavity. This reflects the guiding effect of the loading path on the reconstruction of the shear stress field. Significant differences are observed in the density of shear failure elements within the low-stress regions, following the order M-S-B group > M-B-S group > B-M-S group. This distribution pattern is closely related to the relative position of the stress regions along the loading path. In comparison, the distribution of tensile failure elements across the three groups is relatively consistent, predominantly concentrated around the arch of the central cavity. This indicates that local tensile stress concentration induced by the arched structure governs the tensile failure behavior, while the influence of the non-uniform loading path is comparatively weak.

As shown in Figure 15d–f, the spatial distribution of tensile failure plastic elements in all three groups under different non-uniform loading paths is highly consistent. These elements are primarily concentrated at the top and lateral sides of the cavity, forming a symmetric tensile stress concentration zone centered on the arched cavity. This pattern remains largely unchanged across different stress region layouts, suggesting that geometric stress concentration induced by the cavity structure dominates the tensile failure formation process rather than the loading path. Under external loading, vertical tensile stress tends to concentrate at the arch apex, thereby inducing tensile failure. Additionally, the presence of pore water in the saturated state reduces the tensile strength of the material, further enhancing failure sensitivity around the cavity. Overall, the spatial distribution of tensile failure plastic zones is primarily governed by the combined effects of geometric structure and pore water, while the influence of the non-uniform loading path remains relatively minor, indicating that the spatial evolution of tensile failure is strongly controlled by geometry.

In conclusion, the numerical simulation results reveal the spatial evolution patterns and controlling factors of shear and tensile failure mechanisms in saturated sandstone. The distribution of shear failure plastic zones is influenced by the combined effects of stress zone division, loading path, and geometric disturbances from cavities, showing clear stress sensitivity and path dependence. In contrast, the distribution of tensile failure elements is primarily governed by geometric stress concentrations induced by cavities, exhibiting a high degree of consistency across different loading paths and weaker dependence on loading conditions. The presence of pore water further reduces the tensile strength of the rock mass, intensifies the tensile failure response, and accelerates the development of localized failure.

4.5.3. Stress Analysis of the Upper Part of the Specimen

To analyze the stress distribution characteristics in the upper region of the specimen more clearly, stress monitoring points were set in different stress zones at the top of the numerical model. As shown in Figure 16, the stress monitoring curves for the upper regions of the M-B-S, M-S-B, and B-M-S groups of saturated sandstone specimens are presented. By observing the changes in the stress curves, the upper stress curve can be divided into three phases: the similar phase (I), the sub-discrete phase (II), and the discrete phase (III). From time steps 0 to 4000, the stress curves of the different groups are in a similar phase (I). During this period, the loads applied to the upper regions of the saturated sandstone specimens are averaged, and no non-uniform loading zones have formed. Between time steps 4000 and 6000, the stress curves enter the sub-discrete phase (II), and the effects of non-uniform loading begin to emerge. The upper regions of the saturated sandstone specimens start to exhibit stress partitioning. After time step 6000, the stress curves of the different saturated sandstone specimens show significant discrete behavior, entering the discrete phase (III). The degree of dispersion in the stress curves follows the order MSB > MBS > BMS.

Since the numerical simulation is conducted under idealized conditions, and external factors are excluded, the phenomenon of stress curve dispersion is closely related to the arrangement of non-uniform loading stress zones at the upper part of the model. As shown, in the M-B-S group, the upper stress zones from left to right are the low-stress zone, high-stress zone, and medium-stress zone, with peak strengths of 38.2 MPa, 84.7 MPa, and 60.9 MPa, respectively. In the M-S-B group, the upper stress zones from left to right are the medium-stress zone, low-stress zone, and high-stress zone, with peak strengths of 53.6 MPa, 35.7 MPa, and 96.5 MPa, respectively. In the B-M-S group, the upper stress zones from left to right are the high-stress zone, medium-stress zone, and low-stress zone, with peak strengths of 76 MPa, 56.6 MPa, and 49.5 MPa, respectively. The stress values between adjacent stress zones differ significantly, resulting in an increased degree of stress curve dispersion.

5. Discussion

Under non-uniform loading conditions, this study conducted uniaxial compression tests on saturated sandstone using three different loading sequences to simulate distinct stress zoning patterns. The experimental results revealed the complex interactions among loading sequence, stress distribution, fracture evolution, acoustic emission (AE) characteristics, and internal failure modes.

Among the tested configurations, the M-S-B group exhibited the highest compressive strength due to the central region bearing the maximum load. This suggests that concentrating stress within the structural core enhances the load-bearing capacity of the rock mass. Additionally, the spatial location of the simulated roadway within various stress zones significantly influenced the failure behavior. When the roadway was located in high- or intermediate-stress zones, intense and asymmetric fracture propagation was observed along the sidewalls. In contrast, when positioned in a low-stress zone, the fracture development was more subdued, and the overall failure behavior remained stable. These findings indicate that, in practical engineering applications, roadway placement should preferably avoid zones of high stress concentration to reduce the risk of localized failure and improve structural stability.

The AE characteristics exhibited distinct phase-based evolution throughout the loading process, which can be categorized into four stages: quiet, active, violent, and residual. Precursor signals were commonly observed during the active and violent stages, with a pronounced dual-peak AE count response emerging during the violent phase. This bimodal pattern corresponds to two critical energy release events in the fracture process and serves as a reliable indicator of impending macroscopic failure, providing a valuable reference for the development of real-time early warning systems in underground engineering.

The numerical simulation results closely matched the observed fracture propagation paths, with clear stress concentrations identified near the roadway boundaries. This further validated the effectiveness of the simulation approach in identifying structural weak zones. Shear failures were predominantly concentrated in high-stress regions, while tensile failures were more uniformly distributed, indicating that shear failure is more sensitive to localized stress environments. These observations underscore the importance of implementing targeted reinforcement strategies tailored to the dominant failure mechanisms in different zones.

Moreover, the dispersion observed in the upper stress curves revealed increased stress non-uniformity during vertical stress transmission. This phenomenon is closely associated with delayed failure onset and increased complexity in fracture propagation paths. Recognizing this behavior is critical for informing the design of staged or time-dependent support systems in deep underground projects.

This study not only provides experimental evidence for understanding the failure mechanisms of saturated rock masses under complex loading conditions but also offers theoretical insights and engineering guidance for mining hazard management and underground space design. The key implications are as follows.

(1) Optimized roadway layout:

Avoid placing roadways in high stress concentration zones to enhance surrounding rock stability.

(2) AE-based monitoring systems:

Leverage the dual-peak AE pattern as a critical precursor signal for real-time failure warning.

(3) Zonal support strategy:

Design reinforcement schemes based on the dominant local failure modes to improve efficiency and cost-effectiveness.

(4) Simulation-integrated design:

The validated stress field simulation can reliably identify structural weak zones, supporting its integration into engineering design and layout optimization.

Despite the insights gained from this study regarding the mechanical response and AE behavior of saturated sandstone under non-uniform loading, certain limitations remain. First, the loading path and stress zoning were idealized and did not fully replicate the complexity of multi-axial stress coupling in actual geological conditions, which may limit the direct applicability of the results to real-world engineering scenarios. Second, AE data analysis primarily focused on count-based indicators without incorporating multi-parameter information such as AE energy, which constrains the depth of fracture process characterization. Finally, the simulated roadway was modeled as a symmetric arched structure without considering the effects of varying geometric forms on stress perturbation and failure mechanisms. Future studies should incorporate diverse roadway cross-sectional shapes and stress disturbance scenarios to improve the generalizability and engineering relevance of the findings.

6. Conclusions

In this study, non-uniform uniaxial compression physical experiments were conducted on saturated sandstone specimens to investigate, from a macroscopic perspective, the distribution patterns of the upper stress field, the evolution of crack propagation, and the acoustic emission characteristics under non-uniform loading conditions. Additionally, by employing the FLAC^3D numerical simulation program, a mesoscopic analysis was carried out to examine the influence of non-uniform loading paths on the internal stress field distribution, the spatial patterns of shear and tensile failure elements, and the stress curve characteristics in the upper regions of the specimens. The main conclusions drawn from this study are as follows. According to the theory of material mechanics, using the different physical properties of the modulus of elasticity of the metal gasket, the M-B-S group, M-S-B group, B-M-S group of water-saturated sandstone specimens for the non-uniform load uniaxial compression test, the resulting stress–strain curve is still the existence of the stage characteristics, divided into the compression stage, elasticity, plastic yielding stage, the destruction of the destabilization stage, to obtain the peak uniaxial compressive strength of the peak uniaxial compressive strength, respectively, 70.7 MPa, 95 MPa, 78 MPa; non-uniform load force arrangement order on the peak uniaxial compressive strength of sandstone specimens have a significant effect.

(1) Based on the principles of material mechanics and utilizing the distinct physical properties of the elastic modulus of metal gaskets, non-uniform loading uniaxial compression tests were conducted on the saturated sandstone specimens from the M-B-S, M-S-B, and B-M-S groups. The resulting stress–strain curves exhibit clear characteristic stages, including the compaction stage, elastic stage, plastic yield stage, and failure instability stage. The peak uniaxial compressive strengths for these groups are 70.7 MPa, 95 MPa, and 78 MPa, respectively. The arrangement order of the non-uniform loading forces significantly affects the peak uniaxial compressive strength of the saturated sandstone specimens.

(2) Under the influence of non-uniform loading, crack propagation in the saturated sandstone specimens develops differently across various stress regions. Based on the extent of crack extension, the regions are classified as follows: the high-stress region exhibits intense crack propagation, the medium-stress region shows active crack propagation, and the low-stress region undergoes calm crack propagation. The arrangement of the stress regions significantly influences the failure of the central cavity defect: when the central arched cavity defect is located in the high-stress or medium-stress regions, crack propagation and rupture behavior of both walls are intense. However, when the central arched cavity defect is located in the low-stress region, crack propagation and rupture behavior of both walls are relatively calm.

(3) The acoustic emission (AE) ring counts for the different saturated sandstone groups during non-uniform loading show distinct stage characteristics. Based on the activity of the AE ring count signals, the process can be divided into the calm stage, active stage, intense stage, and residual stage. Pre-warning characteristics are observed during both the active and intense stages for all groups. In the intense stage, all three groups of saturated sandstone exhibit a bimodal trend in AE ring counts. The total AE ring count is highest for the M-S-B group, followed by the M-B-S group, and then the B-M-S group. Additionally, the AE peak frequency displays a banded zoning phenomenon, categorized into low-frequency, medium-frequency, high-frequency, and ultra-high-frequency zones. Under the influence of non-uniform loading, transitional signals in peak frequency appear between different regions, with each group of saturated sandstone showing differentiated characteristics.

(4) A comparative analysis of the internal stress field distributions among different saturated sandstone groups reveals that non-uniform loading induces complex stress transfer phenomena within the rock mass. These phenomena are strongly influenced by the spatial configuration of stress zones: high-stress regions predominantly exhibit stress expansion; medium-stress regions display diverse behaviors including expansion, contraction, or both; whereas low-stress regions consistently exhibit stress contraction. The numerically simulated stress fields are in strong agreement with the macroscopic crack propagation patterns observed in physical model experiments, thereby validating the accuracy and reliability of the simulation approach. Under all three stress distribution patterns, stress consistently concentrates around the central arched cavity walls, identifying this area as structurally vulnerable under non-uniform stress conditions.

(5) Comparing the spatial distribution of failure modes in the different saturated sandstone groups, it is evident that the spatial distribution of shear failure elements is closely related to the different stress regions in the upper part of the sandstone specimens. The density of shear failure elements follows this order: high-stress region > medium-stress region > low-stress region. The spatial distribution of tensile failure elements is relatively uniform and unaffected by the non-uniform stress regions.

(6) A comparison of the upper stress curves of the different saturated sandstone specimens reveals a significant correlation between the degree of dispersion of the stress curves and the arrangement of the upper stress regions. The greater the difference between adjacent stress regions, the higher the degree of dispersion in the stress curves. The degree of dispersion in the upper stress curves follows the order: M-S-B > M-B-S > B-M-S.