Analysis of Extent of Deformation Range and Failure Characteristics of Rocks Surrounding a Tunnel Crossing Fault Zone Based on FDEM

e combined nite-discrete element method (FDEM) and laboratory test were selected to study the extent of deformation range and time-dependent deformation of surrounding rock during tunnel excavation without support in a fault-crossing tunnel project. FDEM was found to accurately reect the deformation and failure characteristics of dierent surrounding rocks during stress release, including conjugate shear and extrusion. Analysis of the results showed that the disturbance range of surrounding rocks could reach 1.5 to 2.5 times the tunnel diameter when crossing the fault zone.e rock surrounding the tunnel was found to incur signicant conjugate shear deformation and extrusion deformation: conjugate shear deformation was identied as dominant in the deep rockmass, whereas extrusion deformation prevailed in the rockmass near the cave wall.e conjugate shear distribution was represented as a spiral line of deformation circling around the tunnel section, with an elliptical main deformation zone with its long axis parallel to the fault plane. Compared with the ndings when crossing the intact rock mass, the deformation of the surrounding rocks when crossing the fault zone was characterized by rapid development, deep expansion area, and large deformation. e study conclusions were that supporting bolts and steel arches should be implemented timely when excavating fault zones and that both lithology and optimal construction timing were essential considerations in determining the length of the supporting bolts.


Introduction
Due to the diversity of stratigraphic conditions, it may be necessary for many mountain tunnels to cross fault zones, some of which may be active. Active fault zones are often accompanied by varying degrees of unfavorable geological conditions. For example, rock mass characteristics within fault zones usually include high susceptibility to fracturing and weathering, poor strength, and signi cant di erences from the surrounding rock. When a tunnel passes through a fault zone, considerable deformation occurs, potentially alongside serious problems such as tunnel face instability, collapsing of the tunnel wall, and supporting structural failure [1][2][3][4][5]. In his study, Terzaghi [6] ascribed the large extrusion deformation in the tunnel to the considerable amount of clay minerals present in the rock, suggesting that the volume of this rock mass slowly increased and then intruded into the tunnel clearance. e actual sampling at the engineering site showed that the rock mass within a certain range of the fault zone and its surrounding area contained very high clay minerals. Terzaghi [6] therefore concluded that the deformation in the vicinity of the tunnel crossing fault zone could be attributed to the signi cant deformation of local soft rocks.
Extensive research has been carried out on fault-crossing tunnels, including analysis models, experiments, and numerical simulation. Key influencing factors of fault zones studied have included the fault zone width, soil properties, and the intersection angle between tunnel axis and fault zone [7,8]. Tunnelling research subjects have encompassed surrounding rock deformation, internal forces, tunnel lining deformation, and the advantages and drawbacks of a range of construction measures [9][10][11][12][13]. In many research hotspots, the deformation of surrounding rocks during excavation has been ignored, that is, the development of crack or deformation of rock mass around the tunnel in the vertical direction, especially in the engineering project crossing the active fault zone. Since active fault zones are usually accompanied by high tectonic stresses, tunnel excavations produce a release of initial stress in the rock mass.
is stress release leads to a deep deformation of surrounding rocks, the most significant instance being the rock burst phenomenon of hard rock with high ground stress. A stress release gradient change occurs from the inner wall of the tunnel to the rock mass, causing problematic issues such as the area of influence of rock mass deformation, and the potential presence of cracks in the rock mass. Fractures within the rock mass have important repercussions on the waterproofing and drainage maintenance systems throughout the tunnel operation period. Rigorous research is therefore urgently required on this subject.
e finite-discrete element method is a common numerical tool to analyze fracture development, in particular the typical one is the combined finite-discrete element method (FDEM) [18][19][20][21][22][23]. It can simulate the behavioral process of materials from continuous deformation to discontinuous deformation. In the field of civil engineering, this method has been applied to analyze the deformation of rocks surrounding highway construction and the development of cracks in concrete structures and to perform simulation tests of the mass strength of various rock and soil types [24][25][26][27], all of which demonstrated good computational and simulation performances.
In the present study, set in an engineering context of a tunnel crossing a fault zone, laboratory testing and the FDEM were implemented to establish the law determining the area affected by rock mass deformation caused by tunnel excavation around the site where the tunnel crossed the fault zone. e failure mechanism of rock mass within the fault zone was revealed, which in the authors' view provided valuable references for preventive measures against rock deformation in future projects involving tunnel excavations.
In 2004, they proposed a complete set of theories and developed the corresponding calculation program Y-Code. However, as the initial version of the computation program, the Y-Code still presents numerous problems to this day. For example, quasistatic friction is not achieved, contact energy dissipation is not considered, and the Mohr-Coulomb shear strength criterion is not realized. erefore, Mahabadi et al.
proposed an improved version of Y-Geo in 2012 based on the Y-Code [31], which made the FDEM constitutive model and strength criterion more consistent with the mechanical properties of rock materials. Moreover, a corresponding preprocessor Y-GUI [32] was developed to quickly assign corresponding attributes to model elements and nodes. e basic principle of FDEM can be summarized as follows: the intact material was divided into triangular elements, and quadrilateral joint elements with initial zero thickness were inserted at the boundary of the triangular elements. e longest side of the quadrilateral elements was shared with a triangular element, and the shortest side of the quadrilateral elements coincided with the line of adjacent nodes, as shown in Figure 1(a) (the initial thickness exists). e triangular elements represented the constant strain elements, and their Cauchy deformation stress was solved by the generalized application of Hooke's law. Moreover, the triangular elements only sustained elastic deformation, as opposed to plastic deformation or fracture failures. e plastic yield and fracture failure of rock materials were represented by the quadrilateral joint elements. e state of the quadrilateral joint elements was determined according to the relative tensile or shear displacement between nodes, as shown in Figure 1(b). When two of the three nodes in the quadrilateral elements (points A, B, and C in Figure 1(a)) reached either the ultimate tensile displacement or the shear displacement sr, the fracture failure occurred in the joint elements. e triangular elements were transformed on both sides from a bonding relationship to a contact relationship. e bond stress calculation program for the joint elements was no longer implemented and the contact stress was solved by potential functions. e advantage of potential functions was that the contact stress consisted of distributed stress rather than concentrated stress, which was more consistent with the real contact relationship of the block, thus avoiding the need to conduct fillet processing. e constitutive equations of the quadrilateral joint element were where σ n and τ are normal and tangential stresses (σ n > 0 represents tensile stress, and σ n < 0 represents compressive stress); o and s are normal and tangential displacements; o p and s p are normal and tangential peak displacements; and o t and s t are normal and tangential ultimate displacements. It can be observed that when the tensile or shear displacement of the joint element reached its corresponding limit value, the joint element fractured and failed; c is the cohesion; φ i is the internal friction angle; f t is the tensile strength; and z is the post-peak softening function [33].

Project Overview
e rock strata around the tunnel line mainly consisted of quartz sandstone, slate, and quartz diorite. e tunnel crossed an active fault zone with a small angle. e fault zone was a normal fault with a dip angle of 64∼80°. e width of the core fault zone was about 7 m, and the width of the fault zone was about 60 m. e tunnel was about 235 m deep, while the depth of groundwater was about 5 m. e results of the ground stress tests showed that the horizontal ground stress of surrounding rocks was dominant, which was measured at about 17.5 MPa. At the same time, the rock mass near the fault zone was fractured and formed part of an area of significant, widespread deformation, which was prone to major tunnel deformation. e tunnel was a double-line tunnel with a diameter (d) of about 13.5 m and an included angle between the tunnel axis and fault strike of about 14°. e plane relationship between tunnel and fault is shown in Figure 2. According to the tunnel crossing the strata, three working cases were selected: (I) the tunnel crossed the intact rock mass; (II) the tunnel crossed the fault fracture zone; and (III) the tunnel crossed the fault core zone. en, the difference in deformation of the surrounding rocks was compared and analyzed at the point where the tunnel effectively crossed the fault zone.

Soil Parameter Test
Rock samples representing different rock masses in three typical sections were obtained from different excavation locations along the tunnel. e three types of rock samples were as follows: (a) weakly weathered quartz diorite representing the original rock; (b) highly weathered quartz sandstone representing the fault zone; and (c) fully weathered soil representing the fault core zone. e production process and core samples of quartz diorite are shown in Figure 3. e core size was 50 mm in diameter and 100 mm in height. e mineral composition and mechanical properties of the rock samples were tested. e main minerals in the rock samples were potassium feldspar, albite, and quartz. Saturated uniaxial compressive strength tests and Brazilian splitting tests were conducted on the samples, and the test results are shown in Table 1.
e rock samples of strongly weathered quartz sandstone are shown in Figure 4. In their natural state, the rock samples were massive and without any obvious structural cleavage. It thus proved challenging to obtain regular cores using the sampler, and the rock samples could be crushed by hand.
e saturated uniaxial compressive strength of the rock samples was less than 1 MPa. e initial average water content and initial density of the rock samples were 1.8% and 2.49 g/cm 3 , respectively. e rock samples were mainly composed of albite and quartz with poor resistance to disintegration. Due to the weakness of the rock samples, they were destroyed and remodeled; the triaxial consolidated drained tests were carried out. e soil parameters obtained in the test are shown in Table 2.
e rock mass in the fault core zone had essentially been fully weathered into the soil, as shown in Figure 5. e soil samples were found to belong to gravel soil, and the grains mainly consisted of sand while also containing some clay and block stones. e block stone size distribution was mainly between 20 and 150 mm. A triaxial consolidated drained test was performed on the undisturbed soil samples containing block stones. e soil parameters obtained in the test are shown in Table 2.

Numerical Model
e FDEM numerical simulation model was established on the basis of three different profiles, as shown in Figure 6. e model size was 140 m × 140 m and was divided into three  Advances in Civil Engineering sectors: a tunnel sector, a mesh refinement sector, and a farfield sector. e diameters of the tunnel and the mesh refinement areas were 13.5 m and 60 m, respectively. e mesh sizes of the tunnel boundary and the model boundary were 0.15 m and 10 m, respectively. Under two-dimensional plane strain conditions, the tunnel excavation process could be divided into two stages: a ground stress loading stage and a tunnel excavation stage. e model boundary was free at the ground stress stage and fixed at the tunnel excavation stage. After the ground stress had been applied and the model reached equilibrium, a core material softening method was adopted to reflect the gradual weakening process of the radial support effect on the tunnel face. In other words, the elastic modulus and viscous damping of the material in the tunnel region were gradually weakened, and the softening of each step had to ensure that the response of surrounding rocks caused by the softening of the previous step reached equilibrium before it could be performed. e input parameters are the ones listed in Table 3.

Development of an Analysis Method of the Area of Surrounding Rock Deformation during Excavation of the Intact
Rock Mass. Figure 7 shows the regional development of deep deformation of surrounding rocks caused by stress release during tunnel excavation of the intact rock mass without support. At the initial stage of excavation, the deformation development area was found to be shallow, mainly occurring at the top and bottom of the tunnel. With the further distribution of stress release of the surrounding rock to the deep area, the deformation zone expanded further and eventually reached an area equal to one time the hole diameter. Within 0.1 d of the vault, the obvious surrounding rock fracture occurs. Figure 8 shows the regional development of deep deformation of surrounding rocks caused by stress release during tunnel excavation of the fault fracture zone without support. At the initial stage of excavation, the deformation only occurred within the crushing zone and mainly at the top and bottom of the tunnel, showing distinct conjugate shear deformation characteristics. With the wider distribution of stress release to the deep area of the surrounding rock, the deformation zone expanded further. e side close to the fault core zone was found to have a deeper development area which could exceed 1.5 times the cavity diameter. e conjugate shear line density was significantly Advances in Civil Engineering 7 higher than that of the intact rock mass excavated. e surrounding rock near the tunnel wall shifted from incurring shear failure to extrusion failure.

Analysis Development of the Area of Surrounding Rock
Deformation during Excavation of the Fault Core Zone. Figure 9 shows the regional development of deep deformation of the surrounding rocks caused by stress release during tunnel excavation of the fault core zone without support. It can be observed that when the fault core zone was being crossed, the surrounding rock deformation zone quickly expanded and that shear deformation and extrusion deformation coexisted at the initial stage of excavation. With the continuous release of stress into the surrounding rock, the deformation zone increased rapidly, whereas the rock mass near the tunnel was mainly characterized by extrusion deformation, the deep rock mass predominantly incurred conjugate shear deformation. e approximate elliptic deformation range was established by taking the axis close to the fault core zone as the long axis, while the main deformation zone could approximately exceed twice the cavity diameter. e conjugate shear line could bypass the tunnel to form a long spiral that snaked its way through up and down, while the main deformation zone formed an ellipse with the long axis parallel to the fault plane. Figure 10(a) shows the final development trend of the surrounding rock deformation zone when crossing the intact rock mass or the fault zone, and the range varied by 2.5 times. Compared with Figures 10(b) and 10(c), the final development depth of the surrounding rock deformation zone was close when crossing the fault fracture zone or the fault core zone, and the deformation was relatively intense. When crossing the fault fracture zone, the dense area of deformation fissures was within the range of 1.0 d. When crossing the fault core zone, the dense area of deformation fissures was within the range of 1.5 d.

Comparative Analysis of Surrounding Rock Deformation Development in Different Excavation Areas.
e development of the deformation zone can be better observed from the displacement field nephogram of surrounding rocks illustrated in Figure 11. When crossing the intact monolayer rock mass, the main deformation of surrounding rocks was in the range of 7 m (about 0.   Figure 12 shows the maximum development range of surrounding rock deformation zones under different analysis steps (time) after excavation of different rock masses. e slope of the two curves during the excavation of the fault zone can obviously be observed to be steeper than that during the excavation of the intact rock mass, indicating that the initial deformation developed faster in the fault zone due to the poor properties of the surrounding rocks. e above analysis is based on unsupported excavation, which is corresponding to the situation in the time interval between the completion of tunnel excavation and the implementation of the support system. e increase in the analysis step represents the increase in the time. It can be seen that the deformation range of the surrounding rock is smaller if the supporting system (supporting bolts) is timelier completed. e development rule of the deformation range of the surrounding rock further indicates that the supporting bolt length is correlated with the construction promptness of the support system and the property of the rock mass.

Conclusions
In this study based on an actual project, the real rock mass parameters were obtained by analyzing the test results of different surrounding rock samples obtained from the project site. On this basis, the deformation development characteristics of surrounding rocks without support following tunnel excavation were analyzed by using the FDEM. e analysis results showed that (1) e rock mass is more disturbed by the stress release from tunnel excavations when these cross a fault zone than under the conditions where tunnel excavations cross an intact rock mass. e range of disturbance can reach 1.5 to 2.5 times the tunnel diameter, and the strong disturbance area (where the displacement exceeds 0.2 m) can reach 1.0 to 1.5 times the tunnel diameter. is will provide guidance for determining the length of the supporting bolts. (2) Compared with the extrusion deformation that occurs when a tunnel crosses an intact rock mass, conjugate shear deformation and extrusion deformation coexist when a tunnel crosses a fault zone. Conjugate shear deformation is dominant in the deep rock mass, and extrusion deformation is dominant in the rock mass near the cave wall. erefore, appropriate supporting measures should be adopted in different zones with different deformation mechanisms.
(3) When crossing an intact rock mass, the surrounding rock deformations mainly occur in an approximately rectangular range that includes the top and bottom of the cave. No penetrating deformation line bypassed the tunnel section. When a tunnel crosses a fault zone, a spiral deformation line is formed around the tunnel section, and the main deformation zone takes an elliptical shape, the long axis of which lies parallel to the fault plane. is conclusion can provide a reference for the selection of the length of supporting bolts in different directions on the tunnel cross-section. (4) Compared with the condition of a tunnel crossing an intact rock mass, the surrounding rock deformation develops more rapidly when a tunnel crosses a fault zone. Depending on the speed and range of development of deformation zones, the difference in length of any supporting bolts affixed to different surrounding rocks is significant. e length of applied bolts is determined both by the properties of the surrounding rock and the timing of application. In addition, when being implemented in a fault zone, the construction and fitting of supporting bolts and steel arches must be completed timely, thus the fracture deformation of deep surrounding rock can be more efficiently controlled.

Data Availability
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.