Shear testing on rock tunnel models under constant normal stress conditions

Bing Yng,Qun Jing,Xiting Feng,Jie Xin,Dingping Xu

a State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,430071,China

b University of Chinese Academy of Sciences,Beijing,100049,China

c Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines,Northeastern University,Shenyang,110819,China

Keywords:Circular tunnel model Compression-shear test Spalling Numerical simulation Fracture surface roughness

ABSTRACT Large shear deformation problems are frequently encountered in geotechnical engineering.To expose the shear failure mechanism of rock tunnels,compression-shear tests for rock models with circular tunnel were carried out,including single tunnel and adjacent double tunnels.The failure process is recorded by the external video and miniature cameras around the tunnel,accompanied by real-time acoustic emission monitoring.The experiments indicate that the shearing processes of rock tunnel can be divided into four steps:(i)cracks appeared around tunnels,(ii)shear cracks and spalling ejection developed,(iii)floor warping occurred,and(iv)shear cracks ran through the tunnel model.Besides,the roughness of the sheared fracture surface decreased with the increase in normal stress.Corresponding numerical simulation indicates that there are tensile stress concentrations and compressive stress concentrations around the tunnel during the shearing process,while the compressive stress concentration areas are under high risk of failure and the existence of adjacent tunnels will increase the degree of stress concentration.

1.Introduction

Increasing demand for energy,resources and transportation will inevitably promote the further development of mining,oil and gas development,tunnel construction,etc.To deep underground areas(Hudson et al.,1997; Qi et al.,2010; Xie,2017).Large shear deformation,which is often caused by weakened geotechnical structures(e.g.fault,weak interlayer or weak shear belt)or earthquakes,is an important manifestation of instability and failure in geotechnical engineering (Hoek and Brown,1997; Kulatilake et al.,2011; Jiang et al.,2019; Duan et al.,2020).Influenced by the sheared zones of the W41 faulting,a displacement of approximately 2 mm appeared in the copper mine at Mount Isa,Australia (Bruneau et al.,2003).Multiple clay rock intercalations in the Gezhouba hydropower station caused the shear dislocation of the sidewall along the intercalation to the free face during the excavation of the foundation pit (Xu et al.,2012).During the excavation of the Baihetan hydropower station,collapse and plastic extrusion failure of the weakened interlayer shear belt at the top arch and sidewall occurred (Duan et al.,2017a).These shear failures with significant damage to the underground structures often occur on the sidewalls of underground engineering,especially the stress-structure failure of surrounding rocks under high geostress condition.

In addition,there have been many examples of large deformations caused by earthquakes.During the Hyogoken-Nambu earthquake,cracks were detected at all corners of the No.2 Kobe tunnel section,and cut-through cracks appeared in the center column along the longitudinal axis of the tunnel(Schiff,1998;Jiang et al.,2010).Additionally,many tunnels suffered various types of damage after the 1999 Chi-Chi earthquake in central Taiwan,such as the lining sheared off and spalling (Wang et al.,2001).Besides,longitudinal cracks with lengths of 20-35 m were detected on the Longdongzi tunnel,and construction joints opened up to 5-15 mm in Wenchuan earthquake (Li,2012).Thus,the mechanical analysis of the shearing mechanism for underground engineering is particularly important.

Physical experimental simulation is an important method for analyzing the mechanical characteristics of engineering structures under specific working conditions.Numerous scholars have carried out modeling tests for underground tunnels.The evolution of fracture around cavities subjected to polyaxial compression was examined early through a series of modeling experiments(Lajtai and Lajtai,1975).To investigate the mechanism of strain rockburst and spalling in deep caverns under high stresses,a series of modeling tests on the tunnels with different shapes or lithologies was conducted under three-dimensional(3D)stress conditions(Gong et al.,2018,2019; Luo et al.,2019; Si et al.,2020; Wu et al.,2020).In addition,based on some specific engineering under complicated stress conditions,scaled geo-mechanical model tests for underground tunnels were carried out for the stability assessment or failure prediction(Zhu et al.,2010;Peng et al.,2015;Fang et al.,2016;Li et al.,2019,2021).Many scholars also carried out tunnel model tests under dynamic loading to investigate the stability of underground excavations (Weng et al.,2018; Wu et al.,2021).Although many achievements have been gained in the modeling tests of underground engineering,rare research on modeling tests under shearing load conditions has been carried out.

Thus,the physical modeling tests of shear failure for rock circular tunnels under compressive stress were carried out to expose the shear failure process of tunnels,including the single tunnel model and adjacent double tunnel model.With acoustic emission (AE)monitoring,video recording equipment,3D scanning technology and scanning electron microscopy (SEM),the failure processes of rock tunnels were comprehensively analyzed.In addition,the stress around the tunnel during the shearing process was further backanalyzed by numerical simulation.It was concluded that tensile and compressive stress concentrations were distributed around the tunnel,and there was spalling near the top,floor warping,and longitudinal cracks in the sidewall.Moreover,the influence of adjacent tunnels may weaken the shear strength of the block.The physical simulation provides a reference for the failure prediction of underground rock engineering under shear deformation.

Fig.1.Basic characteristics of sandstone:(a)The microstructure observed under crosspolarized light of sandstone minerals,and (b) Uniaxial compressive strength of sandstone.

2.Experimental methods

2.1.Specimen description

The specimens selected for the modeling tests were composed of fine-grained,feldspathic quartz sandstone,of which the main mineral components were quartz (Qtz) (60%),plagioclase (Pl),potassium feldspar (Kfs),carbonate mineral filler (Cb) (30%) and a small amount of zircon(Zrn).The mineral particle size ranged from 0.06 mm to 0.25 mm.The microstructure observed under crosspolarized light is presented in Fig.1a.The wave velocity of this sandstone was 3700 m/s.In addition,the compressive strength of the sandstone tested was 44.74 MPa as measured by uniaxial compression tests(Fig.1b).

The shear tests were divided into two groups: one for single tunnel model and the other for double tunnel model,aiming to study the shear failure of single tunnel structures and adjacent double tunnel structures,respectively.The single tunnel model is shown in Fig.2a,with a block size of 300 mm×200 mm×200 mm.Considering the model size and boundary effects,as well as the feasibility of data observations during the test,the diameter of the circular tunnel was set to be 50 mm.The double tunnel model is shown in Fig.2b,where the diameter of both tunnels is 50 mm and the distance between the two tunnels is 50 mm.

2.2.Testing equipment

Shear tests were carried out using the self-developed high-pressure servo-controlled shear test system for rock masses with the capability of shear load up to 2000 kN and normal load up to 1500 kN(Fig.3).The system is capable of implementing complex loading processes,including constant normal stress,constant normal stiffness,return shearing,loading-unloading shearing,etc.,and the servocontrol system can provide convenient shear operation,where the upper shear box is fixed and the shear load is applied by pushing the lower shear box outward through the tangential servo-controlled loading system.Since the rock sample is slightly smaller than the shear box by about 2-3 mm,it is placed directly in the shear box with a layer of friction-reducing material at the top and bottom,eliminating the need for additional fixation means.In addition,the normal load is applied overanarea similar to the size of the shear box,and the stiffness of the shear box is very large so that the effect of uneven load distribution is negligible.The shear box with windows enables realtime observation during the shearing process for the specimen,and the shear strength-displacement curves can be automatically obtained by the data acquisition system.In addition,optical video recording,AE monitoring and 3D scanning technologies were applied for comprehensive analyses of the shear failure process of rock specimens with tunnel models.

An external camera was placed on one side of the shear box to observe the external crack expansion of the tunnel model.The AE detection equipment was placed on the other side of the shear box,where the 16-channel AE monitoring equipment produced by the Physical Acoustic Corporation was used in the shear tests.Three Nano 30 AE sensors with dimensions of 8 mm by 8 mm were arranged around one side of the tunnel model,as shown in Table 1.Miniature cameras were installed at the edge of the tunnel holes to record the inner failure processes of circular tunnels,such as spalling.The loading schemes for the single and double tunnel models are shown in Table 1.The shear tests were carried out on the single and double tunnel models with normal stresses of 2 MPa,4 MPa and 5 MPa,and the shear rate of 0.005 mm/s.

Table 1 Loading schemes for circular tunnel models.

Table 2 Mechanical parameters for numerical simulation.

3.Shear failure process of single tunnel model

Fig.2.Circular tunnel models: (a) Single tunnel model,and (b) Double tunnel model.

3.1.Shear strength characteristics

The shear stress-deformation curves of the single tunnel model with different normal stresses are illustrated in Fig.4.The shear strength of the single-tunnel model increased as the normal stressincreased.In addition,the normal deformations of specimens during the shearing process,i.e.shear dilatancy characteristics,are also demonstrated.According to the slope change and turning point of the shear dilatancy curve,the whole process of the shear test can be divided into four stages:

(1) Compaction stage I:block compaction with negative growth of normal deformation.Since the shear box is about 2-3 mm larger than the sample along the shear direction,the shear displacement at the compaction stage includes the displacement attaching the specimen to the shear box and the shear displacement applied to the specimen.

(2) Elastic deformation stage II: the block expanded and the normal deformation changed to positive growth.

(3) Peak stage III: the normal deformation reached to the extreme value and the block was sheared off to form a through fracture surface.

(4) Residual deformation stage IV: rejoining of the upper and lower parts of the fracture surface,and sudden decrease in normal deformation of the sample.

Fig.3.The servo-controlled shear testing system.

3.2.AE analysis

Fig.4.Shear stress-deformation curves and shear dilatancy of the single tunnel model under different normal stresses of (a) 2 MPa,(b) 4 MPa,and (c) 5 MPa.

AE monitoring was performed simultaneously during the shear test,and the AE threshold value was 40 dB.The AE energy reflects the energy released by the AE sourcein the form of elastic waves(Koerner et al.,1981;Moradian et al.,2010;Zhou et al.,2016),and the AE energy rate R is adopted to show the energy release characteristics of specimen failure during the shearing process,calculated by where R is the AE energy rate,Eiis the AE energy monitored by the AE sensors,and Δt is the time interval.

Fig.5.AE energy rate of single tunnel model under different normal stresses of (a)2 MPa,(b) 4 MPa,and (c) 5 MPa.

Fig.6.Failure process of single tunnel model with normal stress of 2 MPa: (a) External failure,and (b) Internal failure.

Fig.5 illustrates the characteristics of the AE energy rate during the shearing process with different normal stresses.As the normal stress increased,the AE energy rate increased.The AE energy rate of the single tunnel model with a normal stress of 2 MPa (Fig.5a)contained two distinct peaks,corresponding to point 1 of the elastic stage and point 2 of the peak stage in the shear stress-deformation curve,where point 1 represented the emergence of macroscopic tensile cracks accompanied by a relatively low energy release,and point 2 represented the penetration of shear crack with the greatest AE energy release.Fig.5b shows the AE energy rate of the single tunnel model under a normal stress of 4 MPa.The appearance of the shear crack at point 1 at the peak stage caused the first large wave of the AE energy rate.With shear crack penetration at point 2,the AE energy release reached the maximum value.Nevertheless,for the single tunnel model under a normal stress of 5 MPa,there was only a sudden release of violent AE energy (at the position of point 1 at the peak stage),as shown in Fig.5c.Fewer AE signals were monitored before the peak stage,and the AE energy release was concentrated at the moment of penetration of the shear cracks at the peak stage.

3.3.Failure process of single tunnel model

With the help of the external camera and inner miniature camera arranged separately on each side of the shear box,the realtime failure process of each circular tunnel model was recorded through the shear box windows during the shearing process.However,due to the poor lighting inside the tunnel and the limited clarity of the video recorded by the internal camera,the location of the damage is thus highlighted on the photos of failure process.Brief descriptions of the failure processes in single tunnel model under the normal stress of 2 MPa is listed here as an example.

The failure process under the normal stress of 2 MPa is shown in Fig.6.Fig.6a shows the crack propagation process from outside of the model,and Fig.6b presents the internal failure process of the circular tunnel.Fig.6a shows that a group of tensile cracks appeared at the lower left and upper right parts around the tunnel at 630.14 s.Compared with Fig.6b,no spalling occurred in the tunnel at this time.In addition,the AE energy rate in Fig.5a indicated that the AE energy release of this group of tensile cracks was small.The shear crack that extends from the lower right part of the tunnel began to appear at 827.08 s.Later,spalling from the roof and floor warping was detected.Finally,the penetrating shear cracks formed at 851.33 s,and the specimen was divided into upper and lower parts by the fracture surface when this tunnel model reached its peak shear strength with a substantial AE energy release.

Fig.7.Spalling in the single tunnel model: (a) Display of the spalling shape,and (b) Frequency distribution of length-to-width ratio for spalling.

According to the shear failure processes of single tunnel model under different normal stresses,the following points can be concluded:

(1) During the shearing process,the occurrence of tensile cracks did not cause spalling,and the shear cracks were the final reason for block failure.

(2) Before the shear crack penetrated,spalling from the top and floor warping appeared in the tunnel,and the severity may increase with an increase in normal stress.

(3) The shear crack penetrated instantaneously with a concentrated release of AE energy.

3.4.Spalling analysis

The spalling inside the tunnel after shearing of the single tunnel model under each normal stress was collected and analyzed,as shown in Fig.7a.The spalling was presented as pieces and debris,with thicknesses of 1-4 mm,widths of 5-35 mm,and lengths of 10-80 mm,and the pieces were mostly in the form of long strips.The length and width of spalling larger than 10 mm in length were counted,and their length-to-width ratio ranged from 1 to 4.5,as shown in the histogram of the frequency distribution in Fig.7b.The probability density function was right-skewed and satisfied the log-normal distribution of lnX～N(μ,σ2) by the Kolmogorov-Smirnov (K-S) test with a p-value of 0.9425 at the 5% significance level,where μ is the mean value(0.71),and σ is the standard deviation (0.39).

Optical microscopy is the basis for fracture surface analysis,and SEM is most commonly employed in fracture microscopy,from which the failure mechanism can be inferred by observing its microscopic fracture morphology (Hull,1999; Bouchaud and Elisabeth,2003).The spalling from single tunnel model was sampled and scanned by SEM technology,as illustrated in Fig.8.It was observed to be brittle fracture,including crystal cleavage,intergranular fracture and transgranular fracture.The crystal cleavage plane was parallel to the crystal plane,with parallel steps at the front edge,which is a typical fracture morphology under tensile stress.The cracks of intergranular fractures propagated along the grain boundaries,with smooth fracture planes and a minimal number of debris,which is also a typical fracture morphology caused by tensile stress.The crack of transgranular fracture passed through the grain,resulting in rough fracture and debris accumulation,also with the fracture direction parallel to the shear direction,which was shear failure (Hull,1999; Keneti and Sainsbury,2018; Zhong et al.,2020).The spalling morphology in the tunnel included crystal cleavage,intergranular fracture and transgranular fracture,indicating that the spalling caused by macro-shearing had a complex mechanism on the microscale,which was the comprehensive result of tensile and shear failure.

4.Shear failure process of double tunnel model

The interaction between adjacent tunnels will have an obvious impact on the overall failure mode of the underground structure.Thus,shear tests of double tunnel model under different normal stresses were carried out,and the failure processes of adjacent tunnels were preliminarily investigated.

4.1.Shear strength characteristics

Fig.8.Microscopic fracture morphology of the spalling sample from single tunnel mode.

Fig.9.Shear stress-deformation curves and shear dilatancy of the double tunnel model under different normal stresses of (a) 2 MPa,(b) 4 MPa,and (c) 5 MPa.

The shear stress-deformation curves of the double tunnel model under different normal stresses are shown in Fig.9,with the normal deformation of specimens during the shearing process,i.e.shear dilatancy characteristics.As the normal stress increased,the shear strength of the double tunnel model increased.The shear strength of the double tunnel model was lower than that of the single tunnel model under the same normal stress,which means that the influence between adjacent tunnels weakened the overall strength of the structure.Obvious shear dilatancy characteristics were observed,with an increase in normal stress and a decrease in shear expansion.Similar to the single tunnel model,according to the slope change of the shear dilatancy curve,the whole shearing process can also be divided into four stages:

(1) Compaction stage I:block compaction with negative growth of normal deformation,including the displacement attaching the specimen to the shear box and the shear displacement applied to the specimen.

Fig.10.AE energy rate of double tunnel model under different normal stresses of (a)2 MPa,(b) 4 MPa,and (c) 5 MPa.

Fig.11.Failure process of double tunnel model with normal stress of 2 MPa: (a) External failure,(b) Internal failure of Tunnel 1,and (c) Internal failure of Tunnel 2.

(2) Elastic deformation stage II: the block expanded and the normal deformation changed to positive growth.

Fig.12.Spalling in the double tunnel model: (a) Display of the spalling shape,and (b) Frequency distribution of length-to-width ratio for spalling.

Fig.13.Numerical simulation of shearing process for single tunnel model and double tunnel model under the normal stress of 4 MPa:(a,b,c)The maximum principal stresses of single tunnel model at shear deformation of 0.75 mm,1.35 mm and 3 mm,and(d,e,f)The maximum principal stresses of double tunnel model at shear deformation of 0.75 mm,1 mm and 3 mm.

(3) Peak stage III: the normal deformation reached its extreme value and the block was sheared off to form a through fracture surface.

(4) Residual deformation stage IV: rejoining of the upper and lower parts of the fracture surface,and sudden decrease in normal deformation of the sample.

4.2.AE analysis

The shear tests for double tunnel model were also accompanied by AE monitoring with an AE threshold of 40 dB.The characteristics of the AE energy rate during the shearing process under different normal stresses are shown in Fig.10.The energy released in the final failure of the peak stage increased with the increase in normal stress.Fig.10a presents the AE energy rate release during shear damage for the double tunneling model at the normal stress of 2 MPa.The first large AE energy rate was generated at point 1 of the peak stage,where shear cracks developed,followed by shear crack penetration at point 2 of the peak stage,when the AE energy release reached its maximum value.For normal stresses of 4 MPa and 5 MPa(Fig.10b and c),the AE energy rates were concentrated at the peak stage while the shear crack penetrated transiently.Few AE signals were monitored before the peak stage,and the monitored AE signals were concentrated at the peak stage,which was instantaneous,with concentrated and intense energy release.Compared with the single tunnel model,the AE energy rate of the double tunnel model was smaller under the same normal stress,i.e.the influence between adjacent caverns weakened the energy release of structural failure.

4.3.Failure process of double tunnel model

One external camera and two miniature cameras for double tunnels were arranged to record the real-time failure processthrough the shear box windows.The description of the shear failure process for double tunnel model under the normal stress of 2 MPa is listed here as an example by comparing the crack propagation from outside of the specimens and inside of the tunnels.

Fig.14.Maximum principal stresses of monitoring points for single tunnel model.

Fig.15.Peak shear strength of tunnel model with different spacings under the normal stress of 4 MPa from numerical simulation.

The shear failure process of the double tunnel model under the normal stress of 2 MPa is illustrated in Fig.11,in which Fig.11a shows the crack propagation process from outside of the model,and Fig.11b and c presents the internal failure process of tunnels 1 and 2,respectively.No cracks were observed,and no spalling occurred in either of the tunnels before the peak stage.At 1102.25 s at the peak stage,non-penetrated shear cracks appeared between the two tunnels and on the left side of Tunnel 1.In addition,a short tensile crack was observed in Tunnel 2,which was compacted in the subsequent shearing process that is not subsequently visible.At 1114.21 s,the shear crack at the upper left side of Tunnel 1 expanded and began to spall,accompanied by debris injection,while at 1114.26 s,the shear crack on the left side of Tunnel 2 began to spall,accompanied by a large amount of dust and debris diffusing in the tunnel.At 1115.18 s,a shear crack was detected on the lower right side of Tunnel 2,with serious spalling from the top roof and floor warping in both tunnels.At 1115.28 s,the shear crack group of the model penetrated,accompanied by severe spalling and debris ejection,as well as sudden AE energy release.At this time,this double tunnel model reached the peak shear strength,and the block formed the upper and lower walls.The spalling of Tunnel 1 near the shear loading occurred first,0.05 s earlier than that of Tunnel 2.

According to the shear failure processes of the double tunnel model under different normal stresses,the following results were obtained:

Fig.16.Examples of fracture surface and point cloud: (a) Fracture surface of single tunnel model under normal stress of 4 MPa,and (b) Fracture surface of double tunnel model under normal stress of 4 MPa.

(1) The failure process of the two adjacent tunnels was not synchronous,where spalling occurred first in Tunnel 1,followed by Tunnel 2,although with a very small time interval.

Fig.17.JRC of fracture surfaces for single and double tunnel models.

(2) Before the shear crack penetrated,spalling and floor warping appeared in both tunnels.

(3) The shear crack penetrated instantaneously with a concentrated release of AE energy.

4.4.Spalling analysis

The spalling inside the tunnels after shearing of the double tunnel model under each normal stress was collected and analyzed,as shown in Fig.12a.The spalling was presented as pieces and debris,with thicknesses of 1-3 mm,widths of 3-15 mm,and lengths of 10-63 mm.The length and width of spalling larger than 10 mm in length were counted under each normal stress,and the length-to-width ratio was distributed in the range from 1.1 to 6.3,as shown in the histogram of the frequency distribution in Fig.12b.The probability density function was right-skewed and satisfied the log-normal distribution of lnX～N(μ,σ2) by the K-S test with a pvalue of 0.5333 at the 5%significance level,where μ is 0.74 and σ is 0.45.The length-to-width ratio of spalling from the double tunnel model was relatively larger than that from the single tunnel model.

5.Back analysis of numerical simulation

It was difficult to give a theoretical analytical solution for the stress distribution around a circular hole under the shear stress boundary,while numerical simulation became a better tool for visualizing the stress distribution and failure characteristics of the model during the loading process.Based on 3DEC numerical simulation software,simulations of the single tunnel and double tunnel model were established.

5.1.Numerical methods

The single and double tunnel models were analyzed under plane strain conditions,with a model length of 300 mm and model height of 200 mm.The diameter of the circular tunnel and spacing between the adjacent double tunnels were 50 mm.Normal compressive stress was applied at the top of the model.Tangential fixation was applied at the upper right boundary and a tangential velocity was applied at the lower left boundary,as shown in Fig.13a and d.The parameters obtained,i.e.the parameters employed in the numerical simulation,are shown in Table 2.

5.2.Analysis of the shearing process

Fig.13 illustrates the numerical results for the single tunnel model and double tunnel model under a normal stress of 4 MPa,showing the variations of maximum principal stresses at different shear deformations,where the negative values were compressive stresses and the positive values were tensile stresses.For single tunnel model,the calculation results (Fig.13a-c) indicated that under compression and shear loading,there were compressive stress concentrations and tensile stress concentrations around the circular tunnel,in which the lower left and upper right sides were tensile stress concentration zones,while the upper left and lower right sides were compressive stress concentration zones.The compressive stress concentration explained the final failure of the single tunnel model.During the shearing process,a small tensile plastic zone appeared in the tensile stress concentration zones but did not expand at a later point,while the shear plastic zones gradually expanded along the compressive stress concentration zones,and then the block failed along the compressive stress concentration zones.

Fig.18.Schematic diagram of the failure process for single tunnel model.

The numerical result of the double tunnel model (Fig.13d-f)was similar to the single tunnel model,where tensile and compressive stress concentrations around each tunnel were detected,with the lower left and upper right sides of tensile stress concentration zones and the upper left and lower right sides of compressive stress concentration zones.However,the compressive stresses between the two tunnels were the largest.Similarly,the compressive stress concentration also explained the final failure of the double tunnel model,the shear plastic zones gradually expanded along the compressive stress concentration zones,and the block failed along the compressive stress concentration zones.

Based on the experimental results and numerical simulation,it was concluded that the final failure of the tunnel model was caused by the concentration of compressive stresses.Monitoring points were set up in the compressive stress concentration zones of the single tunnel models to intuitively show the change in maximum principal stress(compressive stress)during the shearing process,as illustrated in Fig.14.Simultaneously,one monitoring point in the non-stress concentration zone was selected for comparison,where monitoring points A and B selected from the compressive stress concentration zones and point C selected from the non-stress concentration zone.The existence of the tunnel caused the maximum principal stress in the compressive stress concentration zones around the tunnel to increase obviously during the shearing process.In addition,there was a difference in the magnitude of the stresses between the two compressive stress concentration zones,and region point B had the highest stress and was therefore the first region to yield.

5.3.Influence of adjacent tunnel spacing

Limited by the number of physical model tests and cost control,the influence on the spacing between adjacent circular tunnels was preliminarily discussed and analyzed with numerical simulation.The constitutive model,block size and loading mode were the same as previously described.The diameter D of the circular tunnels was 50 mm.Double tunnel models with tunnel spacings of 0.5D,0.75D,1D,1.25D,1.5D and 2D were established to simulate shear failure under a normal stress of 4 MPa.

Fig.15 illustrates that the peak shear strength of the model tended to increase as the tunnel spacing increased,where the peak shear strength of the model with a spacing of approximately 1.5D was the maximum among all the tunnel spacings.The shear strength of the model with a 2D tunnel spacing decreased slightly compared to that of 1.5D,considering the dimensional limitations between the tunnels to the outer boundaries of the block.Therefore,in actual engineering projects,the spacing between adjacent tunnels is very important for the overall stability of the structure.When using a larger spacing between two tunnels within the limited size of the rock mass,the safe distance from the tunnel to the outer boundary should also be considered.

6.Discussion

6.1.Roughness of fracture surfaces

Rock masses may undergo slip deformation after shear fracture,after which the shear strength will be provided by the fracture surface; thus,it is necessary to study the morphological characteristics of the fracture surface.Fracture surface morphology is the only visual trace left by the rock destruction process,and its surface roughness is closely related to the stress environment(Pokluda and Stanek,1981; Hull,1999; Song et al.,2022).However,few studies have included a correlation analysis of rupture surface roughness and stress environment.The application of 3D scanning technology enables the quantitative characterization of the surface roughness.JRC,as a typical two-dimensional (2D) roughness parameter,is widely employed to calculate the surface roughness and shear strength of joints (Barton and Choubey,1977).The JRC of the standard roughness curves takes the value range of 0-20,and the larger the JRC is,the larger the roughness.

Using 3D scanning technology,point clouds of fracture surface morphology after shearing were obtained for single and double tunnel models.The Artec SPIDER handheld 3D scanner was utilized in this paper,with a scanning accuracy of 0.1 mm.The fracture surfaces of the models after shearing under different normal stresses were scanned,after which 3D point cloud matrices containing X,Y and Z coordinates in the local coordinate system were obtained.Point cloud examples of fracture surfaces from the single and double tunnel models are presented in Fig.16.

Fig.19.Schematic diagram of the failure process for double tunnel model.

Along the shear direction,nine 2D profiles were extracted at equal intervals on each fracture surface,and the average value of JRC was calculated as the final JRC value of each fracture surface.The JRC value can be obtained by fitting the slope root mean square Z2(Eq.(2)) to the parameter JRC according to Eq.(3) (El-Soudani,1978),where Δs is the point cloud interval.The JRC values of shear fracture surfaces for single and double tunnels under different normal stresses are shown in Fig.17.The JRC values ranged between 8 and 16,and the roughness of the fracture surface was directly related to the stress environment,where the roughness tended to decrease as the normal stress increased.It was reasonable to observe this roughness variation trend.As the normal stress increased,the normal stress acted as an enclosing force on the block,limiting the normal deformation of the block.This finding was consistent with the phenomenon that the shear dilatancy decreased as the normal stress increased.Because the smaller the roughness is,the smaller the normal undulation will be,resulting in the smaller shear dilatancy.

6.2.Shear failure comparison between laboratory and onsite engineering

Schematics of the failure process summarized according to the recorded shear crack expansion in the single and double tunnel models under different normal stresses are shown in Figs.18 and 19.The test results indicated that the shear failure process of the tunnel model can be divided into four steps.First,for the single tunnel model,tensile cracks appeared around the tunnel,while the double tunnel model formed incomplete compressive-shear cracks between the two tunnels.Second,incomplete compressive-shear cracks grew,accompanied by severe spalling at the top of the tunnel.Third,warping occurred at the bottom of the tunnel.Fourth,the compressive-shear crack penetrated,and the model fractured to form the upper and lower parts.

Actual engineering cases,for example,typical damage phenomena of tunnels due to excessive tangential displacement or shear loading after an earthquake or affected by a weakened interlayer staggered zone,are illustrated in Fig.20(Kazuhide et al.,2007; Li,2012; Duan et al.,2017b; Jiang et al.,2019).The small frames in these pictures show the damage observed in our circular tunnel model tests.Fig.20a shows the phenomenon of lining spalling and blocks falling near the tunnel vault in the Wanatsu tunnel after the Niigataken-Chuetsu earthquake.Fig.20b shows the damage of floor warping observed in the Longxi tunnel after the 2008 Wenchuan earthquake.In addition,Fig.20c presents the tensile cracks in the wall of tunnel WML2 of the Baihetan hydropower station affected by shear belt LS3319,and Fig.20d shows the collapse of rock masses with staggered zone C4 exposed during the first layer excavation of the Baihetan right transformer room.

Longitudinal cracks,spalling of shoulders,and buckling of the bottom plate,which appeared in the model tests,were observed in the actual engineering cases,indicating that the modeling test results in this paper were credible.However,the blocks were sheared off due to excessive tangential deformation in the modeling tests,and the damages were more exaggerated compared to actual engineering projects,which were rarely encountered in the actual project.It may be the purpose of the model test,through the amplification of the damage to provide an intuitive reference for the construction of a real project.For the shear deformation of circular tunnels,spalling near the top of the tunnel,warping of the bottom plate,and longitudinal cracks in the sidewalls were common failure phenomena that should be considered to take appropriate measures.

Fig.20.Typical shear failure phenomena of the onsite tunnels:(a)Wanatsu tunnel after Niigataken-Chuetsu earthquake,2004(Kazuhide et al.,2007);(b) Longxi tunnel after the 2008 Wenchuan earthquake(Li,2012);(c)WML2 tunnel around the shear belt LS3319 in the Baihetan hydropower station(Jiang et al.,2019);and(d)The tunnel of Baihetan right transformer room with staggered zone C4 exposed (Duan et al.,2017b).

7.Conclusions

The physical experimental simulation described in this paper exposed the failure characteristics of rock blocks with single and double tunnels subjected to compression-shear tests under different normal stresses.Some conclusions can be drawn as follows:

(1) The shear failure process of the tunnel model can be divided into four steps.First,for the single tunnel model,tensile cracks appeared,while the double tunnel model formed shear cracks between two tunnels.Second,shear cracks grew,accompanied by spalling.Third,warping occurred.Fourth,shear cracks penetrated.These failure characteristics were similar to those observed from onsite underground tunnels.

(2) Obvious dilatancy of the tunnel models was detected during the shearing process.At the peak stage,the shear crack penetrated,accompanied by the concentrated and violent release of AE energy.

(3) Spalling in the tunnel exhibited the shape of long strips,of which the aspect ratio satisfied the log-normal distribution,and the SEM results indicated that the spalling was a combination of tensile failure and shear failure.In addition,the roughness of the shear fracture surface decreased with an increase in normal stress.

(4) There were tensile and compressive stress concentrations around the circular tunnel during the shearing process,and the compressive stress concentrations explained the final failure.Besides,the influence of adjacent tunnels will increase the degree of stress concentration,and the distance between adjacent tunnels had an obvious influence on the shear strength of the structures.

Declaration of competing interest

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

Acknowledgments

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos.U1965205 and 51779251).The first author would like to thank the Chinese Scholarship Council for financial support.