Evolution of cracks in the shear bands of granite residual soil

Chengsheng Li,Lingwei Kong,Ran An,c

a Department of Civil and Environmental Engineering,Shantou University,Shantou,515063,China

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

c College of Urban Construction,Wuhan University of Science and Technology,Wuhan,430065,China

Keywords:Shear band Crack classification method Digital volume correlation (DVC)X-ray computed tomography (CT)Granite residual soil

ABSTRACT The evolution of shear bands and cracks plays an important role in landslides.However,there is no systematic method for classification of the cracks,which can be used to analyze the evolution of cracks in shear bands.In this study,X-ray computed tomography (CT) is used to observe the behavior of granite residual soil during a triaxial shear process.Based on the digital volume correlation (DVC) method,a crack classification method is established according to the connectivity characteristics of cracks before and after loading.Cracks are then divided into six classes:obsolete,brand-new,isolated,split,combined,and compound.With evolution of the shear bands,a large number of brand-new cracks accelerate the damages of materials at the mesoscale,resulting in a sharp decrease in strength.The volume of brandnew cracks increases rapidly with increasing axial strain,and their volume is greater than 50%when the strain reaches 12%,while the volume of compound cracks decreases from 54% to 21%.As cracks are the weakest areas in a material,brand-new cracks accelerate the development of shear bands.Finally,the coupling effect of shear bands and cracks destroys the soil strength.

1.Introduction

Granite residual soil is widely distributed in the southeastern coastal area of China.This type of granite residual soil is basically formed by weathering,and cannot be transported (Migoˊn and Thomas,2002),which contains considerable amounts of quartz particles and cracks.The weathering and complex mesostructures of granite residual soil deteriorate its mechanical properties,and the soil exhibits significant anisotropy(Branco et al.,2014;Ip et al.,2019),which may lead to landslide disasters after heavy rainfall(Pradhan and Kim,2014;Coutinho et al.,2019).The shear bands in the soil play an important role in terms of landslides.Due to the complex mesostructures and significant anisotropy of granite residual soil,conventional macromechanical tests and numerical simulations cannot adequately represent the evolution of its shear bands,especially the effect of cracks in shear bands,which makes it difficult for engineering analyses and design studies.

Shear bands are the internal cause of slope failure and play an important role in soil failure during a landslide.Many scholars have studied the evolution of shear bands during landslides.Dey et al.(2016) numerically simulated the propagation of shear bands in sensitive clay landslides.Germanovich et al.(2016)studied the propagation of the tips of shear bands,where the potential fracture surface evolves into a shear band during sliding deformation.Lanting et al.(2020) used transparent soil tests to analyze the internal characteristics during deformation of the slopes.The traditional method for the analysis of soil mechanics problems has been used; however,it is difficult to apply a constitutive model on the macroscopic material scale to describe the disaster phenomena of rock masses with multi-scale mechanical characteristics.

The macroscopic mechanical properties of geomaterials are the statistical results of mesostructure evolution.Therefore,understanding the microscopic mechanisms of complex macroscopic properties of geotechnical materials is necessary to explore their microscopic characteristics,such as microstructure,strain localization,particle breakage,and fracture evolution(Jiang,2019).Cracks are the weakest locations in soil,and they may affect the local stress concentrations and redistribution in shear bands.As a result,cracks may accelerate the connection of shear bands.

Various methods have been used to analyze the evolution of cracks based on data obtained from X-ray computed tomography(CT) scanning,for example,to qualitatively analyze threedimensional (3D) images (Gehre and Aneziris,2011; Sang et al.,2014; Wang et al.,2018a,2020).With the development of image processing technology,several researchers added pseudo-color information to reflect crack thickness to 3D crack visualization(Skaryˊnski and Tejchman,2019) or introduced pore-size distribution curves(Gebrenegus et al.,2011).Additionally,graphs of the density change of materials were used to analyze crack evolution(Tang et al.,2019;Loeffler et al.,2020).These methods are simple and useful but cannot fully exploit the abundant information contained in CT scans.Accordingly,fractal theory was used to quantitatively investigate 3D crack networks at different loading stages,and various effects such as those of confining pressure and vertical cracks were compared(Ju et al.,2018).There is significant directionality of cracks in some materials under external loads,and statistical analyses of the crack density and direction could help researchers understand the evolution of cracks (Wang et al.,2018b).

The digital volume correlation (DVC) method can be used to calculate strain fields of various materials during loading,for example,the evolution of damage fields of materials (Hild et al.,2015).Li et al.(2020) used the DVC method to quantitatively investigate the characteristics of shear bands in granite residual soil,including the tendency,dip angle,thickness,and connectivity of the shear bands.Based on the results of CT reconstructions,finite element models can be constructed,and simulation results can be compared with DVC calculation to verify the mesoscale evolution of cracks (Yang et al.,2017).This may assist in the development of related theories,allowing a deeper understanding of the failure mechanisms of geomaterials.However,there are few studies concerning the quantitative evolution of cracks in shear bands by CT scanning and geotechnical tests.As it is difficult to use these methods to accurately determine which cracks are initiating,propagating or terminating,the evolution and characteristics of 3D crack mesostructure in shear bands are still unclear.

As there are various and complex pre-existing pores and cracks in granite residual soil(Li et al.,2019),it is difficult to use currently available methods to accurately analyze the evolution of cracks in shear bands.To study the evolution of shear bands in granite residual soil with complex mechanical properties during loading,it is necessary to deepen the relationships between shear bands and cracks.In this study,we proposed a quantitative method for classification of the cracks based on DVC.First,the granite residual soil was scanned using CT during triaxial shear testing to obtain volume rendered images at different loading stages.Then,3D strain fields and shear bands were obtained by the DVC method.Finally,the evolution of the cracks and shear bands was analyzed using the new crack analysis method.The results provided a mesoscale insight into the shear failure characteristics of granite residual soil.This insight contributes to understanding of the microscopic relationship between fractures or shear bands and landslides.

2.Materials and methods

2.1.Materials and experimental process

The granite residual soil samples were obtained from a foundation pit close to the Houhai subway station in Shenzhen,Guangdong Province,China.The groundwater level was 4.4 m,and the granite residual soil layer was distributed at a depth of 9.3-20.8 m.Table 1 lists the basic physical properties of the samples.The maximum diameter of the coarse particles exceeded 5 mm,the content of coarse particles larger than 2 mm reached 38%,and the content of coarse particles smaller than 0.075 mm exceeded 47%.If the diameter of the sample is too small,the microstructure obtained by CT scans cannot fully represent the material properties of the granite residual soil.Therefore,the sample diameter not less than 50 mm was used to ensure that the ratio between the maximum particle size and the diameter of the soil sample was 1/10.Then,X-ray triaxial testing was performed (Li et al.,2020).

Table 1 Basic physical properties of the granite residue soil.

CT observations were performed using a Vtomex S micron CT scanner (Fig.1a),which was composed of an X-ray source,a CT imaging system,and a CT detector; and its highest resolution was 2 μm.The sample was placed on a rotating table controlled by a computer.During the test,the sample and table rotated steadily.According to the relationship between the accuracy of the CT scanning equipment and the sample diameter,the resolution was set to 38.96 μm/voxel.

To reflect the real stress state of the soil,the soil sample was gathered from a depth of approximately 10-20 m in the foundation pit.The confining pressure was set to 200 kPa,and the loading rate was 0.12 mm/min for the X-ray triaxial test (Li et al.,2020).The triaxial shear test was conducted after the pore water pressure was decreased to less than 5% of the initial value.Subsequently,the sample was moved out of the pressure chamber and placed on the rotating table,and the middle of the sample was scanned.After a single triaxial shear loading,the sample was scanned again.The average height and diameter of each sample were measured using a Vernier caliper.After the CT scanning step,the sample was placed back in the triaxial pressure chamber and reconsolidated for 20 min.The above steps were repeated until the whole test was completed.The results of the test and the CT scan points are illustrated in Fig.1b.The samples were loaded four times and scanned five times in total (indicated as Nos.1-5 in Fig.1b).

2.2.Crack classification method

2.2.1.Position matching of cracks

Prior to the crack classification analysis,it was necessary to match the 3D spatial positions of the cracks before and after loading.Because the 3D positions of the cracks changed after loading,the cracks at different loading stages could not be directly compared and analyzed (as shown in Fig.2).The particle tracking method (Cheng and Wang,2019) can track the spatial position of particles under different loadings.However,cracks are completely different from hard and stable particles,and their 3D geometry and volume may change,regenerate or vanish.Therefore,it is necessary to accurately transform the spatial positions of the cracks in the initial stage to those in the loading stage prior to classification.The DVC method can be used to accurately calculate 3D displacement fields of materials(Li and Shu,2020).Accordingly,the 3D positions of the initial cracks were transformed to their corresponding positions during the loading stage by DVC.

Fig.1.Overview of the samples and CT scanner:(a)CT scan system;(b)Stress-strain curves and scan points;(c)Photographs of a sample before and after testing;and(d)Image of a deformation volume.

Fig.2.Example of differences in cracks without and with the DVC transformation.

The coordinate transform equation is

where X denotes the 3D coordinate of cracks at the initial stage,X′represents the new 3D coordinate after transformation,and T represents the coordinate transformation formula.

2.2.2.Classification of cracks

It is difficult to use conventional methods to conduct crack analyses quantitatively,especially for granite residual soil,which has a considerable number of cracks in the initial state.It is also difficult to identify the key roles of different kinds of cracks in the evolution of shear bands.If the images of the cracks before and after loading are superimposed,there is a problem related to crack connectivity.For example,the crack initiation may be observed,but it may connect with some other cracks in the loading stage.For this,the crack connectivity coefficient number C is defined as the number of cracks at the initial stage that connect to cracks at the loading stage.

As illustrated in Fig.3,the cracks are classified into six types according to their crack connectivity coefficient number C and other important characteristics:

(1) Obsolete cracks are observed at the initial stage and do not connect with any other cracks during the loading stage:

where Ciis the connectivity number of the ith crack at the initial stage;∏Aand ∏Brepresent the crack group sets at the initial stage and the loading stage,respectively;fiis the number of the ith crack at the initial stage; and ∩ represents the crack connectivity calculation.

(2) Brand-new cracks are produced at the loading stage and do not connect with other cracks at the initial stage:

where Cjdenotes the connectivity number of the jth crack at the initial stage,and fjis the number of the jth crack at the initial stage.

(3) Isolated cracks have one-to-one connectivity with other cracks at the initial stage:

(4) Split cracks form when one crack at the initial stage separates into multiple cracks during the loading stage:

where N indicates the number of the ith crack at the initial stage that is split into,and fjnrefers to the nth crack of the fjNcrack group.

(5) A combined crack forms when multiple cracks at the initial stage connect to form one crack during the loading stage:

where M indicates the number of cracks that the jth crack at the initial stage is split,and fimrefers to the mth crack of the fiMcrack group.

(6) Compound cracks differ from the above five kinds of cracks.This type of crack is complex and exhibits the following characteristics:(i)the crack at the loading stage is connected with multiple cracks at the initial stage;and(ii)those cracks at the initial stage are connected with multiple cracks at the loading stage.

Fig.3.Schematic of the crack classification method.

Fig.4.Calculation domain and bent closed surface.

The crack classification method is applicable to cracks at the initial and loading stages.The crack evolution analysis is conducted as follows:

(1) Reconstruct the CT scanning images to obtain volume images at different loading stages,select the areas to be analyzed and use the DVC method to calculate the 3D displacement field at different loading stages to obtain the displacement fields in the x-,y-,and z-direction,and calculate the strain fields and shear bands.

(2) Segment the volume images by the threshold segmentation method to extract and mark the cracks.

(3) Transform the 3D coordinates of the cracks at the initial stage to the specified loading stages according to Eq.(1).When a complex closed 3D surface is formed,the original regular boundary cannot be maintained after loading(see Fig.4),and thus the cracks at the loading stage do not completely correspond to the cracks at the initial stage after transformation.To improve the calculation accuracy,a complex 3D convex hull surface was taken as the standard boundary,and the cracks at the loading stage were cut (i.e.the cracks outside the standard boundary were deleted).

(4) Classify the cracks as obsolete,brand-new,isolated,split,combined,and compound.

(5) Conduct statistical analysis of various cracks,including the volume content,volume change rate,and 3D visualization;and analyze the relationship between cracks and shear bands.

The flowchart for the crack evolution analysis is illustrated in Fig.5.All the DVC analyses were based on in-house iDVC software(inspire DVC,https://github.com/lichengshengHK/iDVC).

3.Results

3.1.Shear bands

Fig.6 shows the 3D volume images and cracks of granite residual soil at different loading stages.The samples exhibited significant deformation in terms of increase in the axial strain and a shear band at the end of the test.As some large-volume cracks were easily compacted at the initiation of the triaxial shear process,the crack volume decreased slowly with increasing axial strain (see Fig.A1 in the Appendix).

According to the 3D strain field results obtained using the DVC method,the 3D strain field nephograms are shown in Fig.7.The displacement field was considered to exhibit significant banding characteristics when the equivalent strain exceeded 20%.Therefore,the shear band was assumed to occur when the strain exceeded 20%(Li et al.,2020).Under an axial strain less than or equal to 4%,no shear band was formed in the sample.When the axial strain was 8%,a few shear bands appeared in local areas of the sample,and the direction of the shear bands was insignificant.Under an axial strain of 12%,there were some significant shear bands with complex geometric shapes and tilt characteristics were noticed in the sample.The stress-strain curve began to soften at an axial strain of 12%.When the axial strain reached 16%,a mass of shear bands appeared in the sample,and the corresponding stress-strain curve showed a significant stress-softening phenomenon.

Fig.8 shows different CT scanning slices and shear strain nephograms.It is found that the distribution of shear bands was particularly affected in presence of quartz particles.For example,the shear bands were mostly distributed in areas of clay and generally bypassed the quartz particles,or bifurcation occurred.Moreover,most of the large cracks occurred between quartz particles,resulting in fewer large cracks in the shear bands.

3.2.Cracks of the entire sample

According to the proposed crack classification method,the cracks at different loading stages were classified and analyzed.The 3D distribution maps of the six types of cracks are presented in Fig.9,and the volumes of different cracks are shown in Fig.A2 in the Appendix.The evolution of all the cracks is illustrated as follows:

(1) For obsolete cracks,their volume increased slowly with increasing axial strain.The reason was that some cracks were easily compacted and made obsolete during the triaxial shear process.

(2) Brand-new cracks were gradually generated with increasing axial strain.According to the triaxial stress-strain curves in Fig.1b,the sample began to soften and may have been damaged at an axial strain of 12%.With increasing axial strain,the softening of the stress-strain curves was more pronounced,and the volume and number of brand-new cracks increased.

(3) For the isolated cracks,their volume exhibited only a slight growth trend,demonstrating that such local areas were relatively “safe” as it is difficult for extra loading to affect such areas.

(4) A portion of the cracks separated at the initial stage of test loading.These split cracks gradually transformed into other kinds of cracks with increasing axial strain.

(5) For combined cracks,their volume increased slowly with increasing strain.That is,only a small number of these cracks formed when cracks simply combined during loading.

(6) Most of the cracks at the initial stage were compound cracks,and the volume of the compound cracks at different loading stages exhibited a significant attenuation trend,indicating that the crack volume was compressed.

Similar CT tests indicated that there was generally an obvious mass of cracks in brittle materials,such as rock and concrete,and soil under ultra-low or even no confining pressure (Wang et al.,2018b; Skaryˊnski and Tejchman,2019; Tang et al.,2019).However,it was observed that the plastic properties of soils were significantly different from those of brittle materials,and the volume of cracks in the samples did not simply increase with failure development,but exhibited a complex evolution.As there is severe shear deformation in the local shear bands,cracks presented in the initial state may be compressed.As a result,the cracks may not be remarkable under shear deformation as that in soils with characteristics of porosity and plasticity.When there is no enormous shear deformation in other areas,the initial cracks are not compressed,and most of them are retained.It is interesting that those cracks in shear bands directly affect the local strength of the soil,i.e.complex cracks play an important role in shear bands.

Fig.5.Flowchart of the crack evolution analysis.Note that cracks of different colors represent different connected crack groups.

3.3.Cracks in shear bands

In most cases,the failure of geotechnical materials has been primarily attributed to shear band consistency.Therefore,to further understand the failure characteristics of shear bands in granite residual soil,we analyzed the 3D characteristics of the shear bands and specifically,the cracks in the shear bands.

To understand the evolution of cracks in the shear bands of the sample during triaxial shear process,we chose representative 3D shear bands as the reference for the statistical analysis of various cracks.In Fig.7,the spatial connectivity and banding characteristics of the shear bands were significant at an axial strain of 12%,and the corresponding stress-strain curve displayed a stress-softening phenomenon (i.e.the sample was damaged).Accordingly,the shear bands at this stage provided a good reference.Then,the 3D spatial coordinates of the various cracks in the reference shear bands were converted to those at different loading stages.Finally,the distribution,content,and evolution of those cracks were calculated and analyzed.

Fig.10 shows the 3D spatial distribution of the cracks at different loading stages in the shear bands,where the translucent-graywhite regions represent the shear bands and other colors represent different kinds of cracks.As shown in Fig.11,the total volume of the cracks in the reference shear bands did not always increase.Under an axial strain less than or equal to 8%,the total volume of the cracks was relatively stable.Because of the formation of brandnew cracks,the total volume of the cracks increased rapidly as the axial strain reached 12%.

Fig.6.Volume images and cracks at different loading stages.Note that different colors represent different connected crack groups.

Fig.7.3D nephograms of equivalent strain and 3D distributions of the shear bands.

The variations in the total volume of cracks and the percentages of different types of cracks in the shear bands are described as follows:

(1) Under an axial strain of 4%,there were mainly compound cracks,split cracks,and a few brand-new cracks in the shear bands.Compound cracks accounted for 54.23% of the total volume,while brand-new cracks accounted for only 13.4%.

(2) When the axial strain was 8%,compound cracks in the shear bands did not decrease significantly,and their content was 51.18%.However,brand-new cracks in the shear bands showed a rapid growth trend,and their volume content increased to 35.37%.Because cracks constituted the weakest region of soil,the considerable number of brand-new cracks at this stage promoted the development of the shear bands at later stages.As a consequence,a small number of shear bands were formed in the sample at this stage.

(3) Under an axial strain of 12%,the volume and connectivity of the shear bands were notable.Due to the considerable deformation that occurred close to the shear bands,the large volume of the compound cracks was compressed significantly,and their volume content was reduced from 51.18%to 33.54%.Meanwhile,with the severe deformation of the soil,brand-new cracks remained in a state of rapid growth,and their volume content increased from 35.37% to 56.45%.

(4) Under an axial strain of 16%,the volume content of compound cracks in the shear bands continued to decrease,and the volume content of brand-new cracks continued to increase to 69.92%.Combined with the stress-strain curve and the 3D distribution of the shear bands,the mesostructure in the shear bands changed dramatically and ultimately reduced the strength of the soil.

Fig.11c shows the distribution of the pore sizes of the cracks in the shear bands.This figure indicates that most of the pore sizes were approximately 0.08 mm,and the pore size increased gradually with increasing axial strain.Compared with the results in Fig.10,the mesostructure in the shear bands underwent drastic changes with increasing axial strain.Fig.11d shows the evolution curves of the volume content of brand-new cracks in the shear bands,and the connectivity index(Li et al.,2020)of the shear bands displayed a significant positive correlation with the axial strain,i.e.they increased with increasing axial strain.The relationships between the cracks and the shear bands can be simplified as shown in Fig.12.Of the different crack types,brand-new cracks exhibited the closest relationship with the evolution of the shear bands.The development of the shear bands promoted the regeneration of cracks,and brand-new cracks facilitated the development of the shear bands.The coupling effect of shear bands and cracks eventually led to destruction of the soil.

Fig.8.Comparison of the shear bands and CT scanning gray-scale images.

4.Discussion

4.1.Crack classification method

Modern fracture mechanics includes elastic fracture mechanics,elastoplastic fracture mechanics,and other mechanics.The fracture types include type-I,type-II,and type-III fractures.Cracks are classified according to their 3D spatial relationships before and after loading,which is useful for analysis of the evolution of complex cracks.However,this was not included in the frameworks of fracture mechanics.In addition,we identified the following two problems when trying to include fracture mechanics in our study.

(1) Crack geometry simplification

Before predicting the fracture type,we need to simplify the geometry of the 3D reconstructed cracks.Unlike the simple tensile test,the number of initial cracks in a sample is greater than ten million,and their geometry is complex (Fig.13).The cracks do not have simple planar or ellipsoidal geometries,and most of them have thick,complex 3D surfaces.Problems may arise when we classify the failure modes of tens of millions of cracks via fracture mechanics:How effectively or reasonably can cracks with complex geometric shapes be simplified to facilitate their classification according to fracture mechanics? Should they be simplified into simple planes or V-shapes?This simplification will not change the crack properties.However,because the shapes of cracks in soil are complex,a single larger crack probably has different properties from that of a smaller crack.

(2) CT scanning accuracy

At present,many scholars have used the digital image correlation(DIC)method to experimentally measure the crack evolution of different materials (Xu et al.,2017; Baldi,2020; Francesconi et al.,2020; Hassan,2021).According to the investigations of breaking tests using the DIC method,the test material generally has only a single crack,and the local image resolution in the crack is relatively high.To better reflect the characteristics of the material,the resolution of the CT triaxial test in this study is 38.96 μm/voxel.At this accuracy,even though most cracks can be well reconstructed,the accuracy at the tips of the cracks may not be sufficient and may be affected by image noise.As a result,the CT scanning accuracy does not reach the micrometer scale.

Owing to the problems of crack geometry simplification and CT scanning accuracy,it is difficult to accurately locate the tip positions of tens of millions of cracks generated.This affects the use of the DVC method when calculating the displacement field or the strain field,and may ultimately affect the classification of fracture type based on the surrounding displacement field.

4.2.Distinguishing between cracks and pores

In general,the original voids in a sample can be simply considered to be pores because this reflects the characteristics of the void structures of the material in the initial state.Cracks of different scales may form in the interior of a sample under large deformation.These cracks may be of simple strips,and have complex surface shapes or have near-spherical or elliptical shapes.Their shapes are closely related to the local stress characteristics of the material,the difference in the strength distribution of the material,and the CT scanning accuracy.

In this paper,we obtain the 3D spatial positions of different cracks before and after loading using the DVC method and then classify and quantitatively analyze the cracks according to their spatial relationship in 3D space.Here,cracks are tentatively classified according to our crack classification method.For example,the brand-new,split,combined,and compound cracks can be temporarily classified as cracks because the geometric shapes of those cracks at the initial state undergo significant changes.Meanwhile,obsolete and isolated cracks can be classified as pores because their geometry does not change qualitatively.However,this classification method is not strict,for example,compound cracks may contain initial pores and brand-new cracks.In summary,accuracy limits the quantitative crack evolution analysis method developed in this study for distinguishing and analyzing the evolution of pores and cracks.

Fig.9.3D distribution maps of different types of cracks at various loading stages.Note that the colors represent different connected crack groups.

5.Conclusions

In this study,an ex situ X-ray triaxial shear test was used to obtain mesoscale reconstruction of granite residual soil at different loading stages,and a quantitative crack evolution analysis based on the DVC method was proposed to track each crack during the test.Finally,the evolution of the shear bands and the cracks in the shear bands was quantitatively analyzed.The following conclusions can be drawn:

Fig.10.3D distribution of different cracks in the shear band with 12% axial strain as the reference.

Fig.12.Schematic diagram of the evolutionary relationships between the shear band and the cracks.

Fig.13.CT slice of a granite residual soil sample.

(1) A systematic and quantitative method based on the DVC technique was proposed for the analysis of crack evolution.According to their connectivity characteristics before and after loading,cracks were classified as obsolete,brand-new,isolated,split,combined,or compound.Statistical results for the samples showed that brand-new and compound cracks were closely related to axial loading.

(2) Compared with the evolution of shear bands and cracks in shear bands,the total volume of cracks generally increased with increasing axial strain.The volume of brand-new cracks increased rapidly,exceeding 50%,and the volume of compound cracks decreased significantly.

Fig.11.Evolution curves of different cracks in the shear bands:(a)Variation in the total volume content of cracks;(b)Changes in the volume content of different types of cracks;(c)Pore size variation in cracks; and (d) Curves of the volume content and connectivity index of the brand-new cracks.

(3) Of the different types of cracks,brand-new cracks were most closely related to the evolution of shear bands.A small number of brand-new cracks formed in the shear bands at the initial stage.Because cracks are the weakest areas in soil,the brand-new cracks in the shear bands reduced the strength of the soil,accelerating the development of the shear bands.The developed shear bands further accelerated the formation of brand-new cracks,and their coupling eventually damaged the soil.

(4) The proposed crack analysis can be helpful for researchers to understand the relationship between cracks and shear bands or landslides from a microscopic perspective and improve landslide disaster mitigation at the engineering design level.While the crack classification system lacks physical meaning,fracture mechanics could help researchers further understand the shear failure mechanism.Further in-depth research is required to determine how to combine fracture mechanics with crack classification.

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

This work is supported by the Building Fund for the Academic Innovation Team of Shantou University,China (Grant No.NTF21017),the Special Fund for Science and Technology of Guangdong Province in 2021 (Grant No.STKJ2021181),and the National Natural Science Foundation of China(Grant No.11672320).

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2021.12.028.