Journal of Engineering Science and Technology Review 11 (1) (2018) Research Article

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1 Jestr Journal of Engineering Science and Technology Review () (28) Research Article Weathering Mechanis of Soft Rock under the Cobined Effect of Pressure and Teperature Wang Lin-feng,*, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian,2 School of River & Ocean Engineering, Chongqing Jiaotong University, Chongqing 474, China 2 Maeda Kohsen Co. Ltd., Fukui 99422, Japan JOURNAL OF Engineering Science and Technology Review Received 7 June 27; Accepted 26 January 28 Abstract Cause analysis and depth calculation of rock cell can significantly help deonstrate the weathering echanis of the soft rock of the rock cell. However, the current ethods of analyzing weathering echanis attach little iportance to the echanical environent of rock. Daage echanics typically involves the calculation of a daage factor. To explore the weathering echanis of soft rock at the lower part of gently inclining rock slope, this study based on the calculation ethod of a daage factor in daage echanics, proposed a calculation forula for the daage factor of soft rock under the cobined effect of pressure and teperature and the ethod for fatigue rupture. Then, taking the udstone of a single rock cell in Hongyan Mountain of Jiangjin in China as an exaple, the calculation forula and ethod for soft rock were used to analyze its weathering echanis. The analytical paraeters included weathering rate, daage, and fatigue rupture of soft rock. Results show that the axiu influencing depth of teperature on soft rock is approxiately..2, and the weathering rate of the soft rock is faster at the beginning of teperature fatigue loading. Weathering rate slows down with the fatigue nuber increasing. At the lower-level teperature difference, the weathering process of soft rock accelerates when the rock shifts fro low to high teperature. However, when the soft rock is in large teperature difference, the weathering process accelerates at the relatively lower rate. The daage of the soft rock is linearly related to the pressure fro the upper hard rock. Conclusions of this study provide a theoretical basis for the prevention and treatent of collapsed hazards of gently inclining rock slope. Keywords: Soft rock, Weathering, Gently inclining rock slope, Teperature, Pressure, Daage. Introduction Gently inclining rock slope is rock slope with inclination angles of less than. Collapsed rock on gently inclining rock slope is induced by the differential weathering of soft and hard rock. Soft rock at the lower part of gently inclining rock slope has faster weathering rate than the upper hard rock; then, rock cell is fored outside the soft rock, causing the upper hard rock to vacant and eventually collapse []. The rock cell on weathered soft rock is starter of the rock collapse at gently inclining rock slope. Thus, the rock cell ust be treated effectively to avoid collapse-related disasters. Deterining the weathering echanis of soft rock is necessary for the proper treatent of rock cell. The weathering of soft rock at the lower part of gently inclining rock slope is actually produced under the cobined effect of pressure and variations in diurnal teperature difference of upper hard rock. Rock weathering can be divided into three types: physical, cheical, and biological. The weathering of general rock is accopanied by changes in ineral coposition (i.e., cheical weathering) [2-3]. Thus, ost existing researches have ainly adopted field investigation, onitoring, laboratory test, nuerical siulation, and siilar ethods that identify the changing processes of the ineral coposition, ceent dissolution, and strength *E-ail address: wanglinfeng75@63.co ISSN: Eastern Macedonia and Thrace Institute of Technology. All rights reserved. doi:.253/jestr..2 attenuation of weathering rock [3-6]. The positioning of soft rock within rock cell is typified by a relatively dry environent (i.e., free of water, cheical fluids, and plants), and thus, cheical and biological weathering are unlikely. On the basis of field investigations, the weathering of soft rock within a rock cell is ainly caused by the joint action of upper rock fracturing and diurnal teperature difference [4], which suggests that soft rock within rock cell undergoes weathering echanis that differ fro those of coon rock. Hence, the weathering echanis of coon rock has reported in previous work cannot fully explain the weathering echanis of soft rock within rock cell at the lower part of gently inclining rock slope. 2. State of the art The assive destructiveness and abruptness of crag collapse disasters have propted foreign and doestic scholars to conduct studies on the topic. However, these studies have ainly focused on the post-collapse oveent locus of rockfall, passive protections, and failure echanis of upper hard rock. Raer et al. [7] analyzed the effects of rockfall oveent and the intercept capacity of trees on the slope. Lee et al. [8], by taking a typical layered rock slope in Korea as an exaple, studied the stability of a slope, analyzed the strength of structural surfaces and their cobination, and verified the rationality of the study ethod with Universal Distinct Eleent Code software prograing. Zhang et al. [9] analyzed the evolution process of jointed rock slope

2 Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) using fracture echanics and the strength reduction ethod. Xu et al. [-3] analyzed the stability of rock slope using a finite eleent software and by referring to daage echanics. Shukla et al. [4] analyzed the influences of earthquake, crevice water, and overloading on top slope using calculation techniques and found that top-level overloading significantly affects the stability of slope. Wang et al. [5] analyzed the failure echanis of a slope by isolating a group of structural planes, and proposed a ethod to identify the collapsible part of the slope. Chen et al. [6-7] applied fracture echanics and liit equilibriu theory to construct a calculation ethod with a crag stability coefficient. Tang et al. [8-9] conducted echanical analysis to explore the evolution process of a groupoccurring collapse disaster of a gently inclining rock stratu with weak base and applied fracture echanics to develop a ethod for deterining the collapse sequence of rock on a cliff. Zhang et al. [,4], by taking the Hongyan Cave in Chongqing as an exaple, analyzed the stability of crags using liit equilibriu and onitoring data, and it was found that the tensile stress of slope and the developent depth of rock cell significantly affect the foration and destruction of differentially weathering crags. The above studies have ainly focused on the failure echanis of hard rock on cliffs and the oveent locus and prevention of falling rock after collapse, but the foration echanis of rock cell has not been fully explained. Rock cell foration leads to the collapse of rock on slope and the weathering of lower soft rock, especially under the joint action of pressure and teperature. Studying the collapse echanis of rock of gently inclining slope is therefore necessary to establish the weathering echanis of lower soft rock. Several studies have conducted on the weathering of rock. Moeni et al. [2] analyzed the strength attenuation law of rock with different weathering degree by eploying rock uniaxial copression tests, which then provided basis for the initial obtainent of rock strength according to the weathering degree of onsite rock. Proda et al. [2] deterined the variation rule of ineral coposition and changing law of shear strength of siltstones with different weathering degree through field investigation and laboratory tests. Dubois et al. [22] constructed four odels based on carbonate saples to estiate rock densities, Poisson s ratios, and calcite dissolutions for different degree of weathering. Their odels provide theoretical basis for evaluating the strength of carbonatite. Peng et al. [2], by taking Danxia Cave as an exaple, conducted field investigations, physical and cheical tests of rock saples, and analytical experients of water saples to explore the change in ineral coposition of rock and weathering of udstone. They found that the swelling and shrinkage of clay inerals, dissolution of calcareous ceents, and hydration of ferruginous ceents can lead to rock weathering when udstone eets underground water. Jiang et al. [5]siulated and analyzed the weathering process of rock by visualizing the constant weakening of ceentation between particles through discrete eleent software prograing. The coparative results of siulation and laboratory test showed that the destruction of ceentation between particles (i.e., developent of icrocosic defects) can lead to the icroscopic cheical weathering of rock. Chen et al. [3] applied body slice casting, total analysis of rock, scanning electron icroscopy, and other analytical and testing ethods to deterine the weathering echanis of carbonatites. Their researches showed that cheical weathering essentially involved the reaction of corrosive groundwater with rock-foring inerals, and this reaction can cause structural daage to the rock. The above studies have ainly analyzed the ineral coposition, ceent dissolution, and laws of changing strength during rock weathering process, but the echanical environent of the rock (i.e., pressure produced by upper rock or teperature stress which produced by diurnal teperature difference of atosphere) has not been fully investigated. Rock under different stress conditions undergoes different weathering echanis. In other words, different echanical environent cause different degree daage. Siilarly, rock undergoes different weathering rate and peeling of block sizes. The weathering of soft rock beneath gently inclining rock slope is ainly caused by the cobined action of pressure and teperature stress of upper hard rock. Therefore, it is necessary to consider the exact echanical environent of soft rock when explaining the weathering echanis of gently inclining rock slope. On the basis of the existing work, the present study first built the calculation ethod for the daage factor of soft rock beneath gently inclining rock slope by adopting daage echanics and the heat transfer theory, and considered the joint action of pressure and teperature. Then, the study deterined the failure criteria of soft rock according to the fatigue effect of teperature and the accuulation effect of daage. Finally, the study explored the law of weathering and peeling of soft rock under the joint effect of pressure and teperature. The reaining sections of this study are organized as follows. In the third section, the calculation ethod of daage echanics is briefly explained, and the calculation odel and fatigue rupture odel of the daage factor of soft rock are presented by considering the geologic odel of soft rock at the lower part of gently inclining rock slope. In the fourth section, the weathering failure law of udstone is analyzed, and the udstone is located in Siianshan Town, Jiangjin District in Chongqing city of China. In the last section, the results of this study are suarized and the relevant conclusions are presented. 3. Methodology 3. Calculation ethod of daage factor The ethod of continuous echanics is typically adopted in daage echanics to analyze the characteristics of aterials. Under the function of external load or environent conditions, the deterioration of structural acro-echanical properties of aterials caused by the initiation and developent of icroscopic structural defects (e.g., cracks and icro-pores) and other irreversible changes are defined as daage. The weathering of soft rock at the lower part of gently inclining rock slope is essentially a continuous daage of the soft rock under pressure and teperature stress conditions. Subsequently, rock destruction is reached in the final failure ode. The weathering echanis of soft rock can therefore be explained by daage echanics, in which the index used to evaluate the aterial daage is called daage factor. The ethod for calculating the aterial daage factor is briefly described in subsequent paragraphs. Assuing that the strength of soft rock confors with Weibull distribution, the probability density function [23] can be expressed as: 66

3 Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) p ( ) = exp () where is the strain of soft rock; and are the scale and orphological function of Weibull distribution, respectively. According to continuu daage echanics, the daage factor D [23] is defined as: D= H perilous rock (2) p ( ) d D = (3) ( = ) rock cell soft rock h where D is the daage factor, a diensionless variable. The boundary condition of forula (2) is: By integrating forulas () and (3) to forula (2), the daage factor D is given as: D = exp (4) l B The weathering of soft rock beneath gently inclining rock slope is ainly induced by the pressure of upper hard rock and teperature. Fig. presents a typical type of gently inclining slope with rock cell (Fig. 2), in which H is the height and B is the thickness of the hard rock, and h represents clear height. The depth of the rock cell is l. Fig.3 shows the echanics odel of soft rock beneath gently inclining slope. The odel indicates that soft rock ainly bear the pressure of hard rock(i.e., pressure q over resultant force F on the cantilever) and the shear stress of the contact plane between the hard and soft rock. The unifor load q above the soft rock is: q =γh Fig.. Perilous rock odel of interbedded soft hard rock (5) where γ is the unit weight of hard rock. The shear stress τ of the contact plane between the hard and soft rock is: τ = qtanφ + c Fig. 2. Rock cell (6) σx = where ϕ is the internal friction angle of the contact plane and C is the cohesive strength of the contact surface. The resultant force F of the cantilever part of the hard rock acting on the soft rock is given as: F = γ Hl + ] xz (9) 2F sin θcosθ π ρ τ xz = [ 4 τ + γ( z + h 2 ) tan 2F sinθinθ 2θ + π ρ Under the action of pressure and contact load of the hard rock, the internal force at arbitrary point M of the soft rock can be expressed as: h 2F cos θ σ z = q + γ z π ρ h 2 2 (7) 3 2[τ + γ(z + h 2 )tan 3 ] [ ( )] z h 2 () where ρ is the straight distance between point M and the action point of resultant force F ; θ is the angle between the lines, which include point M and action point F along the vertical direction; x is the horizontal coordinate; σ Z is vertical copressive stress; σ X is horizontal tensile stress; and τxz is shear stress. (8) 67

4 Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) According to Hooke s law, the strain of the soft rock along the x-direction under the action of pressure and contact load of the hard rock is given by: 2 µ µ σ x σ E µ x = z () where x is the strain of soft rock along the x-direction; µ is the Poisson s ratio and E is the elastic odulus. The soft rock, which extend toward the ountain interior, can be siply described as a sei-infinite body. Assuing that the atospheric teperature ist, the teperature of the soft rock within the rock cell is T(x,t) (Fig. 4). To siplify the calculation, assuing that the teperature of the soft rock is ainly transferred along the x-direction ( ) = T x = T x,t (4) By integrating forulas (3) and (4) to forula (2), it can be expressed as follows: T ( x,t) T T T x = erf (5) 2At erf (x) = 2 x e t2 dt (6) π where erf(x) is the error function. By transforing forula (5), the teperature of point x at any tie-point is given as: T ( x,t) = T + T T x ( )erf (7) 2At Then, the teperature stress caused by teperature transforation can be expressed as: σ T = E αδt µ = E α T x,t µ ( ) T (8) The strain of the soft rock caused by teperature stress is given as: σt = T E (9) Fig. 3. Mechanics odel of soft rock The total strain of the soft rock along the x-direction under the cobined action of pressure and teperature is expressed as: s = T + x (2) Consequently, the failure criteria of soft rock according to liit strain d is given as: If s < d, then the soft rock is not in failure ode. If s = d, then the soft rock is in critical state. If s > d, then the soft rock is in failure ode. The effective stress σ~ of the rock ass in relation to the soft rock daage[25] is defined as: Fig. 4. Teperature distribution ap of soft rock With the transission of atospheric and soft rock teperature, the control equation [24] can be expressed as: ( ) t T x,t = A 2 T ( x,t) x 2 (2) where T(x, t) is the teperature at any tie-point of the soft rock in arbitrary place x; t is tie; and A is theral diffusivity (/s - ). The boundary conditions of forula (2) are given as follows: T ( x,t) = T t = (3) σ! = σ D (2) where σ is the stress of the rock ass, which does not take into consideration the daage of the soft rock. By integrating forula (4) to forula (2), it can be expressed as follow: σ = σ! exp = E exp (22) The stress strain curve of the rock under uniaxial copression loading is shown in Fig. 5, in which stress peak point is represented by c, while stress and strain are represented byσ c and c, respectively. A derivation of forula (22) is expressed as: 68

5 σ = Eexp E exp Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) factor under the joint action of upper hard rock and teperature stress. According to the calculation results, the (23) weathering daage of soft rock is deterined. which reaches the axiu stress at point c. Thus: σ =c = (24) By integrating forula (23) to forula (24), it s transfored into: c Eexp exp c c Ec = (25) Fig. 5. Stress strain curve of rock ass c Then, siplifying forula (25) as: = (26) By integrating the stress and strain values of point c to forula (22), it can be expressed as: 3.2 Identification of fatigue rupture of soft rock The constant alternation of day and night and the related teperature stress induces a kind of alternating load on soft rock. Under the action of this alternating load, soft rock produce fatigue daage. According to daage echanics, the daage factor after N ties of fatigue action [25] can be expressed as: σ c = E c exp c c Then, transforing forula (27) into: = ln σ c E c (27) (28) D = N N F N F = α ( )( + β) +β α σ T M β (32) (33) Cobining forulas (26) and (28), the can be expressed as: = ln σ c E c (29) By solving forula (26),the orphological function is given as: = c (3) At this point, the calculation forula of the Weibull distribution scale and the orphological function of and have been obtained. Subsequently, substituting these paraeters into forula (2) to obtain the daage factor of rock under arbitrary loading: D = exp ln σ c E c c ln σ c E c (3) The ethod of calculating the daage factor of soft rock (i.e., see forula (3)) can also be applied to the daage where α, β, and M represent the aterial paraeters; N is the nuber of fatigue daage of soft rock; and σ T is teperature stress. Transforing forula (2), the strain of soft rock undergo ith fatigue action is expressed as: i = ln( D i ) (34) where Di is the daage of soft rock during ith fatigue. On the basis of forulas (32) and (34), the total strain of soft rock after N ties of fatigue action can be N expressed as: N = ln N N F +β α (35) According to the superposition principle, the total strain s of soft rock caused by the pressure fro upper hard rock and fatigue action of teperature is: 69

6 s = x + N Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) (36) where xis the strain of soft rock caused by the pressure of upper hard rock, whilen is the strain of soft rock after N ties of fatigue action under teperature stress. If s > d ( d is the critical strain in the failure ode of soft rock), then the soft rock begin to collapse and the rock cell retreats. If the condition is the critical state of s = d, then forula (36) is used to calculate the ties in which soft rock endures the fatigue failure under the cobined action of teperature and pressure. The ethod of identifying the daage and fatigue rupture of soft rock can be used to deterine the weathering and peeling situation of soft rock under the function of teperature fatigue. 4. Result Analysis and Discussion Figs. 6 and 7 present the iages of the udstone beneath a cliff in Hongyan Mountain of Siianshan Town in Jiangjin District. The hard rock above the rock cell is a sandstone. The height of the hard rock is 8 and its thickness is 7 ;the length of the controlling structural plane is 9.5; the depth of the rock cell is 6 and its height is 3 ; and the weight of the sandstone is 25 3 kn/. By contrast, the soft rock is a udstone. The weight of the udstone is 23 3 kn/, the elasticity odulus is 4 2 MPa; theral diffusivity is -3 2 c 3 /s ; and the coefficient of the linear expansion - is 5-6 /C.The aterial daage paraeters of the udstone are, α = -.86, β =.72,and 6 M = 8.6 MPa [24,26]. The tensile strength of the udstone is 5 MPa and its liiting strain is The annual average teperature in Siianshan Town is 287.5K, and this average is designated as the initial teperature of the udstone. Then, the teperature exchanged on August 28, 26 is applied to analyze the weathering of soft rock(i.e., the daily average teperature on that day was 3.5 K). Finally, the teperature change of the udstone is calculated according to the teperature field forula in Section 3. (Fig. 8 and Table ). The surface of the udstone has the highest teperature, as shown in Fig. 8. Furtherore, the teperature of the udstone decreases rapidly as depth increases. After 24 hours of teperature exchange, the axiu influencing depth of the external teperature on the udstone is approxiately. In 26, Siianshan Town had 85 days with an average teperature higher than the average teperature. The average teperature for those 85 days is 297.5K and is considered as the fatigue teperature. Calculations are conducted following the ethod of identifying the fatigue rupture of soft rock (Section 3.2).The udstone start to fall after 58 ties of teperature loading. Fig.9 and Table2 show the relationship between the fatigue tie and total strain of the udstone under the fatigue of K. As depicted by the curve in Fig. 9, the strain on the udstone surface notably increases at the start of the loading. However, as the frequency increases, the rising strain on the udstone surface becoes less apparent (Table 2). Teperature/K x/ Fig. 8. Teperature variation curve of udstone along the x-direction 4. Fig. 6. Hongyan Mountain rock cell 8 s / Fatigue ties 6 Fig.7. Physics odel of the Hongyan Mountain rock cell Fig. 9. Total strain versus fatigue ties 7

7 Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) Table. Teperature value of the udstone along the x-direction Teperature T/K x/ Teperature T/K x/ Teperature T/K x/ Table 2. Mudstone stress versus fatigue ties Fatigue ties/ties N Stress/E-4 s The teperature field forula used to calculate the daage factors (Section 3.) can also be used to deterine the internal teperature distribution of the soft rock with varying teperature difference. Fig. shows the teperature change curve of the soft rock under the different diurnal teperatures of 275.5, 279.5, 283.5, and 287.5K. The teperature of the soft rock surface rapidly decreases as rock depth increases. Fig. shows the axiu influencing depth of the teperature on soft rock under varying diurnal teperature conditions. Given four different situations, the axiu influencing depth of the rock is approxiately..2. Therefore, the ipact of daily diurnal teperature difference on the rock is liited. In other words, the changes in teperature resulted in weathering depths approxiately..2, which is in line with the current onsite situation wherein surface rock is crubly while core rock is relatively unaffected. Furtherore, the curve in Fig. 4 appears nearly flat. The findings iply that the increase in teperature difference only has a inial effect on the axiu depth of soft rock. The presented paraeters are the functions of the active tie of teperature and heat transfer property of rock. Teperature/K K 283.5K 279.5K 275.5K The distance fro the surface/ Fig.. Teperature change of udstone along the x-direction under different external teperature conditions As discussed in section 3., the daage factor D of soft rock can be calculated by considering the variations in teperature difference. Fig. 2 shows the changing curve of the daage factor of soft rock under different diurnal teperature conditions. The diurnal teperature difference is in the range of K. The curve of Fig. 2 also iplies that rock daage increases as the teperature difference increases. The curve also appears nearly flat, which suggests that the rock daage is sensitive to teperature difference. As diurnal teperature difference increases fro to K, the rock daage reaches %. Thus, the larger the diurnal teperature difference is, the faster the weathering rate will be. Influencing depth/ Diurnal teperature difference/k Fig.. Influencing depth of teperature of udstone under varying teperature difference conditions The daage factor of the soft rock caused by varying teperature difference and fatigue nuber was calculated according to the daage factor forula for the ethod of identifying teperature fatigue (Section 3.2). As shown in Fig. 3, the diurnal teperature difference is fro to K. As depicted by the curves, the daage to soft rock is apparent when fatigue nuber increases. As the teperature fatigue load increases, the rock daage rate increased rapidly. As the fatigue nuber continue to increases, the rock daage rate also increases, but at a relative slower pace. When the daage exceeds the critical value, the rock start to fall apart, which corresponds to the onset of weathering and peeling of soft rock. Fig. 3 also shows that when the diurnal teperature difference is relatively sall, the distances between the curves are relatively wide. The finding indicates that when the teperature difference is relatively low even as teperature increases, the rock undergoes serious daage, i.e., weathering rate increases. By contrast, when the external teperature difference of the soft rock is relatively high, any increase in the teperature difference results in an insignificant increase in rock daage, i.e., weathering rate increases at a lower level. 7

8 3. Wang Lin-feng, Sun Hao, Yao Chang-yin, Jin Hong-hua, Tang Hong-ei, Wang Zong-jian/ Journal of Engineering Science and Technology Review () (28) Conclusion D Diurnal teperature difference/k Fig. 2. Daage factor D caused by variations in teperature difference D K 295.5K 29.5K 287.5K 283.5K 279.5K 275.5K Fatigue ties Fig. 3. Fatigue ties versus daage factor D under varying teperature difference conditions Fig. 4 shows the daage to soft rock under the different stress conditions of upper hard rock. As depicted by the figure, the rock daage increases gradually as stress (q) increases. The increase in pressure at the upper part of the rock ass can accelerate the weathering rate of soft rock. Thus, on the basis of point distribution, a linear relationship exists between upper hard rock stress and soft rock daage. Subsequently, the forula can be derived by fitting the daage factor with the press stress of upper hard rock: D =.3q D D =.3q+.226 R² =.9992 (37) q/( 5 )pa Fig.4. Daage factors D under various pressure conditions The ethod for deterining the weathering echanis of soft rock at the lower part of gently inclining rock slope has been established in the study. Then, the forula of the daage factor and the ethod to identify the fatigue rupture of soft rock under the cobined action of hard rock pressure and teperature stress were proposed. The following conclusions can be drawn: () On the basis of the internal distribution law of soft rock under varying diurnal teperature difference conditions, the axiu weathering depth of soft rock caused by teperature changes is..2. The values are in line with the current onsite situation wherein surface rock is crubly and core rock is relatively unaffected. (2) On the basis of the change law for the daage factor of soft rock under varying diurnal teperatures, the weathering of soft rock is sensitive to teperature difference. When the diurnal teperature difference increases fro to K, the weathering rate of the rock increased by %. (3) As the fatigue nuber increases, the daage of the soft rock increases. At the beginning of the loading process, the weathering rate is high, however, as the fatigue nuber increases, the weathering rate slows down gradually. (4) When the teperature difference is low, as the teperature increases, the weathering rate of the soft rock increases. While the teperature difference is large, the teperature has a little influence on the weathering rate of the soft rock. (5) The pressure of hard rock at the top part of the rock ass is linearly related to the daage of the soft rock. As the pressure at the top part of the rock ass increases, the weathering rate of soft rock increases. The forula, ethod, and analytical approaches for soft rock proposed in this study provide a theoretical foundation for the prevention and treatent of near-collapse or postcollapse segents of gently inclining rock slope, which are generally known to easily lead to disasters. The above ethods considered the weathering of soft rock at the two-diensional level only. However, the weathering of soft rock is essentially a three-diensional proble. Thus, subsequent researches ay focus on the three-diensional stress condition of soft rock and the threediensional transission of teperature. The result fro further research ay help explain the weathering echanis of soft rock with higher accuracy. Acknowledgeents The study was financially supported by the National Natural Science Foundation (54884, , and ), Science and Technology Project affiliated with the Education Departent of Chongqing Municipality (KJ437) in 24, the Foundation of Chongqing Jiaotong University (23kjc43), and National Key Research and Developent Plan Project (26YFC8223). This is an Open Access article distributed under the ters of the Creative Coons Attribution Licence 72

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