Methods For Estimating The Roughness And The Peak Shear Strength Of Rock Discontinuities

Rock masses usually contain rocks and discontinuity networks.Discontinuities are interface surfaces or discontinuity surfaces in rock masses,such as bedding planes,joints,faults,fractures and other mechanical defects.Mechanical properties of rock masses are influenced by their discontinuity shear strength.One of the purposes of studying discontinuities is to accurately and quickly estimate their quantitative roughness to then assess their peak shear strength.So,it has great theory significance and engineering application value to study methods for estimating the roughness and the peak shear strength of rock discontinuities.Although the existing roughness estimation methods can effectively describe the morphological features of discontinuities,they may have the following limitations.Specifically,most existing methods estimate the roughness without closely incorporating shear failure mechanisms of discontinuities,making the physical meanings of these roughness parameters unclear and resulting in a weak relationship between the roughness parameters and the peak shear strength of discontinuities.However,a roughness estimation parameter,which has a strong connection with the peak shear strength of discontinuities,may contribute to building a peak shear strength criterion of discontinuities.Considering the importance of research on methods for estimating the roughness and the peak shear strength of discontinuities,the study also takes the limitations existing in the current research into account.For completely matched discontinuities under constant normal load?CNL?conditions,this research is carried out in the following several aspects.Firstly,combined with shear failure mechanism of discontinuities,two different roughness parameters are proposed respectively,including the projection area percentage?denoted as PAP?and the shear force ratio?denoted as SFR?.Then,the computational processes of these two parameters are illustrated through several applications,meanwhile,estimation effects of these two parameters are investigated via comparing with other methods.Secondly,according to point cloud data and corresponding test shear strength data of 30 artificial discontinuities,two peak shear strength criterions,named the PAP model and the SFR model,are established base on JRC-JCS model,respectively.Then the two proposed criterions are applied to estimating the peak shear strength of 11 rock discontinuity specimens,which is used for analyzing the estimation effects of the two criterions.Finally,the proposed two criterions are used to investigate the shear strength parameters of the sliding surface for the Jiweishan rockslide.Additionally,the rockslide stability is analyzed based on the proposed shear strength parameters.According to the research approach mentioned above,research on the methods for estimating the roughness and the peak shear strength of rock discontinuities is carried out.The results are obtained as follows:?1?Method for estimating the discontinuity roughness based on the PAP.It can be proved that,based on some hypotheses,there is a functional relationship between the shear strength of potential contact area and its projection area on the plane which is perpendicular to the shear direction.Therefore,the PAP is put forward as follows:two projection areas of the discontinuity surface are calculated,one is the projection of all of the potential contact areas on the plane which is perpendicular to the shear direction,the other is the projection of the whole discontinuity surface on the horizontal plane,and the PAP is the area ratio of the former to the latter.The roughness of different artificial discontinuity specimens,AD1,AD2 and AD3,are estimated using the PAP,and the results show that the PAP values of these artificial discontinuities indicate anisotropy and sampling interval effects.In addition,a strong linear correlation is detected between the roughness estimation results of the PAP method and the Grasselli method,as well as the back analysis method.?2?Method for estimating the discontinuity roughness based on the SFR.The estimation formula for the shear strength of a triangle within a discontinuity surface is derived based on Patton's model.The SFR is defined as follows:two accumulated anti-shearing force is calculated,one is for all of the potential contact areas on a discontinuity surface,the other is for the horizontal projection plane of the discontinuity surface,and the SFR is the ratio of the former anti-shearing force to the latter.Meanwhile,we hypothesis that the friction angles of the discontinuity surface and its projection plane are equal.Application studies show that?1?for the 64 profiles from published literature,the linear correlation between the SFR and the JRC_back is better than that between Z₂ and JRC_back?joint roughness coefficient calculated by back analysis?;and?2?for the 30 artificial discontinuity specimens,the discontinuity roughness estimated by the SFR demonstrate the anisotropy and sampling interval effects;the SFR value for a discontinuity in a certain shear direction decreases with the normal load increasing;there is a similarity among the roughness estimation results of the proposed method,Grasselli method and back analysis method;the linear correlation between the roughness estimation results of the proposed method and the back analysis method is also stronger than that of Grasselli method and the back analysis method.?3?Two peak shear strength criterions based on PAP,SFR respectively.To reflect the peak dilatancy angle caused by surface roughness,it is important that the proposed criterions should follow the standard formula of Mohr-Coulomb law.According to point cloud data and corresponding test shear strength data of 30 artificial discontinuities,two peak shear strength criterions,named the PAP model and the SFR model,are established based on the JRC-JCS model,respectively.For the 30 artificial discontinuity specimens,there is a strong linear correlation between their peak shear strength values from tests(denoted as?_test)and estimates(denoted as?_PAP,?_SFRFR calculated by the PAP model,SFR model respectively);and the average estimation errors of?_PAP and?_SFR with?_test are 7.06%and 6.87%,respectively.?4?Comparison analyses for application effects of the two proposed criterions.According to point cloud data and corresponding test shear strength data,the peak shear strength values of 11 rock discontinuity specimens are estimated by the PAP model,the SFR model and Grasselli model,respectively.The results show that there is a strong linear correlation between their peak shear strength values from tests(?_test)and estimates(?_PAP,?_SFR);and the average estimation errors of?_PAP and?_SFR with?_test are16.33%and 15.32%,respectively.Compared with Grasselli model,two proposed criterions can estimate the discontinuity peak shear strength with higher accuracy.?5?Roughness estimation for the sliding surface?the strong weathered shale soft layer intercalations?of Jiweishan landslide.The PAP and the SFR values are estimated for 3 discontinuity samples?S6^S8?selected from the sliding surface.The results show that there is a similarity between the roughness estimation results using the PAP and the SFR;the roughness estimation results for S6^S8 are similar to each other;specifically,the roughness for S6^S8 reaches the lowest value in the nearly positive x-axis?the positive x-axis is the shear direction justified by striations in the field?.?6?Investigating the shear strength parameters based on the PAP model and the SFR model for the sliding surface of the Jiweishan rockslide.According to the roughness estimation results of the sliding surface in the shear direction,the peak shear strength values of the sliding surface with different normal loads are estimated via the PAP model and the SFR model,respectively.Then the shear strength parameters of the sliding surface are analyzed by Mohr-Coulomb law.The results show that the shear strength parameters obtained by the PAP model and the SFR model are close;meanwhile,the obtained parameters are between the maximum and the minimum proposed by previous study.Finally,the Jiweishan rockslide stability is analyzed according to the proposed shear strength parameters?other related parameters are gained from published literature?,and the results are consistent with the truth.?7?Comparison analyses for the PAP and the SFR.On the one hand,several similarities between the PAP and the SFR:?1?both the PAP and the SFR,proposed with clear physical meaning and mechanical basis,are closely related to the peak shear strength of rock discontinuities;?2?the roughness estimation results of discontinuities estimated by the PAP and the SFR are similar;and?3?the peak shear strength values of discontinuity specimens estimated by the PAP model and the SFR model are both close to the corresponding test peak shear strength.On the other hand,several differences between the PAP and the SFR:?1?the PAP value of a discontinuity in a selected direction can be obtained according to the geometrical morphology of the discontinuity,which is generally similar with the existing roughness parameters;?2?the SFR value of a discontinuity in a selected direction can be estimated incorporating the normal load and the mechanical properties with the geometrical morphology of the discontinuity;and?3?the linear correlation between the roughness estimation results of the SFR method and the back analysis method is slightly stronger than that of the PAP method and the back analysis method.