Determination Of Three-dimensional Statistical Discontinuity Persistence For A Rock Mass Characterized By Non-persistent Fractures

The discontinuity persistence is an important index to reflect the size of fractures in rock mass,which also plays an important role in evaluating the strength and stability of engineering rock mass.However,up to now,due to the strong non-uniformity and uncertainty of the fracture in the spatial distribution,coupled with the limitations of measurement methods and technical means,there have been few studies of this parameter.Therefore,determining the 3D discontinuity persistence in practical field projects remains difficult,thus is still a subject worthy of further study.This paper takes the dam foundation rock masses of the sluice in Datengxia Hydropower Station as an example to calculate the persistence.On the basis of in-depth investigation and analysis of the engineering geological conditions of the dam foundation rock masses of the sluice,the detailed description of the structural characteristics of fractures of D¹y₁-3 and D¹y₁-2 from the Yujiang Formation of 28#dam section is focused,and on this basis,the three-dimensional fracture network simulation and persistence research are carried out.After systematic study,the following conclusions are obtained.（1）The discontinuities such as soft layer and structural fracture are well developed in the rock mass of sluice gate.Among them,the soft layer is a definite structural plane with a spacing of about 2m⁵m,while the number of structural fractures is large and the distribution is abnormally discrete.The existence of these fractures greatly reduces the strength of the dam foundation and easily constitutes the potential failure surface.Considering the development characteristics of soft layer and structural fracture,the rock masses of the sluice gate may exhibit failure along the failure surface combined by the soft layers and fractures.（2）In order to study and calculate the three-dimensional persistence of the rock mass of the sluice gate,it is necessary to comprehensively consider three-dimensional characteristics such as shape,size and orientation.In practice,only two-dimensional information of fractures on the outcrop can be collected.Therefore,it is necessary to simulate three-dimensional fracture network based on the two-dimensional information of fractures collected on the outcrop.（3）The geological analysis indicates that the three-dimensional discontinuity persistence is a function related to two two-dimensional discontinuity persistence.Such derivation indicates that the calculation for determining the 3D discontinuity persistence will be substantially simplified.In this paper,Dijkstra algorithm is used to search the potential failure path on the two-dimensional scale.The percentage of the total fracture trace length to the length of the potential failure path is the two-dimensional persistence.This method has clear physical meaning with simple and fast calculation process.（4）It is a reasonable method to calculate multiple persistence values and make statistical analysis.In this paper,Bayesian bootstrap method is used to estimate the overall statistical parameters of the persistence,and the posterior distribution range value is the recommended reference value of persistence parameters.This method can solve the uncertainty problems caused by the randomness of 3D fracture network simulation and the lack of persistence samples,so as to improve the reliability of persistence analysis results.（5）Through calculation,the population mean,standard deviation,and p-value of3D persistence of D₁y¹-3 are 38.7%³9.6%,50.2%⁵5.6%,and 48.85%⁵0.05%,respectively.The population mean,standard deviation,and p-value of 3D persistence of D₁y¹-2 are 46.00%⁴6.66%,46.0%⁵1.0%,and 55.3%⁵6.5%,respectively.For engineering design,the mean value and p-value can be properly selected as the final result of persistence for subsequent strength and stability analysis.Considering the high safety requirements of the project,this paper suggests that the maximum value of p-value,i.e.50.05%for D₁y¹-3 and 56.5%for D₁y¹-2,should be used for the subsequent analysis of the strength and stability of the dam foundation rock mass.