A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model

Flexural toppling occurs when a series of layered rock masses bend towards their free face.It is important to evaluate the maximum bending degree and the requirement of supports of flexural toppling rock mass to prevent rock mass cracking and even failure leading to a landslide.Based on the rock tensile strain-softening model,this study proposes a method for calculating the maximum curvature(C_(ppmax))of flexural toppling rock masses.By applying this method to calculate Cppmax of 9 types of rock masses with different hardness and rock layer thickness,some conclusions are drawn:(1)the internal key factors affecting C_(ppmax)are E^(⋆)(E^(⋆)=E_(ss)/E_(0),where E_(0)and E_(ss)are the mean deformation moduli of the rock before and after reaching its peak tensile strength,respectively),the strainεt corresponding to the tensile strength of rock,and the thickness(h)of rock layers;(2)hard rock layers are more likely to develop into block toppling than soft rock layers;and(3)thin rock layers are more likely to remain in flexural toppling state than thick rock layers.In addition,it is found that C_(ppmax)for flexural toppling rock masses composed of bedded rocks such as gneiss is related to the tensile direction.

Degree of bending of concrete-filled rectangular hollow section K-joints under balanced-axial loadings

It has been found that the fatigue life of tubular joints is not only determined by the hot spot stress,but also by the stress distribution through the tube thickness represented as the degree of bending(DoB).Consequently,the DoB value should be determined to improve the accuracy of fatigue assessment for both stress-life curve and fracture mechanics methods.Currently,no DoB parametric formula is available for concrete-filled rectangular hollow section(CFRHS)K-joints,despite their wide use in bridge engineering.Therefore,a robust finite element(FE)analysis was carried out to calculate the DoB of CFRHS K-joints under balanced-axial loading.The FE model was developed and verified against a test result to ensure accuracy.A comprehensive parametric study including 190 models,was conducted to establish the relationships between the DoBs and four specific variables.Based on the numerical results,design equations to predict DoBs for CFRHS K-joints were proposed through multiple regression analysis.A reduction of 37.17%was discovered in the DoB,resulting in a decrease of 66.85%in the fatigue life.Inclusively,the CFRHS K-joints with same hot spot stresses,may have completely different fatigue lives due to the different DoBs.