jointly distributed random variables method

Probabilistic seismic slope stability analysis provides a tool for considering uncertainty of the soil parameters and earthquake characteristics. In this paper, the Jointly Distributed Random Variables (JDRV) method is used as an analytical method to develop a probabilistic model of seismic slope stability based on Bishop''s method. The selected stochastic parameters are internal friction angle, cohesion and unit weight of soil, which are modeled using a truncated normal probability density function (pdf) and the horizontal seismic coefficient which is considered to have a truncated exponential probability density function. Comparison of the probability density functions of slope safety factor with the Monte Carlo simulation (MCs) indicates superior performance of the proposed approach. However, the required time to reach the same probability of failure is greater for the MCs than the JDRV method. It is shown that internal friction angle is the most influential parameter in the slope stability analysis of finite slopes. To assess the effect of seismic loading, the slope stability reliability analysis is made based on total stresses without seismic loading and with seismic loading. As a result two probabilistic models are proposed.

Determination of site liquefaction potential and taking deterrent action can prevent a significant damage to structures. In this way, a probabilistic liquefaction assessment can develop potential flexibility and risk management decisions. Based on the advantage of probabilistic assessment, considerable research has been carried out in the past few years on liquefaction potential. In this research,the jointly distributed random variables method is used as an analytical method for probabilistic analysis and reliability assessment of liquefactionpotential based on cone penetration test results.The selected stochastic parameters are corrected CPT tip resistance and stress reduction factor, which are modeled using a truncated normal probability density function and the peak horizontal earthquake acceleration ratio and earthquake magnitude, which are considered to have a truncated exponential probability density function. The depth of water table and fines content are regarded as constant parameters. The results are compared with those of the Monte Carlo simulation. Comparison of the results and parametric analysis indicates very good performance of the proposed approach in assessment of reliability. A sensitivity analysis shows that themoment magnitudeis the most effective parameter in soil liquefaction potential.

During earthquake seismic waves propagate vibrations that carry energy from the source of the shaking outwards. Seismic waves can be distinguished by the velocity and shape of propagation. The velocity of waves depends on the elastic properties and density of the soil layers through which the waves pass. Probabilistic analysis of earthquake waves can be used as an effective tool to evaluate inherent uncertainty in the soil properties and the resulting uncertainty in site classification. In this research the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of shear wave velocityrelationship. The selected stochastic parameters are density, elastic modules and Poisson''s ratio which are modeled using truncated normal probability distribution functions. The results are compared with the Monte Carlo simulation, point estimated method and first order second moment method. Comparison of the results indicates very good performance of the proposed approach for assessment of reliability. It is shown that this method can correctly predict the influence of stochastic input parameters and capture the expected probability distribution of shear wave velocity correctly. It is also shown that the modulus of elasticity is the most effective parameter in shear wave velocity.

Slope stability analysis is a branch of geotechnical engineering that is highly amenable to probabilistic treatment. Probabilistic analysis of slope stability has received considerable attention in the literature, and has been used as an effective tool to evaluate uncertainty that is so prevalent in variables. In this research, the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of the stability of infinite slopes without seepage. The selected stochastic parameters are internal friction angle, cohesion and unit weight, which are modeled using a truncated normal probability distribution function. The geometric parameters, such as height of slope and angle of slope relative to horizontal, are regarded as constant parameters. The results are compared with the Monte Carlo, Point Estimated, and First Order Second Moment methods. Comparison of the results indicates the superior performance of the proposed approach for assessment of reliability.