System Reliability Analysis And Calculation Method Of Anchor Retaining Wall

Anchored slopes have a number of complicate uncertain factors and cannot bedesigned or analyzed by using traditional methods of medium value of factor of safety,since this method is not only able to demonstrate the complexity and uncertainty ofthis issue, but also is incapable of evaluating the long-term stability accurately.Herein a novel design approach was developed by taking the time-varying of loadsand resistance into account based on the probability statistics theory. This workcombining with National Natural Science Funds (50878082) and Western Project ofMinistry of Communication (200631880237) devoted into the establishment ofanalytical model of system time-varying reliability and corresponding calculationmethod for anchored retaining wall considering the statistical characteristic ofcomputational parameters of both anchorage and soils. The content and achievementswere listed as follows:(1)Assuming a log-spiral sliding surface passing through the toe of retaining wall,based on energy method, the upper bound of active earth pressure for rough walls withinclined backfill was formulated. The formula can be applied to sandy soil and clayedsoil. Extracting the screw-in angle θ0and screw-out angle θhthrough the slope asvariable, hybrid particle swarm optimization was used to search the most dangeroussliding surface globally. For sandy soil, the earth pressure coefficients in this workagree with the classical upper bound solutions of limit analysis when the inclinationof wall is small, but obviously bigger than the classical solutions while the wall angleis larger than30°. Compared to other well-known solutions obtained by limitequilibrium based on optimum principle, the solution herein is more approximate thanthe classical upper bound solution.(2)System reliability of anchored retaining wall of rib-reinforced plate wasanalyzed by considering and ignoring the failure sequence of anchor. When thesequence is ignored, the limit state equation was established by summing resistance ofall the anchors as the total resistance of system anchor. When the sequence isconsidered, the rib column is idealized to a continuous beam and anchor to be elasticsupport, the general computational formula of load acting on each anchor was derivedby using displacement method and introducing a compound stiffness coefficientdefining anchor and the surrounding soil of anchorage. Furthermore, considering multiple failure modes of anchor and relativity of each failure mode, the analyticalmethods of system reliability and corresponding computational programs weredeveloped, for both serial system of three failure modes of single anchor and parallelsystem of multiple anchors.(3)Some main failure modes, such as failures of horizontal beams and verticalbeams on the stretching and working period of framework beam, failures of normaland diagonal sections of beam and anchor failure, were molded to be a serial systemand the analytical model of system reliability for retaining wall of pre-stressed anchorcable with double beams and double columns. Based on the correlation coefficientmatrix of performance functions of every failure mode, the calculation method andprogram of its system reliability was developed.(4)Calculation model and program of internal forces for retaining wall withframework and prestressed anchor cable was developed based on matrix displacementmethod. Anchor failure was defined to be a medium state of brittle failure and ductilefailure, and the upper and lower limits of system failure probability were computedaccording to brittle and ductile failures respectively. Computed results of practicalcase indicate that when anchor is a brittle structure, the failure of one anchor willincrease marvelously the failure probability of its neighboring anchors, which verifiedthe assumption of idealizing the indeterminate structure composed of brittle elementsto a serial system; then the upper and lower limits of system failure probability foranchor under brittle failure was obtained based on correlation coefficient matrix ofperformance function of each anchor; finally performance function of anchor systemunder ductile failure was derived and its lower limit of failure probability wasobtained on the ideal state while all the anchors on the column come into the limitstate simultaneously.(5)A design technique of slope anchor by total probability method was proposed.Design point method is incapable of solving for designing parameters directlyaccording to the object of reliability index obtained by iterative computation.Computing procedure of total probability based on method of bisection is able tosearch for designing parameters on the object of reliability index in several iterations.An optima design model of anchored retaining wall based on reliability wasestablished and computed by using particle swarm algorithm.(6)Decaying functions of shearing strength parameters and anchor resistance overtime were assumed referring to the published research works and engineeringexperience, thus an analytical model of time-varying reliability for anchored retaining wall considering middle principle stress coefficient was obtained by introducingunified strength theory. The corresponding computer program was used to analyze ananchored retaining wall of soil slope. Results comparison reveals that the influence oftime-varying on computed results is larger than that rendered by middle principlestress.