The Deterministic Analysis Method And The Partial Coefficient Method Of The Internal Stability Of Reinforced Slopes

Due to the less embankment volume, short construction period, economic, safety and other advantages, the reinforced slope has been widely used at home and abroad. However the existing theoretical development of reinforced slope compared to its engineering practice is relatively slow, so to carry out in-depth research of the related stability analysis method of reinforced slope for its design is of great significance. Based on the principle that the inclined interfaces in reinforced slope should not cross the reinforcement, author explores three possible failure patterns under the theoretical framework of upper bound method with inclined slice interfaces established by Donald and Chen Zuyu in reinforced slopes, and the upper bound method of reinforced slope stability based on the Coulomb sliding mode has been proposed. On the basis of this simple and clearly defined method, author put forward corresponding limit state equation and compiled Excel VBA program to calculate the safety factor, reliability index and partial factor of the reinforced slope according to FOSM method and checking point calibration method, thus the traditional safety factor method is extended to the level of reliability analysis. In accordance with the concept of relative safety rate, the safety criterion of the certainty analysis method, the partial coefficient method and the reliability analysis method are established on the same risk standard. The main conclusions got through series theoretical analysis and calculation examples are as follows:(1) According to the failure mode of the inclined interface formed by the partition of the reinforced material, the three sliding modes of the active, Coulomb and passive are proposed respectively by discussing the possible velocity fields. It has been found that within the design range for geo-rib spacing of our professional practice, the Coulomb’s mode that adopts a straight line slip surface always gave the smallest factor of safety. Therefore, author proposed the upper bound method with with inclined slice interfaces based on the Coulomb sliding mode as the certainty analysis method for reinforced slopes.(2) In the calculation of reinforced slopes, it is necessary to determine that whether the critical slip surface and each layer reinforcement with effective length were intersected, because of the limited length of reinforcement and the anchorage length to ensure the ultimate tensile strength of the material could develope. Since the actual design of reinforced earth retaining wall situation is more complicated, author have added the function of using Coulomb model to calculate the safety factor of reinforced earth retaining wall in the EMU program which was developed by Zuyu Chen and so on.(3) Based on the determinative approaches of Coulomb’s upper bound method, the author applied the theory of reliability analysis on a target example with a specified reliability index of 3.7 and allowable factor of safety of 1.35 (slightly higher than that required by codes for ordinary slopes). Given the coefficients of variability for cohesion c, friction f and geotextile strength T, which are 0.2,0.1 and 0.07 respectively, the author obtained the calibrated partial factors that are yc=1.40, γy=1.25 and γT=1.05 respectively, being close to the Chinese and overseas specifications.(4) The universal applicability of these calibrated values has been demonstrated using the criteria of’Ratio of safety margin’ proposed by the Zuyu Chen’s research team by varying the slope height, gradient and material properties. It has been found that in all these circumstances, very good regressions were obtained, demonstrating that the calibrated allowable factor of safety and partial factors can assure the results representing the risk level indicated by the reliability index involved in the slope under investigation. In particular, it was found that there exists a smooth transmission regarding all the calculated safety indices when the slope gradient becomes steeper. Therefore, the subjective specification of identifying whether a structure belonging to a wall or a slope is unnecessary.(5) To facilitate engineering design to quickly find the safety factors or the desired reinforcement spacing, the author developed a series of stability chart for homogenous reinforced slope when slope angle is 70 °,80 ° and 90°, which were based on a large number of calculations by the determinative approaches of Coulomb’s upper bound method and partial factor solution methods. And a number of simplified engineering examples’ stability were checked by the stability charts, which certificated their feasibility.(6) Through the Chengde engineering case example, considered that the Chengde reinforced slope meet the safety requirements.And confirmed that the simplified partial coefficient method is quite safe with the determinated method based on the design value of strength parameter, and they changed with the same trend. The calculated results of the traditional determinated method which only reducted the strength of reinforcement, even more closer to the results of the determinated method based on the design value of strength parameter, however, they do not move in consident.