LOWER BOUND ANALYSIS OF SLOPES UNDER VARIABLE REPEATED DYNAMIC LOADS BY STRNGHT REDUCTION METHOD

Stability of slopes against seismic loads has always been a great cause of concern in seismic regions. Pseudo-static, dynamic and mixture of Pseudo-Static and dynamic methods are utilized to evaluate the behaviour of slopes against earthquake loading. Common to all the aforementioned approach is that all of them suppose earthquake loads is imposed on the slope for one time only. In reality, slopes can be subjected to many earthquakes with different characteristics during their lifetime.In general, response of mechanical systems to repeated loads might be classified into three groups. 1) If the intensity of the applied load is small enough, the whole body reflects back to its initial position and behaves solely in an elastic manner. 2) Under large repeated load intensity, plastic strain accumulation results to the collapse of the system due to excessive deformation (ratcheting). 3) A range of load intensity in between the first two groups can be imagined under which, the loaded body initially develop plastic strains, but plastic strain decrement gradually tends to diminish so that the system behaves elastically after some load repeatition. This kind of phenomenon is recognized as shakedown.In order to investigate the behaviour of slope against repeated earthquake loading, two different approaches may be followed. The first way is to conduct a load-displacement nonlinear dynamic analysis, which in addition to being time consuming, is no trustable due to uncertainties in load characteristics. The second approach is to take advantage of shakedown limit theorems that directly attain a load domain under which, slope can be regarded to be safe and cease to develop further permanent deformation after a limited number of cyclic load imposition.Shakedown limit theorems, similar to collapse limit theorems, have been developed in the form of lower and upper bound theorems. Ceradini (1980) developed the lower bound dynamic shakedown theorem and Maier and koiter (1973, 1974) presented the upper bound dynamic shakedown theorem.The first numerical shakedown solutions by finite element method and mathematical programming, is attributed to Maier (1969). Although shakedown approach has been used extensively in various fields of engineering, the first serious application of shakedown theory conducted by Sharp and Booker (1984) to find the shakedown solution of road pavements under repeated wheel loading. Most of the works on shakedown limit of geotechnical structures have been devoted to pavement design under traffic loads. Hossain and Yu (1996) and Yu and Hossain (1998), extended the method of Bottero et al. (1980) which was used previously to find the limit loads of shallow footings, to shakedown problems. This method consists of finite element elastic analysis, finite element stress analysis and linear programming. In seismic regions, slopes are subjected to variety of earthquake loading with different characteristics during their lifetime. In this regards, shakedown theory can be utilized for seismic stability of slopes. Arvin et al. (2012) and Askari et al. (2013) extended the method of Hossain and Yu (1996) to dynamic lower bound shakedown analysis and evaluated the safety of embankment and slopes under repeated seismic loads. In their study, variation of dynamic shakedown factor versus Ts/Tm is presented where Ts and Tm are the dominant period of slope and medium period of earthquake respectively. They showed that slopes might be stable under major earthquakes, but fail duo to repetition of minor seismic loads. In this paper, strength reduction method is employed to determine the safety factor of slopes against Dynamic repeated loads.

کلیدواژه ها:

Slope Stability ، Shakedown ، Dynamic Load ، Factor of Safety ، Strength Reduction.