| The most common and destructive natural random vibration is earthquake. China is one of country that earthquakes often take place. The earthquakes happened in China have great intensity, frequency and sallow earthquake focus. So landslides and other geology disasters Caused by them are also serious. At present, the study on vibration-induced slope mostly focuses on the post-survey analysis. Because Rock and soil are complexity, the slope is open and the affect factors of slope deformation and failure are diversity, the slope stability impacted by random vibration has many problems. This paper study the slope stability impacted by earthquake to study the slope stability impacted by random vibration.Vibration systems refer to the installation or operation that reflect the relationship between reasons and results, divided into time-invariant systems (constant parameter systems) and time-varying systems (change parameter systems). Random vibration is movement that can not used the function to describe. Soil seismic response is a typical random vibration, It's process of movement is unpredicted, it's movement will not repeat under the same conditions, has clear randomness. Random process usually uses n-dimensional probability distribution function F(x1,t1; ..., xn,tn) or n-dimensional probability density function f(x1,t1; ... , xn,tn)to describe. The method to describe random vibration system is impulse response method and frequency response method. The n-freedom random vibration system almost is continuous and non-linear, which used discrete model and approximate method to handle and solve.The fundamental reason of homogenous, soil-slope deformation and damage is the shear stress greater in slop than the shear strength. When slope soil vibration impact by vibration load, the relationship between siol dynamic stress and soil dynamic strain is nonlinearity, hysteresis and deformation accumulation. Soil dynamic shear modulus G decrease when shear strain increase. The relationship between soil dynamic shear modulus G and the power function of average effective stressσ0 is linear. Soil damping Ratio increase when shear strain increase.The slop soil deformation has three stages: elastic state, slasto-plastic stage, creep stage. Soil visco-plastic deformation that parallel to the slope is another slope deformation form. Slope analysis of soil response to vibration is very complex, the common analytical method is one-dimensional vibration analysis and and finite element method.The minimum earthquake magnitude to induced landslide is ML=4.5～4.7 according to the scope of slope damage induced by earthquake, dangerous degree and engineering significance. The smallest degree of seismic intensity induce to landslide isⅥ. The relationship between the earthquake-induced landslide area S ( km2) and magnitude MW is logS=MW-3.46(±0.4). The relationship between total volume of landslide and magnitude MW is logV=1.44(±0.21)MW-2.34(±1.5). Landslide amount of erosion increase when magnitude is increase.Earthquake-induced landslide controled by regional tectonic that lead to earthquake, along the fault rupture direction. The direction of landslide axial controlled by topography, the direction of landslide is sliding attack. The result of the homogenous soil hillside left to Boqishan landslide shows that: soil PGA decrease when slop depth increase, and tends to a constant, the changes is largest in 10m depth. The soil restore elastic deformation is more when soil impacted by low-intensity vibration. Ground PGA is larger when landslide is thin, the relationship is linear.The positive displacement of the homogeneous hillside is 0.00～470.86cm, The minus displacement is 0.00～118.24 cm when the homogeneous hillside impacted by random vibration. The damage probability is 3.8% during next 50 years.
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