| Slope is a kind of inclined geologic body with certain surface angle against horizon, which could be natural or human-made. The definition of slope contains both landslide and side slope Landslide is a kind of particular serious natural hazard, and among all kinds of slope hazard, landslide is the most dangerous one. Specifically, landslide trigged by earthquake can cause more severe hazard. Landslide triggered by Wenchuan earthquake is the major geo-hazard type in this area. The research of landslide triggered by earthquake requires the researchers to combine serial discipline together:engineering geology, hydraulic geology, constructive geology, earthquake engineering, rock and soil mechanics, etc.This issue is written to analyze the dynamic behavior of the slope under seismic load. This issue is about to research the stability issues of certain type of slope, for the benefit of human beings.The technical routine of this paper is to research the problem of general slope under equilibrium condition, and broad the result to the field of slope dynamic analysis and landslide dynamic analysis. The details of the technical routine are as follow:(1) Based on the basic evaluating methods of the safety of slope, this issue defines the coefficient of stability in three ways:the basic definition of coefficient of stability, and definition based on the integration of the stress of sliding plane, and the definition of the reduction coefficient. The relationship among these define ways is carefully analyzed. The basic definition of coefficient of stability, and definition based on the integration of the stress of sliding plane is deeply relevant, the former is the advanced interpretation of the latter on the large scale. The definition of integration is the macroscopic definition compared to the basic one, both of them are defined under the reorganization of the unchanging state of stress and the material is viewed as frictional, and the coefficient is defined as the division of resisting stress to the frictional stress. And the reduction coefficient is based on the theory of finding the point of destruction, and defines the coefficient by reducing the strength. In the simple block conditions, strength reduction definition and the basic definition of law is equivalent, but in a complex stress field conditions, the situation is very different. To reveal the strength reduction coefficient with two different definitions, this paper explores the rock mass stress field and the physical and mechanical properties of the link between fields and then presented and proved the lemma of overall limited equilibrium state. Strictly through the lemma, the issue gives the prove that the mechanics and the golden section method based on the dichotomy of strength reduction and the definition of sliding surface stress integration is not equivalent, the equivalence is true with generalized strength reduction coefficient. The author defined that the so-called generalized strength reduction method is the stress field in the points with different reduction factors, the existence of an equivalent overall strength reduction factor is proved by the integral mean value theorem, which reflects the overall strength. This definition of coefficient is completely equivalent to the definition of coefficient based on the sliding surface stress integration. However, the theoretical value of the theory of generalized strength reduction is much larger than the practical value; there is no effective implementation algorithm for it.(2) Discussed the applicability of strength reduction method. The usual bisection method provides a single reduction factor of strength, which is easily to utilize but not guaranteed. Although in most cases, the approximation is good, but it does not rule out the possibility of deviation under certain condition, especially when the geometry of the model is complicated. Numerical analysis shows the result of partial plastic flow, different from the whole stability we usually concerned. With this respect, the research on the circular arc sliding plane searching method under the definition of sliding plane stress integration is still needed for practical concern. By using the branch prediction, simultaneous multi-threading algorithm of bisection method is proposed, and applied to strength reduction calculation. A detailed analysis of the performance of parallel algorithms is presented, and the estimation formula of acceleration ratio is provided. Explored external plug-in for FLAC3D secondary development, changed the traditional FLAC3D environment strength reduction into parallel mode, which significantly improved the efficiency of calculation, gained nearly 4 times of acceleration when calculation with 7 multiple parallel threads.(3)From view of informatics, concluded the question of slide plane searching, strictly proved that the searching for sliding plane of slope is one of the NPC type problem. This proved that is impossible to design the accurate algorithm with polynomial time complexity. Just for the good result of solving NPC problem as large groups of intelligent algorithms, using intelligent algorithms to find approximate solutions group to solve the problem of direction is applicable. Practice shows that, using particle swarm optimization (PSO) could obtain approximate solutions with good performance. The significance of that is, from the science of information it confirms that the dichotomy and the golden section method based on the strength reduction with the conventional definition of stability factor approach is not entirely equivalent, which fixed the argue of this issue.(4) Studied non-circular critical slip surface searching method based on particle swarm optimization (PSO). The method uses sliding surface stress integration method to define the slope stability factor, and uses particle swarm optimization (PSO) to dynamically search the critical slip surface. The particle swarm optimization (PSO) applied to the critical slip surface searching method and implementation steps are completely stated. The multi-level particle swarm algorithm (PSO) is proposed, which established the foundation of combining the PSO algorithm with other optimization methods. Extend the PSO algorithm to parallel processing, which greatly increased the efficiency of slip surface searching, gained nearly 4 times of acceleration when calculation with 8 multiple parallel threads. Proposed the sliding surface dynamic random generation technology. In certain sense, the difficulty of introducing the particle swarm algorithm into a specific area, is not the particle swarm algorithm itself, but on how to associate the specific issues with the framework of algorithms. For the searching of sliding plane, the key factor for successfully utilizing PSO lies on the method of generating sliding plane with geometrical boundaries randomly. In this paper, for the example Australian Computer Aided Design Society (ACADS) examination questions EX1C, elaborated on randomly generated dynamic sliding surface technology, and on to program high-quality code under the specific situation..(5) Presented the principle of velocity-type seismometer, details of the algorithm for removing instrument response, and developed the relevant interface software, which fills the blank of similar software for Windows. The software can automatically read the State Seismological Bureau of the SAC format, using time-domain filtering algorithm to remove instrument response, and automatically output speed and acceleration time series with the certain format which can be read directly for SeismoSignal software for further analysis. It is noteworthy that the main shock wave in Wenchuan is only speed-type seismograph records, but the speed type seismometer can not directly record the signal of acceleration process, in order to get the acceleration from the velocity record, numerical differentiation algorithm is demanded, the problems faced by numerical differentiation is the amplification of the data error. This is commonly referred to as the tendency of instability of differential. This paper describes and compares the accuracy of different algorithms for division of differential, pointing out that calculation is essentially equivalent to delay filtering, the higher the order of the more obvious of this equivalence, and in the contrary to the usual process of "smoothing", the acceleration calculation must reserve the minute information of the record. As well, the severe seismic condition of Wenchuan, it is not enough to record by speed type seismometer, instead, more accurate record requires strong seismometer with bigger measuring range.(6) discussed in detail the solving process of dynamic problem of the slope with FLAC3D. Discussed in detail the boundary conditions, mechanical damping parameter selection method, mesh size and dynamic load matching filter choosing problem. Based on the record of Chendu(CD2), the EX1C example and the combination of vertical and horizontal seismic waves loading is applied to research on the dynamic behavior of models. Different from the regular one type seismic wave loading, this paper applied both vertical and horizontal waves, which are directed in EW and NS, separated in horizontal and vertical, so the true behavior is approach to the best extent. By using the parallel particle swarm algorithm of the slope of non-circular critical slip surface searching, obtain the position of most dangerous sliding plane at different time, and the corresponding record of stability coefficient versus time. By analyzing the stability of the coefficient curves of the frequency characteristics of the slope stability factor that has obvious frequency selectivity, prove that the frequency response of the dynamic load is uneven. Specifically for EX1C example, it is more sensitive to the low-frequency dynamic loads of 0.8HZ-3.2HZ.(7) Developed a FLAC3D three-dimensional stress field conditions (including physical indicators parameter field) algorithm for fast access. Taking the directly to indirectly, space for time, serial to parallel as guiding ideology, increase the efficiency of the algorithm hierarchically and gradually. Eventually the paper completed the stress field generation in the multi-threaded parallel algorithm, which has produced extraordinary efficiency, high-speed access technology laid the foundation for the further stress field for complex conditions to a big degree of freedom dynamic analysis of slopes, making stress field generated and accessible time-constrain is no longer a bottleneck for dynamic response analysis. The author also developed a finite-element-method-based three-dimensional stress field conditions (including physical indicators parameter field) algorithm for fast access. Based on finite difference methods, most of the parameters of finite element stored in the grid node index, the situation should be more complicated. In this paper, an algorithm based on the volume weight to achieve the three-dimensional stress field under the conditions of the rapid access is applied, and inherited the FLAC3D rapid stress condition generation technology, finally accomplished the multi-threaded parallel computing.(8) combined the basic method of slope dynamic analysis and the technology of non-arc sliding plane searching for slope, and utilize them in the research of dynamic behavior of slope. Take the Jingucun landslide of Beichuan City, Sichuan Province as example, this paper discussed the laws of dynamic pull-out area in time dimension, and the frequency characteristics of stability factor of the slope.The innovations of this paper are as follow:(1) Strictly through the lemma, the issue gives the prove that the mechanics and the golden section method based on the dichotomy of strength reduction and the definition of sliding surface stress integration is not equivalent, the equivalence is true with generalized strength reduction coefficient, made a closer of the 35-year long dispute in the rock mechanics field. It is pointed that the broad strength reduction method is more evaluable with its theoretical respect, there is no sufficient algorithm for it now. With the respect of informatics, strictly proved that the searching for sliding plane of slope is one of the NPC type problems.. The significance of the proof are:First, it is impossible to design a polynomial time complexity with the exact solution algorithm, using intelligent algorithms to find approximate solutions group to solve the problem; Secondly, the dichotomy-based (including golden section method) of strength reduction with conventional definitions of stability factor approach is not completely equivalent.(2) Invented the parallel-thread strength reduction method. A detailed analysis of the performance of parallel algorithms is presented, and the estimation formula of acceleration ratio is provided. Explored external plug-in for FLAC3D secondary development, changed the traditional FLAC3D environment strength reduction into parallel mode, which significantly improved the efficiency of calculation, gained nearly 4 times of acceleration when calculation with 7 multiple parallel threads.(3) Developed a FLAC3D three-dimensional stress field conditions (including physical indicators parameter field) algorithm for fast access. Improve the efficiency of the algorithm, eventually make possible the stress field generated by multi-threaded parallel algorithm, greatly improving efficiency, made it no longer the bottleneck of the dynamic analysis, which clean the barrier of dynamic analysis based on the stress field generation. In addition, in the field of seismic interpretation, developed the interface software to remove instrument response, which fill the blank of similar software for Windows.(4) Studied non-circular critical slip surface searching method based on particle swarm optimization (PSO). The method is applied to dynamic analysis of slopes, combined with spectral analysis theory, it is proved that the slope stability factor has obvious characteristics of frequency selectivity. Combined the basic method of slope dynamic analysis and the technology of non-arc sliding plane searching for slope, and utilize them in the research of dynamic behavior of slope. Take the Jingucun landslide of Beichuan City, Sichuan Province as example, this paper discussed the laws of dynamic pull-out area in time dimension, and the frequency characteristics of stability factor of the slope.Dynamic analysis of slope is a young field of research, many of the basic theory of slope stability analysis needs to learn, absorb and integrate. Current research still in its infancy, many theories and methods is not perfect. This is only a preliminary exploration, the following areas still need further research:(1)The method brought in this thesis is specifically for soil slope, the comparative method for rock slope demands further research. To do so, two possible ways should be carefully developed:One is to take the equivalent treatment of the fractured rock mass following the idea of 'equivalent parameters of rock mechanics', which could make the usage of uniform parameters possible for certain rock mass with similar topological structure. And the other one is to use of engineering geological research method to analyze the possible existence of a group or several groups of potential sliding surface for specific rock slope, according to network simulation results, add the controlling surface into the model established in order to use a special contact element analysis of the mechanical response. Both of the two way above are about to reflect the mechanical characteristics of fractured rock mass to certain extent, and then search the potential sliding plane using the method brought by this thesis. Therefore, it is participated that the dynamic response of rock slope can be fixed by using the method brought by this thesis, and its time domain, space domain, and frequency domain analysis method is consistent.(2) reliability of Dynamic stability of slope. Currently in geotechnical engineering, the dynamic response analysis of rock and soil parameter value is a matter of concern. It is generally believed that laboratory parameters can not be directly used as the numerical simulation input parameters, but should select the appropriate value for analysis under the broad framework of the geological analogy. In this way, different scholars will arbitrary value, how to prove the impact of on different values on the final evaluation of the stability needs for reliability studies. At present the research of the reliability of dynamic stability of slope is very limited, which will be the further research directions.(3) Continue to manage to combine the swarm intelligence algorithms with the research field of slope, and do further research on that. In this paper, the multi-level parallel particle swarm optimization of non-circular critical slip surface search of the slope allow integration with optimizations, the next step will be researching on the association of other optimizing algorism in order to solve and actual problems more properly and more accurately.(4) Research of the ratio of similitude of model under complex conditions. Dynamic analysis found that in practical use, due to the spatial scale, often on the hundreds of kilometers, the short of efficiency of calculation is inevitable no matter how carefully the program has been written or how many the parallel analysis threads have been utilized. There are two possible ways to solve this problem:one is to research on the ratio of similitude, in other words, to use small scale models with proper parameters to preclude the full scale model; and the utilization of the philosophy of dimensionlessness of fluid mechanics. However, because of the time dimension in dynamic analysis, and the unsupportiveness of main software, the last way is hard to achieve., the next step should be to research in this area.(5) Research of High Performance Computing method of Geotechnical engineering. Another way to solve the problem of deficiency of calculating ability is to invent more powerful calculation method, and there some several directions for this endeavor:parallel calculating, calculating based on GPU(Graphic Processing Unit), distributed cluster computing and cloud computing, among all those directions the cloud computing is most powerful. The next step is to rewrite all program code, to make the program appropriate to do dynamic analysis under the three-dimension complex geological conditions, including searching the sliding plane, time, and frequency analysis.
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