Literature shows that at present, scholars at home and abroad have put forward about 40 landslide prediction models and methods. Table 4.3 lists the existing representative landslide quantitative prediction models and methods. These landslide prediction models are mainly corresponding models with the development of mathematics, including deterministic prediction model, statistical prediction model and nonlinear prediction model. Deterministic model is to digitize various parameters related to landslide and its environment with real measurement, and make a clear judgment on the stability or occurrence of landslide through mathematical and mechanical reasoning or experimental methods. The statistical prediction model mainly uses various statistical methods and theoretical models of modern mathematical statistics, focusing on the macro investigation and statistics of the relationship between existing landslides and their geological environment factors and external factors, and obtains its statistical laws, which are used to fit the displacement-time curves of different landslides, and extrapolate the prediction according to the established model. Nonlinear prediction model is a landslide prediction model based on nonlinear scientific theory, which is very effective in dealing with complex problems.

Table 4.3 List of landslide prediction models and methods

sequential

A large number of landslide prediction examples show that although nearly 40 kinds of landslide prediction models and methods are listed in Table 4.3, there are not many prediction models and methods with good operability and reliability in actual landslide prediction. This manual recommends several models and methods for predicting landslides in the medium, long-term, short-term and imminent earthquakes, which are suitable for general use and have certain operability.

4.6.2. 1 medium and long-term prediction model and method of landslide

A. Stability evaluation and prediction based on limit equilibrium theory

The deformation and failure of slope is a complicated geomechanical process. In this evolution process, with the continuous development of deformation, the stability of slope is decreasing. The concrete index describing slope stability is stability coefficient, which can be calculated quantitatively by various stability calculation methods of limit equilibrium theory. Therefore, the slope stability coefficient can be used as an important index for long-term slope prediction. However, the stability of slope can only reflect the evolution stage of slope from a macro perspective, and can not directly calculate and predict the specific time of landslide.

B. GMD numerical prediction based on numerical simulation

The deformation and failure of slope is a complicated geomechanical process, and it is also a process of deformation from quantitative accumulation to qualitative change. The biggest feature of this process is that with the formation and deformation of the slope, the potential sliding surface inside the slope gradually breeds, the "damage" gradually accumulates and the strength gradually decreases, which is a quantitative change process; When the deformation develops to a certain extent, the strength reduction caused by the accumulation of "damage" of the potential sliding surface can no longer maintain the stability of the slope, which leads to the gradual infiltration of the sliding surface, qualitative change and landslide.

In order to accurately describe the development and evolution process of the above slope, a numerical prediction model describing the slope deformation and failure process can be established by establishing the geological model of the slope, combining with the mechanical mechanism analysis of deformation and failure and the actual displacement monitoring data. This model can organically couple geology (G), mechanical mechanism (M) and deformation (D), and essentially clarify the geological-mechanical mechanism connotation of landslide deformation and instability represented by various means, which we call GMD model. Relying on GMD model, by means of numerical simulation, the time is further extended and the conditions are changed, so as to evaluate the current deformation stability and predict the future development trend. Therefore, we call this landslide prediction method GMD numerical model prediction.

C. Extrapolation prediction of slope development and evolution trend (regression analysis, neural network)

At each stage of slope evolution, the usual practice is to predict the future development and evolution trend by extrapolating the existing monitoring data at any time. From a mathematical point of view, there are two main methods of extrapolation and prediction: one is to use functional expressions (such as polynomials, exponential functions, etc. ) The existing monitoring data are fitted by regression, and the regression equation of slope evolution is constructed, and then the prediction is extrapolated. The other is artificial neural network method. Neural network method mainly simulates the thinking and working mode of human beings in analyzing and solving problems. Firstly, a network system composed of multiple neurons is constructed to simulate the nerve cells of the human brain. By "learning" the existing monitoring data and storing the learning results in the "memory", the association prediction can be realized according to the new requirements. The practical results show that the neural network has strong extrapolation and prediction ability for the monitoring data with strong regularity.

However, it is impossible to directly determine the landslide occurrence time only by extrapolation of monitoring data, so it is necessary to predict the landslide occurrence time according to some basic characteristics of monitoring curves or matching criteria of extrapolation prediction methods.

D. golden section method for landslide occurrence time prediction

Through the research and statistical analysis of displacement observation curves of dozens of examples of rock mass instability at home and abroad, Huang Runqiu and Zhang Zhuoyuan found that in the three-stage curve of slope evolution with time, there is a golden section relationship between the time spent in linear stage and the sum of the time spent in linear and nonlinear stages. Specifically, it can be expressed by the following formula:

Handbook of landslide disaster early warning and prediction in Three Gorges reservoir area

Where: t1-the duration of linear stage in slope evolution;

T2- duration of nonlinear phase.

The monitoring data show that the three-stage theory of slope evolution is not only applicable to deformation, but also to other state variables that can reflect the development and evolution of slope, such as acoustic emission frequency. The golden section number in the process of slope evolution is universal. For the deformation curve, the linear stage in the above formula corresponds to the constant-speed deformation stage, and the nonlinear stage corresponds to the accelerated deformation stage. Therefore, the golden section method can be expressed as: the duration of constant-speed deformation stage in the slope evolution process is 0. 18 times of the total duration of constant-speed deformation stage and accelerated deformation stage. Therefore, if there are monitoring data since the slope has been deformed at constant speed, once the slope has entered the accelerated deformation stage, the sliding time of the landslide can be roughly estimated by the golden section method, and it is not necessary to wait until the slope has entered the accelerated deformation stage to make a prediction.

On the other hand, if the slope evolution has not entered the stage of accelerated deformation, it is difficult or even impossible to predict the specific time of landslide, which has been determined by the principle of minimum entropy generation in nonlinear scientific theory.

Short-term impending slip prediction model and method in 4.6.2.2

A. Saito Xiao Di prediction model

Japanese scholar Hideo Saito suggested that when the slope enters the accelerated deformation stage, it can be predicted according to the displacement-time curve. Take three points t 1, t2 and t3 on the slope displacement-time curve to make the displacement between t2-t 1 and t3-t2 equal, and the calculation formula of landslide failure time tr is:

Handbook of landslide disaster early warning and prediction in Three Gorges reservoir area

Saito Xiaodi method is only applicable to the time prediction after the landslide enters the accelerated deformation stage. Equation (4. 13) can also be used to directly calculate the time tr of landslide by the drawing method shown in fig. 4.2 1. In the figure, mm' and nn' are arcs with A2 as the center.

B. Grey system prediction model

Grey system theory is a new interdisciplinary subject founded by Professor Deng Julong, a famous Chinese scholar, in 1982. It takes the uncertain system with "some information is known and some information is unknown" as the research object, and realizes the correct understanding and effective control of the system operation behavior mainly by generating, developing and extracting valuable information from "some" known information. The basic idea of grey prediction model is to regard landslide as a grey system. According to the monitoring time series data of landslide changing with time, after proper data processing, it is transformed into an increasing time series, and then it is approximated by a suitable curve as a prediction model to predict the system. See appendix 1. 1 for the specific modeling process and method of grey system prediction model.

Fig. 4.2 1 diagram for calculating landslide occurrence time according to accelerated deformation stage curve (Saito Difa)

The midpoint of M.t 1 and t2; Midpoint of N.t 1 and t3

C.Verhulst forecasting model

Based on the similarity between the process of landslide deformation, development, maturity and destruction and the process of biological reproduction, growth, maturity and extinction, the German biologist Verhulst put forward the biological growth model, namely Verhulst model. Yan et al. (1988) think that the evolution of landslide also has a process of deformation, development, maturity and destruction, and the two are similar in development and evolution. Therefore, the model is introduced into the prediction of landslide deformation and time. Please refer to appendix 1.2 for the basic principle and modeling process of Verhulst.