Calculation method of toppling dangerous rock surge based on wave maker theory

Abstract

A method for calculating surge waves caused by toppling dangerous rock masses, based on wave-making machine theory, targets the most dangerous conditions of a toppling dangerous rock mass. The toppling dangerous rock mass is simplified as a rectangular rigid block, and the maximum surge wave amplitude is assumed to occur during the rock mass's toppling. Using differential theory, a torque balance equation is established for the entire rotational process of the dangerous rock mass. An iterative solution is used to determine the velocity of the toppling dangerous rock mass at any given moment. The toppling process is then simplified to multiple shaking-plate wave-making machines generating regular waves at different times and locations. These regular waves are then superimposed and summed as the surge wave for the toppling dangerous rock mass, ultimately determining the maximum surge amplitude for the toppling dangerous rock mass.

Description

Technical Field

[0001] The invention belongs to the fields of hydrogeology and ocean engineering, and relates to a method for calculating overturning dangerous rock surges based on wave-making machine theory. Background Art

[0002] Landslide surge is a unique wave phenomenon caused by a landslide entering a body of water. Characterized by high speed, large wave height, and strong destructive power, it poses a serious threat to human activities and the ecological environment in coastal areas. Therefore, the observation and study of landslide surge is of great scientific and practical significance.

[0003] Most of the existing landslide surge prediction formulas are aimed at landslide bodies, while there are few surge prediction formulas for dangerous rock bodies. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating surge waves caused by toppling dangerous rocks based on wave maker theory, so as to solve the problem of predicting surge waves caused by toppling dangerous rocks.

[0005] In order to solve the above problems, the technical solution of the present invention is:

[0006] S1, obtain the generalized model of the dangerous rock mass, use a rectangle to include the dangerous rock mass, and obtain data, including the dangerous rock mass height H, dangerous rock mass thickness B, dangerous rock mass center initial deflection angle a0, dangerous rock mass base height h1, water depth h w and the height of the trailing edge fracture head h2;

[0007] S2, calculate the moment of inertia J of the generalized model according to the position of the dangerous rock mass base,

[0008]

[0009] S3, establish the moment balance equation for the generalized rigid body according to the rotation angle of the center of mass of the dangerous rock mass.

[0010]

[0011] S4, decompose the rotation process of the dangerous rock body into multiple Δα. At each rotation of Δα, the dangerous rock body performs uniform angle acceleration motion, and the calculated final value of a is set to the angle a1 when the dangerous rock body just enters the water. The number of iterative calculations is recorded as i;

[0012] S5, solve the angular acceleration in S3 The time for each iteration is Angular velocity ω(i)=ω(i-1)+ω′(i-1)t(i)i=2,3,4...n;

[0013] S6, obtaining a curve of the angular velocity ω of the toppling dangerous rock with respect to time t;

[0014] S7, combined with the position function X0 and velocity potential of the shaking plate wave maker

[0015] S8, solve the position function X0(i) and wave equation η of the shaking plate wave maker according to the geometric relationship of the dangerous rock mass i (x, 0, t),

[0016] where X a (i) = X0(i) - X0(i-1) is the swing amplitude at each iteration;

[0017] S9, sum the wave equations and solve the surge wave equations.

[0018]

[0019] S10, find η i The maximum value of (x,0,t) is taken as the maximum amplitude of the surge wave of the toppling dangerous rock.

[0020] The beneficial effects of the present invention are as follows: By utilizing wave-making machine theory, the derivation process of the formula for overturning dangerous rock surge is greatly simplified. The velocity of the dangerous rock mass is iteratively calculated using differential theory. Using wave-making machine theory, the regular surge waves generated in each iteration are superimposed and summed to obtain the maximum surge amplitude. This significantly enriches the formula calculation method for overturning dangerous rock surge, making it easy to obtain calculation results using a computer or manual calculation, and thus possessing high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention will be further described below with reference to the accompanying drawings:

[0022] Figure 1 is a flow chart of the calculation method of the present invention,

[0023] Figure 2 The generalized model and coordinate system of the toppling dangerous rock of the present invention are as follows:

[0024] Figure 3 This is a schematic diagram of the principle of regular wave superposition of the present invention.

[0025] Figure 4 Schematic diagram of the calculation results of the dangerous rock mass that collapsed in the Furnas Canyon in Brazil. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0027] The calculation method of overturning dangerous rock surge based on wave machine theory specifically includes the following steps:

[0028] S1: First, generalize the overturned dangerous rock into Figure 2 The center of mass of the dangerous rock mass is located at the center of the rectangle, and data are obtained, including the height H and thickness B of the dangerous rock mass, in meters; the initial deflection angle a0 of the center of mass of the dangerous rock mass, in degrees; the height h1 of the base of the dangerous rock mass and the water depth h w , unit is m; trailing edge fracture head height h2, unit is m.

[0029] S2: Find the rotation axis position of the dangerous rock mass according to the geological profile, and calculate the moment of inertia J of the generalized model according to the position of the base of the dangerous rock mass.

[0030]

[0031] After the moment of inertia J is obtained, the initial conditions of the iteration are calculated. The initial conditions of the iteration calculation are substituted as follows: a(1)=a0, w(1)=0 and

[0032] S3, according to the rotation angle α of the center of mass of the dangerous rock mass, establish the moment balance equation for the generalized rigid body.

[0033]

[0034] S4, decompose the rotation process of the dangerous rock body into multiple Δα. At each rotation Δα, the dangerous rock body performs uniform angle acceleration motion, and the calculated final value of α is set to the angle a1 when the dangerous rock body just enters the water. The number of iterative calculations is recorded as i.

[0035] S5, solve the angular acceleration in S3 The time for each iteration is Angular velocity ω(i)=ω(i-1)+ω′(i-1)t(i) i=2, 3, 4...n.

[0036] S6, obtaining a curve of the angular velocity ω of the toppling dangerous rock with respect to time t, and a one-to-one correspondence between ω(i) and t(i) through iterative calculation.

[0037] S7, combining the position function X0 and velocity potential function of the shaking plate wave maker S8, combine the one-to-one correspondence between w(i) and t(i) with the geometric relationship of the dangerous rock mass to solve the position function X0(i) and the wave equation η of the shaking plate wave maker i (x, 0, t),

[0038]

[0039] where X a (i) = X0(i) - X0(i-1) is the swing amplitude obtained in each iteration.

[0040]

[0041] S9, sum up the regular waves to solve the surge wave equation of the overturned dangerous rock.

[0042]

[0043] S10, find η i The maximum value of (x, 0, t) is taken as the maximum amplitude of the surge wave of the toppling dangerous rock.

[0044] Through the above-mentioned specific steps and details, this patent can realize the calculation of the maximum surge wave amplitude of toppling dangerous rocks, providing important technical support for the research and disaster prevention and mitigation of toppling dangerous rock surges in reservoir areas.

[0045] Take the dangerous rock mass that collapsed in the Furnas Canyon in Brazil as an example. According to the data, the initial conditions of the dangerous rock mass are H = 30m, B = 4m, a0 = 3°, h 1＝ 3m,h 2＝ 4m and h w＝ 4m. The angular velocity curve of the dangerous rock mass movement is calculated as follows Figure 4 (a), and then the final surge wave surface equation is solved by entering the wave-making plate theoretical formula as follows: Figure 4 As shown in (b), the maximum surge amplitude of the dangerous rock mass that collapsed in the Furnas Canyon, Brazil, was 3.57 m.

[0046] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for calculating toppling rock surge based on wave maker theory, characterized by: The following steps are involved: S1, obtain the generalized model of the dangerous rock mass, use a rectangle to include the dangerous rock mass, and obtain data, including the dangerous rock mass height H, dangerous rock mass thickness B, dangerous rock mass center initial deflection angle a0, dangerous rock mass base height h1, water depth h w and the height of the trailing edge fracture head h2; S2, calculate the moment of inertia J of the generalized model according to the position of the dangerous rock mass base, S3, establish the moment balance equation for the generalized rigid body according to the rotation angle of the center of mass of the dangerous rock mass. S4, decompose the rotation process of the dangerous rock body into multiple Δα. At each rotation of Δα, the dangerous rock body performs uniform angle acceleration motion, and the calculated final value of a is set to the angle a1 when the dangerous rock body just enters the water. The number of iterative calculations is recorded as i; S5, solve the angular acceleration in S3 The time for each iteration is Angular velocity ω(i)=ω(i-1)+ω'(i-1)t(i)i=2,3,4...n; S6, obtaining a curve of the angular velocity ω of the toppling dangerous rock with respect to time t; S7, combined with the position function X0 and velocity potential of the shaking plate wave maker S8, solve the position function X0(i) and wave equation η of the shaking plate wave maker according to the geometric relationship of the dangerous rock mass i (x, 0, t), where X a (i) = X0(i) - X0(i-1) is the swing amplitude at each iteration; S9, sum the wave equations and solve the surge wave equations. S10, find η i The maximum value of (x, 0, t) is taken as the maximum amplitude of the surge wave of the toppling dangerous rock.

2. The method for calculating overturning dangerous rock surge based on wave maker theory according to claim 1, characterized in that: In step S8, X a (i) = X0(i) - X0(i-1) is the swing amplitude at each iteration,

Images