Method and system for acquiring critical flow velocity of debris flow for driving giant stone to roll

Abstract

The invention relates to the technical field of debris flow disaster analysis, in particular to a debris flow critical velocity acquisition method and system for driving a giant stone to roll. The method comprises the following steps: acquiring basic parameters of debris flow and giant stone; based on the basic parameters, an impact force equation of the debris flow to the giant stone is established according to the mutual mechanical effect of the debris flow and the giant stone; based on the basic parameters, an equilibrium equation of the giant stone is established according to stress characteristics of the giant stone; and in combination with the impact force equation and the balance equation, constructing a debris flow critical flow velocity solving model, and solving the debris flow critical flow velocity solving model to obtain the debris flow critical flow velocity for driving the giant stone to roll. According to the method, the nonlinear mathematical programming model of the critical flow velocity of the debris flow for driving the huge stone to roll is constructed based on geometric parameters and physical and mechanical parameters of the huge stone, the debris flow and the slope surface, so that the critical flow velocity of the debris flow for driving the huge stone to roll is obtained, and the critical flow velocity of the debris flow for driving the huge stone to roll is accurately calculated.

Description

Technical Field

[0001] The present invention relates to the technical field of debris flow disaster analysis, and in particular to a method and system for obtaining the critical flow velocity of a debris flow that drives boulders to roll. Background Art

[0002] Debris flows are fast-moving geological disasters consisting of large amounts of sediment, rocks, and water, often occurring in mountainous and hilly areas. They are typically triggered by heavy rain, snowmelt, or other heavy precipitation events. Their movement severely damages terrain and vegetation, posing a serious threat to human life and property. Debris flows driven by large boulders are particularly destructive. Understanding and calculating the critical velocity of debris flows is crucial for predicting and preventing boulder impact disasters.

[0003] The velocity of a debris flow is directly related to the size and density of the particles it carries. When the velocity reaches a certain critical value, the debris flow can drive boulders into motion, thereby increasing its destructive power. Currently, research on debris flows, both domestically and internationally, focuses on their causes, material composition, and basic motion characteristics. However, systematic studies on the critical velocity of debris flows that drives boulders into motion are relatively limited. This is because the dynamics of debris flows are complex, involving multiple disciplines such as non-Newtonian fluid mechanics, multiphase flow dynamics, and particle dynamics.

[0004] Existing methods for studying debris flow velocity primarily include field observations, laboratory simulations, and numerical simulations. Field observations are limited by the uncontrollable and dangerous nature of natural conditions; laboratory simulations, while conducted under controlled conditions, struggle to fully replicate the complexities of natural conditions; and numerical simulations rely on the accuracy of mathematical models and computer processing power. While these methods each have their advantages and disadvantages, there remains a lack of an effective and universally applicable method for determining the critical velocity of debris flows that drives boulder movement. Summary of the Invention

[0005] In response to the shortcomings of existing methods and the needs of practical applications, in order to improve the adaptability of calculating the critical velocity of debris flows that drive boulder rolling, and accurately calculate the critical velocity of debris flows that drive boulder rolling, the present invention provides a method for obtaining the critical velocity of debris flows that drive boulder rolling, comprising the following steps: obtaining basic parameters of the debris flow and the boulder; establishing an impact force equation of the debris flow on the boulder based on the basic parameters and the mechanical interaction between the debris flow and the boulder; establishing an equilibrium equation of the boulder based on the basic parameters and the force characteristics of the boulder; combining the impact force equation and the equilibrium equation to construct a debris flow critical velocity solution model, solving the debris flow critical velocity solution model, and obtaining the critical velocity of the debris flow that drives the boulder rolling.

[0006] Based on the geometric parameters and physical and mechanical parameters of boulders, debris flows, and slopes, the present invention constructs a nonlinear mathematical programming model of the critical flow velocity of debris flows that drive boulders to roll, and then obtains the critical flow velocity of debris flows that drive boulders to roll, solving the problem of accurately calculating the critical flow velocity of debris flows that drive boulders to roll. The present invention has a clear concept, high calculation accuracy, simple application, and high adaptability.

[0007] Optionally, the basic parameters of the debris flow and boulders include the geometric parameters of the boulders, the physical and mechanical parameters of the boulders, the physical and mechanical parameters of the debris flow, and the geometric parameters of the slope. The present invention takes into account the actual mechanical parameters of the boulders and debris flows, which facilitates the accurate calculation of the critical flow velocity of the debris flow that drives the boulders to roll.

[0008] Optionally, based on the basic parameters and according to the mechanical interaction between the debris flow and the boulder, an impact force equation of the debris flow on the boulder is established, which satisfies the following formula:

[0009] in, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, The critical velocity of a debris flow that drives boulders is represented by the impact force equation constructed based on the mechanical interaction between the debris flow and the boulders. This accurately describes the mechanical interaction between the debris flow and the boulders, further facilitating the accurate calculation of the critical velocity of a debris flow that drives boulders.

[0010] Optionally, establishing the equilibrium equation of the boulder based on the basic parameters and according to the force characteristics of the boulder comprises the following steps: Based on the boulder's force characteristics, an equilibrium equation for the boulder perpendicular to the slope is established. Based on the boulder's critical equilibrium state, an equilibrium equation for the moment of roll around the boulder's contact point with the slope is established. This method analyzes the boulder's force characteristics and constructs equilibrium equations, describing the boulder's force state from multiple perspectives. This further facilitates the accurate calculation of the critical velocity of the debris flow that drives the boulder's roll.

[0011] Optionally, based on the force characteristics of the boulder, an equilibrium equation of the boulder in the direction perpendicular to the slope is established, which satisfies the following formula:

[0012] in, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Represents the normal force acting on the boulder by the slope.

[0013] Optionally, based on the critical equilibrium state of the boulder, a moment balance equation for rolling around the contact point between the boulder and the slope is established, satisfying the following formula:

[0014] in, represents the boulder diameter, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. Represents the rolling friction couple of the slope surface on the boulder.

[0015] Optionally, combining the impact force equation and the equilibrium equation to construct a debris flow critical velocity solution model includes the following steps: An objective function for solving a debris flow critical velocity model is established; a critical equation for boulder rolling is established based on the equilibrium equation; and a debris flow critical velocity solution model is constructed by combining the objective function, the critical equation, the equilibrium equation, and the impact force equation. The present invention constructs a debris flow critical velocity solution model by combining the objective function, the critical equation, the equilibrium equation, and the impact force equation, which facilitates rapid and accurate determination of the debris flow critical velocity that drives boulder rolling.

[0016] Optionally, the critical equation of boulder rolling is established based on the equilibrium equation, satisfying the following formula: ,

[0017] in, represents the rolling friction couple of the slope surface on the boulder, represents the normal force acting on the boulder by the slope, It represents the rolling friction coefficient of the boulder on the slope.

[0018] Optionally, the debris flow critical velocity solution model satisfies the following formula: ,in, represents the minimum function, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. represents the normal force acting on the boulder by the slope, represents the boulder diameter, Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. represents the rolling friction couple of the slope surface on the boulder, represents the normal force acting on the boulder by the slope, represents the rolling friction coefficient of the boulder on the slope, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, represents the critical velocity of debris flow that drives boulders to roll, represents the boulder density, Represents the acceleration due to gravity.

[0019] In a second aspect, to efficiently execute the method for obtaining the critical velocity of a debris flow driven by a rolling boulder provided by the present invention, the present invention also provides a system for obtaining the critical velocity of a debris flow driven by a rolling boulder, comprising a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, wherein the memory is used to store a computer program, wherein the computer program includes program instructions, and the processor is configured to call the program instructions to execute the method for obtaining the critical velocity of a debris flow driven by a rolling boulder as described in the first aspect of the present invention. The system for obtaining the critical velocity of a debris flow driven by a rolling boulder of the present invention has a compact structure and stable performance, and is capable of stably executing the method for obtaining the critical velocity of a debris flow driven by a rolling boulder provided by the present invention, further enhancing the overall applicability and practical application capabilities of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart of a method for obtaining the critical flow velocity of a debris flow that drives boulders to roll, provided by an embodiment of the present invention; Figure 2 This is the force analysis diagram of the spherical boulder; Figure 3 A framework diagram of a system for acquiring the critical flow velocity of a debris flow that drives boulders to roll, provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] Specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the present invention. In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that these specific details are not necessarily required to practice the present invention. In other instances, well-known circuits, software, or methods are not specifically described to avoid obscuring the present invention.

[0022] Throughout this specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present invention. Therefore, appearances of the phrases "in one embodiment," "in an embodiment," "an example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combinations and / or subcombinations in one or more embodiments or examples. Furthermore, those of ordinary skill in the art will appreciate that the figures provided herein are for illustrative purposes only and are not necessarily drawn to scale.

[0023] See also Figure 1 In order to improve the adaptability of calculating the critical velocity of debris flow that drives the boulder rolling, the critical velocity of debris flow that drives the boulder rolling is calculated accurately. The present invention provides a method for obtaining the critical velocity of debris flow that drives the boulder rolling, such as Figure 1 As shown, in one embodiment, the method includes the following steps: S1. Obtain the basic parameters of debris flow and boulders.

[0024] In the embodiment, the basic parameters of the debris flow and the boulder include the geometric parameters of the boulder, the physical and mechanical parameters of the boulder, the physical and mechanical parameters of the debris flow, and the geometric parameters of the slope.

[0025] Specifically, the geometric parameters of the boulder refer to the diameter of the boulder and the vertical distance from the point where the impact force of the debris flow on the boulder acts to the slope surface.

[0026] Furthermore, the physical and mechanical parameters of the boulder refer to the boulder density and the rolling friction coefficient of the boulder on the slope.

[0027] Furthermore, the physical and mechanical parameters of the debris flow refer to the debris flow pressure coefficient and the debris flow density.

[0028] Furthermore, the geometric parameter of the slope refers to the angle between the slope and the horizontal plane.

[0029] For further information, see Figure 2 , the angle between the slope and the horizontal plane is Force analysis of boulders on slopes, centroid of boulders O Gravity , at the point of contact between the boulder and the slope A At the point where the normal force acting on the slope is directed towards the boulder , the tangential force of the slope on the boulder , rolling friction of the slope on the boulder , at the point where the debris flow contacts the boulder BThe effect is the impact of debris flow on boulders .

[0030] S2. Based on the basic parameters and the mechanical interaction between the debris flow and the boulders, an impact force equation of the debris flow on the boulders is established.

[0031] Specifically, based on the basic parameters and the mechanical interaction between the debris flow and the boulders, an impact force equation of the debris flow on the boulders is established, which satisfies the following formula:

[0032] in, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, Indicates the critical flow velocity of debris flow that drives boulders to roll.

[0033] S3. Based on the basic parameters and the force characteristics of the boulder, establish the equilibrium equation of the boulder.

[0034] In an embodiment, establishing the equilibrium equation of the boulder based on the basic parameters and according to the force characteristics of the boulder includes the following steps: S31. Based on the stress characteristics of the boulder, establish the equilibrium equation of the boulder in the direction perpendicular to the slope.

[0035] Specifically, based on the force characteristics of the boulder, the equilibrium equation of the boulder in the direction perpendicular to the slope is established, which satisfies the following formula:

[0036] in, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Represents the normal force acting on the boulder by the slope.

[0037] S32. Based on the critical equilibrium state of the boulder, establish the moment balance equation for rolling around the contact point between the boulder and the slope.

[0038] Specifically, based on the critical equilibrium state of the boulder, a moment balance equation for rolling around the contact point between the boulder and the slope is established, which satisfies the following formula:

[0039] in, represents the boulder diameter, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. Represents the rolling friction couple of the slope surface on the boulder.

[0040] S4. Combining the impact force equation and the balance equation, constructing a debris flow critical velocity solution model, solving the debris flow critical velocity solution model, and obtaining the debris flow critical velocity that drives the boulder to roll.

[0041] In the embodiment, step S4 combines the impact force equation and the balance equation to construct a debris flow critical velocity solution model, including the following steps: S41. Establish the objective function of the debris flow critical velocity solution model.

[0042] Specifically, let the critical velocity of the debris flow that drives the boulder rolling be the objective function, which is as follows:

[0043] in, represents the minimum function, Indicates the critical flow velocity of debris flow that drives boulders to roll.

[0044] S42. Based on the equilibrium equation, establish a critical equation for boulder rolling.

[0045] Specifically, according to the equilibrium equation, a critical equation for boulder rolling is established, which satisfies the following formula: ,in, represents the rolling friction couple of the slope surface on the boulder, represents the normal force acting on the boulder by the slope, It represents the rolling friction coefficient of the boulder on the slope.

[0046] S43. Construct a debris flow critical velocity solution model by combining the objective function, the critical equation, the equilibrium equation, and the impact force equation.

[0047] In the embodiment, a debris flow critical velocity solution model is constructed by combining the objective function, the critical equation, the equilibrium equation, and the impact force equation, satisfying the following formula: ,in, represents the minimum function, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. represents the normal force acting on the boulder by the slope, represents the boulder diameter, Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. represents the rolling friction couple of the slope surface on the boulder, represents the normal force acting on the boulder by the slope, represents the rolling friction coefficient of the boulder on the slope, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, represents the critical velocity of debris flow that drives boulders to roll, represents the boulder density, Represents the acceleration due to gravity.

[0048] Furthermore, the impact force equation and the balance equation are combined to construct a debris flow critical velocity solution model, and the debris flow critical velocity solution model is solved to obtain the debris flow critical velocity that drives the boulders to roll.

[0049] Specifically, the known parameters 、 、 、 、 、 、 Substitute the nonlinear mathematical programming model of the critical flow velocity of the debris flow that drives the boulder rolling to obtain the critical flow velocity of the debris flow that drives the boulder rolling. As the objective function, 、 、 、 As the decision variable, the “penalty function method” is used to solve the nonlinear mathematical programming model, namely the debris flow critical velocity solution model, to obtain the critical velocity of the debris flow that drives the boulders to roll, as well as the calculation results of the decision variables.

[0050] For example, the geometric parameters and physical and mechanical parameters of boulders and debris flows are formulated according to the actual situation, including: the boulders are spherical in shape, the diameter of the boulders is 2.5m, and the density of the boulders is 2400kg / m 3 The debris flow pressure coefficient is 1.3, and the debris flow density is 1780 kg / m 3 The vertical distance from the point where the debris flow impacts the boulder to the slope is 1.667m; the angle between the slope and the horizontal plane is 13 degrees, and the rolling friction coefficient of the boulder on the slope is 0.6m.

[0051] The known parameters 、 、 、 、 、 、 Substitute the nonlinear mathematical programming model of the critical velocity of debris flow that drives the boulder rolling, take the critical velocity of debris flow that drives the boulder rolling as the objective function, and 、 、 、 The nonlinear mathematical programming model is solved by using the “penalty function method” and the critical velocity of the debris flow that drives the boulder rolling is obtained to be 3.89 m / s. The calculation results of the decision variables are shown in Table 1.

[0052]

[0053] Table 1 Statistical table of calculation results of the embodiment See also Figure 3 In an embodiment, to efficiently execute the method for obtaining the critical velocity of a debris flow driven by boulder rolling provided by the present invention, the present invention also provides a system for obtaining the critical velocity of a debris flow driven by boulder rolling, comprising: an input device, an output device, a processor, and a memory, wherein the input device, output device, processor, and memory are interconnected, and the memory contains program instructions for the steps of the method for obtaining the critical velocity of a debris flow driven by boulder rolling. The system for obtaining the critical velocity of a debris flow driven by boulder rolling provided by the present invention has a compact structure and stable performance, and is capable of stably executing the method for obtaining the critical velocity of a debris flow driven by boulder rolling provided by the present invention, further enhancing the overall applicability and practical application capabilities of the present invention.

[0054] In an embodiment, the processor may be a central processing unit (CPU), which may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc. The input device may be used to obtain data information. The output device may be used to output the results obtained by storing the program instructions contained in the computer program in the memory provided by the present invention. The memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory.

[0055] In one possible implementation, the memory may include a program storage area and a data storage area, wherein the program storage area may store an operating system and at least one application required for a function, etc.; the data storage area may store data created during use. In addition, the memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include NVRAM. The memory stores an operating system and operating instructions, executable modules or data structures, or a subset thereof, or an extended set thereof, wherein the operating instructions may include various operating instructions for implementing various operations. The operating system may include various system programs for implementing various basic tasks and processing hardware-based tasks.

[0056] An embodiment further provides a storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method for obtaining the critical flow velocity of a debris flow that drives boulders to roll are implemented.

[0057] The storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., which can store program codes.

[0058] In summary, the present invention constructs a nonlinear mathematical programming model of the critical flow velocity of the debris flow that drives the boulder rolling based on the geometric parameters and physical and mechanical parameters of the boulders, debris flows, and slopes, and then obtains the critical flow velocity of the debris flow that drives the boulder rolling, solving the problem of accurately calculating the critical flow velocity of the debris flow that drives the boulder rolling. The present invention has a clear concept, high calculation accuracy, simple application, and high adaptability.

[0059] Therefore, the present invention effectively overcomes various shortcomings of the prior art and has high industrial utilization value.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope described in the present invention.

Claims

1. A method for obtaining the critical velocity of a debris flow that drives boulders to roll, characterized in that: The following steps are involved: Obtain basic parameters of debris flows and boulders; Based on the basic parameters and the mechanical interaction between debris flow and boulders, an impact force equation of debris flow on boulders is established; Based on the basic parameters and the force characteristics of the boulder, the equilibrium equation of the boulder is established; Combining the impact force equation and the balance equation, a debris flow critical velocity solution model is constructed, and the debris flow critical velocity solution model is solved to obtain the debris flow critical velocity that drives the boulders to roll.

2. The method for obtaining the critical flow velocity of a debris flow that drives boulders to roll according to claim 1, characterized in that: The basic parameters of debris flow and boulders include geometric parameters of boulders, physical and mechanical parameters of boulders, physical and mechanical parameters of debris flow and geometric parameters of slope surface.

3. The method for obtaining the critical flow velocity of a debris flow that drives boulders to roll according to claim 1, characterized in that: Based on the basic parameters and the mechanical interaction between the debris flow and the boulders, the impact force equation of the debris flow on the boulders is established, which satisfies the following formula: ,in, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, Indicates the critical flow velocity of debris flow that drives boulders to roll.

4. The method for obtaining the critical velocity of a debris flow that drives boulders to roll according to claim 1, characterized in that: The method of establishing the equilibrium equation of the boulder based on the basic parameters and the force characteristics of the boulder comprises the following steps: Based on the force characteristics of the boulder, the equilibrium equation of the boulder in the direction perpendicular to the slope is established; Based on the critical equilibrium state of the boulder, the moment equilibrium equation of the boulder rolling around the contact point between the boulder and the slope is established.

5. The method for obtaining the critical flow velocity of a debris flow that drives boulders to roll according to claim 4, characterized in that: Based on the force characteristics of the boulder, the equilibrium equation of the boulder in the direction perpendicular to the slope is established, which satisfies the following formula: ,in, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Represents the normal force acting on the boulder by the slope.

6. The method for obtaining the critical velocity of a debris flow that drives boulders to roll according to claim 4, characterized in that: Based on the critical equilibrium state of the boulder, the moment balance equation of rolling around the contact point between the boulder and the slope is established, which satisfies the following formula: ,in, represents the boulder diameter, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. Represents the rolling friction couple of the slope surface on the boulder.

7. The method for obtaining the critical velocity of a debris flow that drives boulders to roll according to claim 1, characterized in that: The method of combining the impact force equation and the equilibrium equation to construct a debris flow critical velocity solution model includes the following steps: Establish the objective function of the debris flow critical velocity solution model; According to the equilibrium equation, establish the critical equation of boulder rolling; A debris flow critical velocity solution model is constructed by combining the objective function, the critical equation, the equilibrium equation and the impact force equation.

8. The method for obtaining the critical velocity of a debris flow that drives boulders to roll according to claim 7, characterized in that: According to the equilibrium equation, the critical equation of boulder rolling is established, which satisfies the following formula: ,in, represents the rolling friction couple of the slope on the boulder, represents the normal force acting on the boulder by the slope, It represents the rolling friction coefficient of the boulder on the slope.

9. The method for obtaining the critical velocity of a debris flow that drives boulders to roll according to claim 7, characterized in that: The debris flow critical velocity solution model satisfies the following formula: ,in, represents the minimum function, represents the self-weight of the boulder, represents the angle between the slope and the horizontal plane. represents the normal force acting on the boulder by the slope, represents the boulder diameter, Indicates the impact force of debris flow on boulders, It represents the vertical distance from the impact point of the debris flow on the boulder to the slope surface. represents the rolling friction couple of the slope on the boulder, represents the normal force acting on the boulder by the slope, represents the rolling friction coefficient of the boulder on the slope, Indicates the impact force of debris flow on boulders, represents the debris flow pressure coefficient, represents the density of debris flow, represents the critical velocity of debris flow that drives boulders to roll, represents the boulder density, Represents the acceleration due to gravity.

10. A system for obtaining the critical velocity of debris flow that drives boulders to roll, characterized by: The system for obtaining the critical flow velocity of a debris flow that drives boulders to roll includes: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory includes program instructions, and the program instructions are used to execute the method for obtaining the critical flow velocity of a debris flow that drives boulders to roll as described in any one of claims 1 to 9.

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