不同失稳模式的典型危岩体崩塌产生涌浪公式法体系研究

张杰; 黄波林; 董星辰; 李秋旺

doi:10.16031/j.cnki.issn.1003-8035.202407017

不同失稳模式的典型危岩体崩塌产生涌浪公式法体系研究

张杰^{1, 2,},
黄波林^{1, 2, ,},
董星辰^{1, 2},
李秋旺^{1, 2}

1.
防灾减灾湖北省重点实验室，湖北宜昌　443002
2.
三峡大学土木与建筑学院，湖北宜昌　443002

基金项目: 国家自然科学基金区域创新发展联合基金项目（U23A2045）；重庆市规划和自然资源局科研项目（KJ-2023046）；三峡大学土木与建筑学院科研创新基金项目（2024SSCX007）

详细信息

作者简介:
张　杰（1999—），男，湖北利川人，硕士研究生，主要从事危岩体涌浪灾害研究。E-mail：202308180021014@ctgu.edu.cn

通讯作者:
黄波林（1979—），男，湖北仙桃人，研究员、博士生导师，主要从事水库地质灾害及涌浪灾害方面的教学与研究工作。E-mail：bolinhuang@aliyun.com

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出版历程
- 收稿日期: 2024-07-17
- 修回日期: 2025-03-17
- 录用日期: 2025-03-18
- 网络出版日期: 2025-03-24

Study on the surge formula system of typical dangerous rock mass collapse with different instability modes

Jie ZHANG^{1, 2,},
Bolin HUANG^{1, 2, ,},
Xingchen DONG^{1, 2},
Qiuwang LI^{1, 2}

1.
Hubei Key Laboratory of Disaster Prevention and Mitigation, Yichang, Hubei　443002, China
2.
College of Civil Engineering and Architecture, China Three Gorges University, Yichang, Hubei　443002, China

施引文献

摘要

摘要:
峡谷区高陡危岩崩塌产生涌浪危害巨大，严重危及航道及景区安全；但危岩崩塌产生涌浪的系统性研究不够，针对性快速评估技术有待加强。本文旨在建立一个针对不同失稳模式的危岩体涌浪公式计算体系，以加强峡谷区高陡危岩崩塌产生涌浪灾害的快速评估技术。通过系统梳理了适用于危岩体不同失稳模式的涌浪计算公式，并建立了适用于不同失稳模式的危岩体涌浪全过程公式计算体系，以此体系为基础编制了危岩涌浪计算引擎。通过对典型压溃式龙门寨危岩体运用公式法计算体系进行涌浪计算，发现175 m水位时最大首浪高度为13.9 m，传播至2 km处传播浪高度为1.75 m，码头处爬高值为2.91 m，与数值模拟结果误差在20%以内，验证了计算体系的可行性，并进行了涌浪危险性分析。随后运用该计算体系对典型坠落式渔峡口危岩体和典型倾倒式巴西卡皮托利乌危岩体进行了涌浪计算，两者危岩体涌浪传播200 m后都进入低风险区域，体现了该计算体系在不同失稳模式下的应用情况。
- 危岩体 /
- 涌浪 /
- 公式法 /
- 涌浪计算体系 /
- 失稳模式
Abstract:
The collapse of high and steep dangerous rock in the gorge area produces huge surge hazards, which seriously endangers the safety of waterways and scenic spots. However, the systematic research on the surge caused by perilous rock collapse is not enough, and the targeted rapid assessment technology needs to be strengthened. The purpose of this paper is to establish a calculation system of dangerous rock surge formula for different instability modes, so as to strengthen the rapid assessment technology of surge disaster caused by high and steep dangerous rock collapse in canyon area. The surge calculation formulas suitable for different instability modes of perilous rock mass are systematically sorted out, and the calculation system of the whole process formula of perilous rock mass surge suitable for different instability modes is established. Based on this system, the calculation engine of perilous rock surge is compiled. By using the formula method to calculate the surge of the typical crushed Longmenzhai dangerous rock mass, it is found that the maximum first wave height is 13.9 m at 175 m water level, the propagation wave height is 1.75 m at 2 km, and the climbing height at the wharf is 2.91m. The error with the numerical simulation results is within 20 %, which verifies the feasibility of the calculation system and analyzes the surge risk. Then, the calculation system is used to calculate the surge of the typical falling Yuxiakou dangerous rock mass and the typical toppling Brazilian Capitoliu dangerous rock mass. Both dangerous rock masses enter the low-risk area after 200 m surge propagation, which reflects the calculation system under different instability modes.
- dangerous rock mass /
- surge /
- formula method /
- surge calculation system /
- instability mode

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图 1 涌浪传播区域图

Figure 1. Surge propagation area diagram

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图 2 坠落式危岩涌浪灾害示意图

Figure 2. schematic diagram of falling dangerous rock surge disaster

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图 3 压溃式涌浪灾害示意图

Figure 3. Chart of crushing surge disaster

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图 4 倾倒式涌浪灾害示意图

Figure 4. schematic diagram of toppling surge disaster

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图 5 涌浪公式计算引擎流程图

Figure 5. Surge formula calculation engine flow chart

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图 6 涌浪公式计算引擎与计算过程

Figure 6. Surge formula calculation engine and calculation process

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图 7 龙门寨危岩体剖面图（郑嘉豪等，2020）

Figure 7. Profile of Longmenzhai perilous rock mass (Zheng Jiahao et al., 2020)

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图 8 压溃式涌浪公式计算体系计算结果

Figure 8. The calculation results of the collapse surge formula calculation system

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图 9 渔峡口危岩体涌浪过程

Figure 9. Surge process of Yuxiakou perilous rock mass

（a） t = 0 s；（b） t = 4 s；（c） t =8 s；（d） t =14 s

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图 10 坠落式涌浪公式计算体系计算结果

Figure 10. The calculation results of the falling surge formula calculation system

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图 11 Capitólio危岩体涌浪过程（Maciel，2023）：（a）危岩体原始尺寸；（b）发生倾倒及概化尺寸；（c）形成飞溅及入水速度

Figure 11. Surge process of Capitólio perilous rock mass (Maciel, 2023)

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图 12 倾倒式涌浪公式计算体系计算结果

Figure 12. Calculation results of toppling surge formula calculation system

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表 1 涌浪研究方法及优劣

Table 1 Surge research methods and advantages and disadvantages

方法	公式法	概化物理试验模型法	缩尺物理模型试验法	数值模拟法
准确度	中	中-高	高	高
时间	少	少	非常多	多
经费	低	低	非常高	中等
技术门槛	低	中等	高	高

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表 2 最大首浪公式

Table 2 Part of propagation wave formula

公式	来源	适用模式	适用条件
$V = \frac{v}{\sqrt{g h_{w}}}$ $\frac{H_{s}}{h_{w}}$ $\frac{H_{max}}{H_{s}}$	Noda^[15] （1970）	坠落式倾倒式	h_落＞h_w
$\frac{H_{max}}{h_{w}} = 1.17 \frac{v}{\sqrt{g h_{w}}}$	潘家铮^[16] （1980）	坠落式	0.5<Fr数<2
$\frac{H_{max}}{h_{w}} = 0.159 a^{- 0.641} {(\frac{v}{\sqrt{g h_{w}}})}^{1.6} {(\frac{h_{1}}{h_{w}})}^{0.839} {(\frac{d}{h_{w}})}^{0.23} {(\frac{h_{1}}{h_{2}})}^{0.294}$ $v = 0.636 a^{0.172} {(g h_{1})}^{0.5} {(\frac{h_{1}}{h_{w}})}^{- 0.007} {(\frac{h_{2}}{h_{w}})}^{0.156} {(\frac{h_{1}}{h_{2}})}^{- 0.003}$	张全等^[17] （2021）	压溃式	2<a<16 30 m<h₂<120 m
式中，v为入水最大速度，h_w为水深，H_s为滑坡体厚度，由V与 $\frac{H_{s}}{h_{w}}$ 确认波浪特性，H_max为最大首浪高度，由V与 $\frac{H_{max}}{H_{s}}$ 确认涌浪高度，h_落为坠落高度；a为柱体高宽比，h₁为危岩体高度，h₂基座高度，d为危岩体宽度；F_r为相对Froude数，可根据 $F_{r} = \frac{v}{\sqrt{g h_{w}}}$ 进行计算。

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表 3 部分传播浪公式

Table 3 Part of propagation wave formula

公式	来源	范围	适用条件
$\frac{H_{P}}{h_{w}} = 1.67 \sin (α) \cos^{2} (\frac{2}{3} γ) {(\frac{ρ}{ρ_{w}})}^{\frac{1}{4}} {[\frac{V_{s}}{(d {h_{w}}^{2})}]}^{\frac{1}{2}} {(\frac{r}{h_{w}})}^{- \frac{2}{3}}$	Huber and Hager^[13](1997)	近场环状传播	高倾角入水
$\frac{H_{P}}{h_{w}} = \frac{3}{4} {(\frac{v}{\sqrt{g h_{w}}} {(\frac{s}{h_{w}})}^{0.5} {(\frac{ρ V_{s}}{ρ_{w} d {h_{w}}^{2}})}^{0.25} {(\cos (\frac{6}{7} α))}^{0.5} {(\frac{x}{h_{w}})}^{- \frac{1}{3}})}^{\frac{4}{5}}$	Huber and Hager^[13](1997)	沿程平行传播	高倾角入水
$\frac{H_{P}}{h_{w}} = 1.47 \frac{H_{max}}{h_{w}} {(\frac{x}{h_{w}})}^{- 0.5}$	殷坤龙和汪洋^[27](2008)	近场环状传播	0.063<Fr数<0.9 5°<α<45°
$\frac{H_{P}}{h_{w}} = \frac{H_{max}}{h_{w}} e^{- 0.4 (\frac{x}{h_{w}}) 0.35}$	殷坤龙和汪洋^[27](2008)	沿程平行传播	0.063<Fr数<0.9 5°<α<45°
$\frac{H_{P}}{h_{w}} = 2.75 F_{r}^{0.67} S M^{0.6} {(\frac{r}{h_{w}})}^{- 1} f_{γ}$ $f_{γ} = \cos^{2 (1 + e^{- 0.2 (\frac{r}{h_{w}})})} (\frac{2}{3} λ)$	Heller and Spinneken^[25] (2015)	近场环状传播	0.54<Fr数<2.47 α=45°
式中，H_P为传播浪高度， $Θ$ 为入水角度，©为滑动方向与径向夹角， $λ$ 为危岩体密度， $λ_{w}$ 为水密度，V_s为体积，r为径向距离，x为距危岩体距离；S为滑坡相对厚度，可根据 $S = \frac{H_{s}}{h_{w}}$ 进行计算，M为危岩相对质量，可根据 $M = \frac{m}{ρ_{s} w h_{w}^{2}}$ 进行计算，m为危岩体质量。

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表 4 部分爬高浪公式

Table 4 Part of climbing wave formula

公式	来源	适用范围	适用条件
$\frac{H_{R}}{h_{w}} = 2.831 (\cot β)^{\frac{1}{2}} {(\frac{H_{P}}{h_{w}})}^{\frac{5}{4}}$	Synolakis ^[28] (1987)	正对岸爬高	坡比1:19.85
$\frac{H_{R}}{h_{w}} = 1.25 {(\frac{90}{β})}^{0.2} {(\frac{H_{P}}{h_{w}})}^{1.25} {(\frac{H_{P}}{L})}^{- 0.15}$	Müller ^[29] (1995)	正对岸爬高	坡比1:1、1:3或坡度90°
$\frac{H_{R}}{h_{w}} = 2.3 \frac{H_{P}}{h_{w}} {(\frac{90}{β})}^{0.2}$	殷坤龙和汪洋^[27](2008)	正对岸爬高	0.063<Fr数<0.9 5<α<45
$\frac{H_{R}}{h_{w}} = ((2.3 {(\frac{90}{β})}^{0.2} - 1) \cos δ + 1) \frac{H_{P}}{h_{w}}$	殷坤龙和汪洋^[27](2008)	沿程爬高	0.063<Fr数<0.9 5<α<45
式中，H_R为爬高，®为岸坡坡角，L为坝前波长；™为爬坡方位角，根据河道宽度B和计算点与滑坡的水平距离x_s计算 $\cos δ = \frac{B}{\sqrt{B^{2} + x_{s}^{2}}}$ 。

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表 5 危岩体计算参数

Table 5 Calculation parameters of dangerous rock mass

符号	g	h_w	v	h₁	h₂	d	a	V_s
参数	重力加速度（m/s²）	水深（m）	入水速度（m/s）	高度（m）	基座高度（m）	宽度（m）	柱体高宽比	体积（万m³）
145m	9.8	65	27.1	190	12	40	4.75	30.4
175m	9.8	95	25.6	190	12	40	4.75	30.4

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表 6 危岩体计算参数

Table 6 Calculation parameters of dangerous rock mass

符号	g	h_w	v	H_S	V_s
参数	重力加速度（m/s²）	水深（m）	入水速度（m/s）	平均厚度（m）	体积（万m³）
渔峡口危岩体	9.8	63	30	3	0.01

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不同失稳模式的典型危岩体崩塌产生涌浪公式法体系研究

作者简介:
张　杰（1999—），男，湖北利川人，硕士研究生，主要从事危岩体涌浪灾害研究。E-mail：202308180021014@ctgu.edu.cn

通讯作者:
黄波林（1979—），男，湖北仙桃人，研究员、博士生导师，主要从事水库地质灾害及涌浪灾害方面的教学与研究工作。E-mail：bolinhuang@aliyun.com

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Study on the surge formula system of typical dangerous rock mass collapse with different instability modes

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不同失稳模式的典型危岩体崩塌产生涌浪公式法体系研究

作者简介: 张 杰（1999—），男，湖北利川人，硕士研究生，主要从事危岩体涌浪灾害研究。E-mail：202308180021014@ctgu.edu.cn

通讯作者: 黄波林（1979—），男，湖北仙桃人，研究员、博士生导师，主要从事水库地质灾害及涌浪灾害方面的教学与研究工作。E-mail：bolinhuang@aliyun.com

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Study on the surge formula system of typical dangerous rock mass collapse with different instability modes

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作者简介:
张　杰（1999—），男，湖北利川人，硕士研究生，主要从事危岩体涌浪灾害研究。E-mail：202308180021014@ctgu.edu.cn

通讯作者:
黄波林（1979—），男，湖北仙桃人，研究员、博士生导师，主要从事水库地质灾害及涌浪灾害方面的教学与研究工作。E-mail：bolinhuang@aliyun.com