落石对缓冲土层的冲击力及冲击深度理论与试验研究

王玉锁; 杨竣翔; 肖宗扬; 李传宝; 田四明; 王伟; 姚庆晨; 赵状

doi:10.3969/j.issn.0258-2724.20230303

落石对缓冲土层的冲击力及冲击深度理论与试验研究

doi: 10.3969/j.issn.0258-2724.20230303

1.
西南交通大学土木工程学院，四川成都 611752
2.
中国铁路经济规划研究院有限公司，北京 100080

基金项目: 四川省自然科学基金项目（2022NSFSC1127）；中国国家铁路集团有限公司科技研究开发计划（N2021G005）

详细信息

通讯作者:
王玉锁（1974—），男，副教授，研究方向为隧道及地下工程，E-mail：wangysuo@swjtu.edu.cn

中图分类号: P642.21
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-27
- 修回日期: 2023-09-21
- 网络出版日期: 2024-06-17
- 刊出日期: 2023-10-07

Theoretical and Test Study of Impact Force and Impact Depth of Falling Rocks on Buffering Soil Layers

1.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 611752, China
2.
China Railway Economic and Planning Research Institute, Beijing 100080, China

摘要

摘要:
为阐明基于Hertz接触理论的落石冲击力、冲击深度计算方法及缓冲土层强化系数确定方法的适用性和可行性，通过足尺模型试验、反演分析及数理统计，开展体积约1 m³重约2 t的立方体和球顶锥体2种落石形状、1～10 m下落高度及0.5～2.0 m缓冲土层厚度的落石冲击试验研究，进行砂土缓冲层强化系数的确定及落石冲击力、冲击深度理论与试验结果的对比分析. 研究结论表明：根据试验结果反演分析，99.7%置信区间的砂土缓冲层强化系数建议取值范围为0.25～10.00 GN/m^5/2；理论计算得到的立方体落石冲击力均值较试验值平均偏大140%，球顶锥体偏大21%；理论计算得到的立方体落石冲击深度均值较试验值平均偏大112%，球顶锥体偏大5%；在强化系数99.7%置信区间内计算得到的落石冲击力和冲击深度范围值可包含全部的落石冲击力和冲击深度；相同条件下球顶锥体落石的冲击深度试验值大于立方体的冲击深度试验值，缓冲层厚度越大时冲击深度增大，而落石冲击力离散性较大，与落石形状和缓冲层厚度无明显相关性.
- 落石冲击力 /
- 落石冲击深度 /
- 缓冲土层 /
- 弹塑性强化
Abstract:
To elucidate the applicability and feasibility of the calculation methods for impact force and impact depth of falling rocks based on Hertz contact theory, as well as the determination method for the reinforcement coefficient of buffering soil layers, full-scale model tests, inversion analysis, and mathematical statistics methods were employed. The falling rock impact tests were carried out, involving cubic rock and conical rock with a spherical top, each with a volume of approximately 1 m³ and a weight of about 2 t. They were dropped from heights ranging from 1 to 10 m onto buffering soil layers with thicknesses of 0.5–2 m. Then, the reinforcement coefficient of buffering sand layers was determined, and theoretical and test results for impact force and impact depth of falling rocks were comparatively analyzed. The research conclusions are as follows: Based on inversion analysis of the test results, it is recommended that the reinforcement coefficient of buffering sand layers within the 99.7% confidence interval should range from 0.25 GN/m^5/2 to 10.00 GN/m^5/2. The theoretically calculated average impact force of cubic rock is 140% larger than the test value, while that of conical rock with a spherical top is 21% larger than the test value. The theoretically calculated average impact depth of cubic rock is 112% larger than the test value, while that of conical rock with a spherical top is 5% larger than the test value. Within the 99.7% confidence interval of the reinforcement coefficient, the range of calculated impact force and impact depth of rock can encompass 100% of the test results. Under the same conditions, the test value of the impact depth of conical rock with a spherical top is greater than that of cubic rock. The impact depth increases with the increase in the thickness of the buffering layer, while the variability in the impact force of falling rocks shows no significant correlation with the rock shape and buffering layer thickness.
- impact force of falling rocks /
- impact depth of falling rocks /
- buffering soil layer /
- elastoplastic strengthening

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图 1 落石-上覆土层-拱形明洞间的冲击缓冲传力过程示意

Figure 1. Impact buffering and force transmission process among falling rocks, overlying soil layer, and arched tunnel

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图 2 试验装置布置

Figure 2. Experimental apparatus layout

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图 3 加速度测试

Figure 3. Acceleration test

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图 4 冲击深度测试

Figure 4. Impact depth test

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图 5 落石形状及尺寸（单位：m）

Figure 5. Shape and dimensions of falling rocks (unit: m)

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图 6 落石冲击力和冲击深度试验与理论（k按文献[7]）结果

Figure 6. Test and theoretical results of impact force and impact depth of falling rocks （k according to reference [7]）

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图 7 落石冲击力和冲击深度试验与理论（k按3σ准则确定）结果

Figure 7. Test and theoretical results of impact force and impact depth of falling rocks （k determined by 3σ criterion）

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表 1 落石冲击试验工况

Table 1. Impact test conditions for falling rocks

落石形状	工况	缓冲层厚度/m	H/m
立方体	1	2.0	1
	2	2.0	5
	3	2.0	10
	4	1.0	1
	5	1.0	5
	6	1.0	10
	7	0.5	1
	8	0.5	5
	9	0.5	10
球顶锥体	10	2.0	1
	11	2.0	5
	12	2.0	10
	13	1.0	1
	14	1.0	5
	15	1.0	10
	16	0.5	1
	17	0.5	5
	18	0.5	10

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表 2 土体参数

Table 2. Soil parameters

名称	取值
c/kPa	2
φ/（°）	20
E/（MN·m⁻²）	4
μ	0.39
重度 γ/（kN·m⁻³）	14.9

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表 3 试验与理论结果

Table 3. Test and theoretical results

工况	a_max/ （m·s⁻²）	试验值		理论值
		F_max/kN	δ_max/m	F_max/kN		δ_max/m
		F_max/kN	δ_max/m	k_min	k_max	k_min	k_max
1	120.97	266.13	0.17	41.70	371.27	0.33	0.06
2	102.76	226.07	0.40	162.00	975.16	0.63	0.11
3	379.79	835.54	0.51	280.00	1480.00	0.83	0.15
4	39.50	86.90	0.08	41.70	371.27	0.33	0.06
5	61.18	134.60	0.15	162.00	975.16	0.63	0.11
6	121.11	266.44	0.22	280.00	1480.00	0.83	0.15
7	22.40	49.28	0.08	41.70	371.27	0.33	0.06
8	142.56	313.63	0.11	162.00	975.16	0.63	0.11
9	293.10	644.69	0.19	280.00	1480.00	0.83	0.15
10	79.23	180.64	0.35	38.30	348.05	0.36	0.08
11	237.22	540.87	0.48	133.00	914.15	0.69	0.14
12	381.71	870.29	0.66	230.00	1390.00	0.91	0.17
13	101.30	230.96	0.22	38.30	348.05	0.36	0.08
14	106.52	234.34	0.35	133.00	914.15	0.69	0.14
15	376.43	828.14	0.45	230.00	1390.00	0.91	0.17
16	127.53	280.58	0.24	38.30	348.05	0.36	0.08
17	166.60	366.51	0.30	133.00	914.15	0.69	0.14
18	213.22	469.09	0.37	230.00	1390.00	0.91	0.17

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表 4 相关性分析

Table 4. Correlation analysis

因变量	分析项	落石形状	缓冲层厚度	H	落石冲击力	冲击深度
落石冲击力	皮尔逊相关性	0.258	0.253	0.769^**	1	0.751^**
	显著性（双尾）	0.301	0.311	0.000		0.000
	个案数	18	18	18	18	18
冲击深度	皮尔逊相关性	0.531^*	0.585^*	0.541^*	0.751^**	1
	显著性（双尾）	0.023	0.011	0.020	0.000
	个案数	18	18	18	18	18
注：. 在 0.05 级别（双尾），相关性显著；*. 在 0.01 级别（双尾），相关性显著.

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表 5 砂土缓冲层k值

Table 5. k value for buffering sand layer GN/m^5/2

工况	k	工况	k	工况	k
1	2.26	7	1.42	13	1.65
2	0.518	8	5.50	14	0.83
3	1.50	9	5.79	15	1.80
4	2.52	10	0.64	16	1.61
5	1.37	11	1.20	17	1.68
6	1.78	12	1.19	18	1.38

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表 6 正态性检验

Table 6. Normality test

变量	柯尔莫戈洛夫-斯米诺夫^a			夏皮洛-威尔克
变量	统计	自由度	显著性	统计	自由度	显著性
k	0.312	18	0.000	0.703	18	0.000
lg k	0.196	18	0.066	0.923	18	0.148
注：a. 里利氏显著性修正（指在进行假设检验时，当样本量较小或者总体方差未知时，为保证检验结果的可靠性，对原本的检验统计量进行修正，使最终的检验结果更加准确）.

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落石对缓冲土层的冲击力及冲击深度理论与试验研究

doi: 10.3969/j.issn.0258-2724.20230303

通讯作者: 王玉锁（1974—），男，副教授，研究方向为隧道及地下工程，E-mail：wangysuo@swjtu.edu.cn

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出版历程

Theoretical and Test Study of Impact Force and Impact Depth of Falling Rocks on Buffering Soil Layers

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出版历程

目录

通讯作者:
王玉锁（1974—），男，副教授，研究方向为隧道及地下工程，E-mail：wangysuo@swjtu.edu.cn