扰动冲击下弱胶结红砂岩的能量耗散与分形特征

张慧梅; 陈世官; 王磊; 程树范; 杨更社; 申艳军

doi:10.11779/CJGE202204004

扰动冲击下弱胶结红砂岩的能量耗散与分形特征 English Version

1.
西安科技大学力学系, 陕西西安 710054
2.
西安科技大学建筑与土木工程学院, 陕西西安 710054
3.
武汉大学土木建筑工程学院, 湖北武汉 430072
4.
西安科技大学地质与环境学院, 陕西西安 710054

基金项目:

国家自然科学基金项目 12172280

国家自然科学基金项目 42077274

国家自然科学基金项目 41907259

陕西省自然科学基金重点项目 2020JZ-53

详细信息

作者简介:
张慧梅（1968—），女，山西大同人，现任教授、博士生导师，主要从事岩土工程稳定性评价及岩石力学理论与应用。E-mail：zhanghuimei68@163.com

通讯作者:
陈世官, E-mail: 18992178070@163.com

中图分类号: TU458.3
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出版历程
- 收稿日期: 2021-06-09
- 网络出版日期: 2022-09-22
- 刊出日期: 2022-03-31

Energy dissipation and fractal characteristics of weakly cemented red sandstone under disturbance impact

1.
Department of Mechanics, Xi'an University of Science and Technology, Xi'an 710054, China
2.
College of Architecture and Civil Engineering, Xi'an University of Science and Technology, Xi'an 710054, China
3.
School of Civil and Architectural Engineering, Wuhan University, Wuhan 430072, China
4.
School of Geology and Environment, Xi'an University of Science and Technology, Xi'an 710054, China

摘要

摘要: 为探索动态扰动后西部矿区软岩夹层的能量耗散规律和破坏模式，利用分离式霍普金森压杆装置对弱胶结红砂岩进行动态冲击破坏试验，分析该类红砂岩在受到不同加载速率、不同次数扰动冲击以及是否扰动的条件下，试样在相同加载速率破坏性冲击过程中的能量耗散与分形特征。试验结果表明：在不同速率扰动冲击作用下，随着扰动冲击次数的增加反射能递增而透射能和耗散能呈减小趋势，其中较高速率扰动冲击下试样的反射能高于低速率扰动冲击，耗散能则相反，且低速率扰动冲击下试样的耗散能、能量耗散率和能量耗散密度高于较高速率扰动冲击，表明低速率扰动冲击下试样的能量利用率更高；在破坏性冲击试验中，随着扰动冲击次数的增加，低速率扰动后试样的破碎程度相较于未扰动与高速率扰动更为严重，对应分形维数D_b低速率扰动 > 未扰动 > 高速率扰动，表明分形维数与扰动冲击次数呈正相关，与扰动冲击速率呈负相关；在相同扰动冲击次数下，低速率扰动试样的D_b所对应累积耗散能和耗散能密度高于较高速率扰动试样，而对应的累积反射能则相反。
- 弱胶结砂岩 /
- 扰动冲击 /
- SHPB /
- 能量耗散 /
- 分形维数
Abstract: To explore the energy dissipation law and failure mode of soft rock interlayer in western mining areas of China after dynamic disturbance, the dynamic impact failure tests on weakly cemented red sandstone are carried out by using the separated Hopkinson compression bar device. Under the impact of this red sandstone under different loading rates, different times of disturbance and whether there is the disturbance or not, the energy dissipation and fractal characteristics of the samples during the same loading rate impact failure are analyzed. The experimental results show that under different disturbance impact rates, with the increase of disturbance impact times, the reflection energy increases, while the transmission energy and dissipation energy decrease. The reflection energy of the samples under the impact of high-speed disturbance is higher than that of the low-speed disturbance impact, while the dissipative energy is the opposite. Moreover, the dissipative energy of the samples under the impact of low-speed rate disturbance is opposite. The energy dissipation rate and energy dissipation density are higher than those of the high-speed disturbance impact, which indicates that the energy utilization rate of the samples is higher under the impact of low-speed disturbance. In the impact failure tests, with the increase of the number of disturbance impact, the fragmentation degree of the sample after the low-speed rate disturbance is more serious than that of the undisturbed and high-speed rate disturbance. The low-speed rate disturbance of fractal dimension D_b > undisturbed > high-speed rate disturbance shows that the fractal dimension is positively correlated with the number of disturbance shocks. The results show that the impact rate is negatively correlated with the disturbance. Under the same number of disturbance impact, the cumulative dissipation energy and energy density of D_b of the low-speed rate-disturbed samples are higher than those of the high-speed disturbed samples, while the cumulative reflection energy is opposite.
- weakly cemented sandstone /
- disturbance impact /
- SHPB /
- energy dissipation /
- fractal dimension

HTML全文

孙建生老师对敝人《稳定安全系数计算公式中荷载与抗力错位影响探讨》^[1]（以下简称原文）提出了宝贵的指导及讨论意见,非常感谢！

业界普遍认为边坡稳定安全系数目前主要有两种定义方法：①为抗滑力矩与下滑力矩之比（通常可简化为抗力荷载比）,相应的稳定安全系数计算方法一般采用单一安全系数法（原文即采用此法）,以瑞典条分法为代表；②定义为滑动面上的抗剪强度与实际产生的剪应力之比,相应的稳定安全系数计算方法一般采用强度（抗剪强度）折减法,以毕肖普法（Bishop）及简布法（Janbu）为代表。宋二祥等^[2]倾向于第二种定义。孙文中 $\sum R \div K = \sum S$ ,对所有抗滑力除以了同一安全系数K、即均进行了折减,从公式表达来看与单一安全系数法没什么不同,与强度折减法仅对岩土体的抗剪强度进行折减明显不同。

但文献[3]认为“抗滑稳定安全系数K是表达……实际……滑动力 $\sum S$ 与理论极限（虚拟概念）抗滑力 $\sum R$ 的极限平衡接近程度”,之后的论述绕此展开。“实际滑动力”、“理论极限抗滑力”及“极限平衡接近程度”等用语是理解文献[3]观点的关键。

第②种定义中的“抗剪强度”及“剪应力”也可表达为“抗力”及“荷载”或“抗滑力”及“滑动力”,从文献[3]角度来看,极限抗滑力是理论的,故是“虚拟概念”；实际滑动力即实际发生的荷载,与抗滑力相等时则土体处于极限平衡状态；在安全系数K计算过程中通过逐步折减而逼近极限平衡状态,表达了实际滑动力与抗滑力的接近程度,故文献[3]更适合从第②种定义及强度折减法的角度去理解。倘若如此,则：

（1）文献[3]认为原文极限平衡力学基本概念混淆、错误、缺失。笔者认为,原文没有明示但实质上依据的是第一种定义,文献[3]讨论的实质上属于第②种定义,两种定义中的概念不同是正常现象。

（2）文献[3]认为“分子与分母加减项的变化必然影响到安全系数计算结果,但这绝不是极限平衡概念的滑动力荷载与极限抗滑力概念错位问题的探讨依据”,笔者同意。“分子与分母加减项的变化必然影响到安全系数计算结果”正是原文目的,原文探讨的就是加减项中的那些不合理项导致的按第一种定义编写的安全系数计算公式有时并不完全符合第一种定义这种现象；“计算结果……不是概念错位问题的探讨依据”,因为定义形式不同,当然不能把根据第一种定义获得的计算结果当作探讨第二种定义概念的依据。

（3）文献[3]认为抗滑力是虚拟受力。笔者认为,抗滑力大于滑动力时可如此认为,小于时（处于极限平衡状态或滑坡时）则不是虚拟的、而是实际发生的。

（4）文献[3]认为“在 $K = \frac{\sum R}{\sum S}$ 公式中,分子抗滑力 $\sum R$ 包含所有极限虚拟概念状态的抗滑力因素,不论正负......分母滑动力 $\sum S$ 包含所有实际切向滑动力因素,不论正负”,笔者没有理解。①所有的抗滑力均应是同向、即“正”的,“负抗滑力”指的是什么呢?如果是负的,与抗滑力反向的,就应该是滑动力；但如果是滑动力,就应该如第②种定义及文献[3]前述,是实际发生的,那么就不是“虚拟概念”的,因为“虚拟概念”的是抗滑力；但如果是抗滑力,就应该与其它“正”抗滑力同向、不应为负,故“负抗滑力”到底是什么力,很难理解；②同理,所有的滑动力均应是同向、即“正”的,“负滑动力很难理解；③假定部分滑动力也可以“虚拟概念”、即作为“负抗滑力”计入分子 $\sum R$ ,部分抗滑动可以实际发生、即作为“负滑动力”计入分母 $\sum S$ ,那么,哪些滑动力可以计入分子、哪些抗滑力可以计入分母?

仍以瑞典条分法为例,当滑弧中心点O位于边坡上方时,如图1所示,土条1~（m-1）的重力产生滑动力 $\sum_{i = 1}^{m - 1} G ti$ ,土条m~n的重力产生抗滑力 $\sum_{i = m}^{n} G ti$ ,两者作用方向相反,围绕着两者关系如何处理产生4种稳定安全系数K计算公式,其中前2种工程应用广泛：

$K = \frac{\sum_{i = 1}^{n} (G_{n i} \tan φ_{i} + c_{i} l_{i})}{\sum_{i = 1}^{m - 1} G_{t i} - \sum_{i = m}^{n} G_{t i}}$ ,

(1)

$K = \frac{\sum_{i = 1}^{n} (G_{n i} \tan φ_{i} + c_{i} l_{i})}{\sum_{i = 1}^{m - 1} G_{t i} + \sum_{i = m}^{n} G_{t i}}$ ,

(2)

$K = \frac{\sum_{i = 1}^{n} (G_{n i} \tan φ_{i} + c_{i} l_{i}) - \sum_{i = m}^{n} G_{t i}}{\sum_{i = 1}^{m - 1} G_{t i}}$ ,

(3)

$K = \frac{\sum_{i = 1}^{n} (G ni \tan φ i + c i l i) + \sum_{i = m}^{n} G ti}{\sum_{i = 1}^{m - 1} G ti}$ 。

(4)

图 1 瑞典条分法边坡稳定分析简图

Figure 1. Sketch about slope stability analysis by Swedish Slicing Method

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式（1）～（4）从文献[3]角度来看：①式（1）将 $\sum_{i = m}^{n} G_{t i}$ 放在分母与滑动力 $\sum_{i = 1}^{m - 1} G_{t i}$ 相减,可认为是 $\sum S$ 中的“负滑动力”；②式（2）将之放在分母与滑动力相加,可认为是 $\sum S$ 中的“正滑动力”；③式（3）将之放在分子与抗滑力 $\sum_{i = 1}^{n} （ G_{n i} tan φ_{i} + c_{i} l_{i} ）$ 相减,可认为是 $\sum R$ 中的“负抗滑力”；④式（4）将之放在分子与抗滑力相加,可认为是 $\sum R$ 中的“正抗滑力”。那么, $\sum_{i = m}^{n} G_{t i}$ 到底是“负滑动力”、“正滑动力”、“负抗滑力”还是“正抗滑力”?这个问题文献[3]没有指明如何处理,却正是原文所讨论的核心内容,换句话说,在这个问题上原文所讨论的内容与孙文观点是互补的。

（4）其余意见详见笔者对文献[2]的回复意见,不再赘述。

总结：①业界对边坡稳定安全系数的主要定义形式有两种,原文依据的是第一种,孙文实质上依据的是第二种,故概念有所不同；②文献[3]提出了“负抗滑力”及“负滑动力”等观点但没有提出实现方法,没有解决原文讨论的安全系数计算公式中抗力与荷载错位（从文献[3]角度可理解为抗滑力与滑动力应用不当）的问题。

笔者对文献[3]理解不准确及本回复意见不妥之处,敬请孙老师及读者们谅解及继续批评指正。

图 1 红砂岩试样

Figure 1. Red sandstone sample

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图 2 试验方案流程图

Figure 2. Flow chart of experimental scheme

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图 3 动态应力平衡验证

Figure 3. Verification of dynamic stress equilibrium

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图 4 动态冲击应变时程曲线

Figure 4. Curves of strain and time under impact

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图 5 不同加载速率扰动冲击下入射能量时程曲线

Figure 5. Time-history curves of incident energy under disturbance impact with different loading rates

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图 6 扰动冲击下砂岩各能量随冲击次数的变化关系

Figure 6. Relationship between energy of sandstone and impact times under disturbance impact

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图 7 不同加载速率循环扰动后试样损伤形态

Figure 7. Damage morphology of samples after cyclic disturbance at different loading rates

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图 8 扰动冲击下耗散能密度与冲击次数的关系

Figure 8. Relationship between dissipative energy density and impact times under disturbance impact

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图 9 扰动与未扰动试样冲击破坏后的破碎形态

Figure 9. Fracture morphology of disturbed and undisturbed samples after impact failure

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图 10 扰动与未扰动试样冲击破坏后的破碎块度分布

Figure 10. Fragmentation distribution of disturbed and undisturbed samples after impact failure

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图 11 SHPB冲击试验中lg[M_R/M_T]–lgR曲线

Figure 11. Curve of lg[M_R/M_T]–lgR in SHPB impact tests

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图 12 分形维数与各累积能量关系曲线

Figure 12. Relationship between fractal dimension and cumulative energy

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表 1 红砂岩基本物理力学参数

Table 1 Basic physical and mechanical parameters of red sandstone

密度/(g·cm^-3)	纵波波速/(m·s^-1)	单轴抗压强度/MPa	弹性模量/GPa	孔隙度/%
1.874	1897	13.78	1.22	22.8

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表 2 扰动作用下红砂岩冲击破碎块度的筛分结果

Table 2 Screening results of impact fragmentation of red sandstone under disturbing action

试件编号	筛分直径/mm										总质量/g	D_b
试件编号	0.080	0.160	0.315	0.630	1.250	2.500	5.000	10.000	15.000	30.000	总质量/g	D_b
A1-Z	2.18	3.56	1.52	1.20	0.80	3.44	6.48	2.53	35.82	39.18	96.71	2.365
A3-Z	2.78	4.41	1.33	1.20	0.72	2.65	7.46	3.33	33.96	37.35	95.19	2.403
A5-Z	5.49	10.54	3.23	3.35	2.00	6.95	13.39	13.18	9.37	34.07	101.57	2.592
C1-Z	7.84	5.34	1.38	1.35	0.70	3.35	13.89	24.45	36.46	0.00	94.76	2.586
C3-Z	8.68	12.39	3.50	3.43	2.15	6.68	12.68	15.64	30.57	0.00	95.72	2.644
C5-Z	9.40	17.37	4.56	3.35	1.80	7.91	15.73	16.52	16.6	0.00	93.24	2.673
DZ	3.66	10.41	2.95	2.28	1.19	4.11	4.87	8.50	34.84	23.01	95.82	2.537
注：试件编号说明，A和C分别表示较高速率扰动组和低速率扰动组，编号1，3，5表示需要进行扰动的次数，-Z表示每组所有扰动次数完成后的破坏性冲击试验，DZ表示对照组。

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