循环冲击载荷作用下页岩动力学响应及能量耗散特征

王宇; 翟成; 唐伟; 石克龙

doi:10.11883/bzycj-2022-0248

循环冲击载荷作用下页岩动力学响应及能量耗散特征

doi: 10.11883/bzycj-2022-0248

王宇^{1, 2,},
翟成^{1, 2, ,},
唐伟^{1, 2},
石克龙^{1, 2}

1.
中国矿业大学安全工程学院，江苏徐州 221116
2.
中国矿业大学煤矿瓦斯治理国家工程研究中心，江苏徐州 221116

基金项目: 国家重点研发计划（2020YFA0711800）

详细信息

作者简介:
王　宇（1999－　），男，博士研究生，tb21120024b1@cumt.edu.cn

通讯作者:
翟　成（1978－　），男，博士，教授，greatzc@126.com

中图分类号: O341
计量
- 文章访问数: 714
- HTML全文浏览量: 173
- PDF下载量: 217
- 被引次数: 7
出版历程
- 收稿日期: 2022-06-07
- 修回日期: 2022-09-13
- 网络出版日期: 2022-09-14
- 刊出日期: 2023-06-05

Dynamic response and energy dissipating characteristics of shale under cyclic impact loadings

WANG Yu^{1, 2
,},
ZHAI Cheng^{1, 2
, ,},
TANG Wei^{1, 2},
SHI Kelong^{1, 2}

1.
School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
2.
National Engineering Research Center for Coal Gas Control, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

摘要

摘要: 采用 $\varnothing$ 50 mm分离式霍普金森杆(split Hopkinson pressure bar，SHPB)实验系统开展页岩循环冲击实验，研究不同循环冲击载荷作用下页岩动力学响应及损伤演化特征，同时揭示了控制入射总能量不变条件下，不同气压梯度循环冲击页岩能量演化规律。随着冲击气压升高，试样破裂所需的冲击次数呈线性减少，峰值应力随循环冲击次数的增加先升高后降低，极限应变先减小后增大，试样在循环冲击下表现出先压密后损伤的力学机制。基于Weibull分布的统计损伤模型表明，升高循环冲击气压，试样损伤破坏形式由缓慢劣化逐渐转变为骤然破坏。入射总能量恒定的情况下，通过控制循环入射能量梯度能够产生不同的损伤效果，降压冲击和升压冲击下的能量吸收比均大于恒压冲击下的，且气压梯度的绝对值与能量吸收比呈现正相关性。
- 页岩 /
- SHPB实验 /
- 循环冲击 /
- 损伤演化
Abstract: The formation of complex fracture networks in the shale subjected to cyclic impact loading is an important scientific problem for water-free fracturing technologies of shale reservoirs, such as explosive fracturing and high-energy gas fracturing. Two cyclic impact experiments based on a split Hopkinson pressure bar (SHPB) system were conducted on the freshly exposed black mud shale taken from the Wufeng Formation-Longmaxi Formation in Changning County, Sichuan Province, to investigate the kinetic response and damage evolution characteristics of the shale under different cyclic impact gas pressure and different cyclic impact gas pressure gradients, respectively, and to reveal the energy evolution law of the cyclic impact shale using different impact gas pressure gradients under the condition of controlling the constant total incident energy. The main conclusions are as follows. With the increase in impact pressure, the number of impacts required to rupture the specimen decreases, and the fragmentation and peak stress increase. The specimen undergoes cyclic impact showing the mechanical response characteristics of compaction first and then gradual damage. The damage degree of the shale specimens during cyclic impact was calculated by a dynamic damage model based on the Weibull distribution, and the results show that the damage of the specimen gradually changes from slow deterioration to sudden damage by increasing the cyclic impact pressure. Different cyclic impact experiments with different impact gas pressure gradients were conducted. The results show that under the condition of constant total incident energy, different cyclic incident energy gradients could produce different damage effects, and the energy absorption ratio of the negative or positive gas pressure gradient of cycle impact is greater than that of the zero ones. The absolute value of the pressure gradient shows a positive correlation with the energy absorption ratio. It indicates that under the condition of constant total impact energy, increasing the absolute value of the cyclic impact gradient can produce a better damage effect. The findings of the shale cyclic impact experiments can provide theoretical support for the technological design of multi-stage pulsed high-energy-gas-fracturing.
- shale /
- SHPB experiment /
- cyclic dynamic loading /
- damage evolution

HTML全文

针对结构的抗震研究发展了大量的分析方法, 其中, 波动法不单独研究分析荷载, 而是将介质与结构作为一个整体加以分析研究, 求解波动场与应力场^[1]。20世纪70年代, Y.H. Pao等^[2]利用波函数展开法研究了不同形状物体在稳态和瞬态应力荷载下的动应力集中问题。D.Liu等^[3]将复变函数法拓展到动态应力集中问题, H.Qi等^[4-5]将其扩展到半空间界面、双向介质内圆孔、夹杂等方面。V. W.Lee等^[6]采用大圆弧假定方法将直边界问题转为曲边界问题, 给出了半空间中单个圆孔对P波、SV波散射的解析解。D.N.Chen等^[7-8]进一步研究了地表覆盖层对半空间内单、多个圆孔、圆夹杂受平面SH波作用时的散射和动应力集中因子的影响。本文中利用大圆弧法对地表软覆盖层中单个圆形夹杂在SH波作用下的动应力集中问题进行研究。

1. 理论分析

1.1 问题模型

地表软覆盖层中含有单个圆夹杂的问题模型如图 1(a)所示。半空间为区域Ⅰ, 覆盖层为区域Ⅱ, 厚度为h, 上、下边界分别为T_U和T_D。夹杂为区域Ⅲ, 边界为T_C, 半径为r。各区域的密度、剪切模量、SH波波数分别为ρ₁, G₁, k₁, ρ₂, G₂, k₂, ρ₃, G₃, k₃, 下标代表区域范围。采用大圆弧法, 将T_U和T_D用半径极大的同心圆弧近似, T_U变为 $\overset\frown{{{T}_{\text{U}}}}$ , T_D变为 $\overset\frown{{{T}_{\text{D}}}}$ 。以圆杂圆心为原点O₂, 平行于T_U的直线为X₂轴建立直角坐标系X₂O₂Y₂, 以大圆弧圆心为原点O₁建立直角坐标系X₁O₁Y₁, 使Y₁轴和Y₂轴在同一直线上。O₂距T_U的距离为h₁, 距T_D的距离为h₂。SH波在区域Ⅰ中以入射角α₀入射(X₁轴逆时针旋转至入射方向)。引入复变函数z_S=X_S+iY_S, 其中S=1, 2, 建立复平面(z₁, z₁)和(z₂, z₂), 直角坐标系X₁O₁Y₁和X₂O₂Y₂分别对应复平面(z₁, z₁)和(z₂, z₂)。各量的变换关系如下:

$\left\{ \begin{array}{l} h = {h_1} + {h_2}\\ {R_{\rm{U}}} = h + {R_{\rm{D}}}\\ {z_2} = {z_1} - {\rm{i}}\left( {{R_{\rm{D}}} + {h_2}} \right) \end{array} \right.$

(1)

图 1 地表覆盖层及半空间问题模型示意图

Figure 1. Schematic diagram of the layer half space and the half space model

下载: 全尺寸图片幻灯片

半空间中含有单个圆形孔洞的问题模型如图 1(b)所示。当图 1(a)中区域Ⅰ和区域Ⅱ的各参数均相同时, 半空间和覆盖层融为一体, 覆盖层下边界T_D不存在。当图 1(a)中区域Ⅲ的参数ρ₃和G₃均为0时, 圆形夹杂变为圆形孔洞, 此时图 1(a)所示问题退化为图 1(b)所示问题。

1.2 控制方程

本文中研究SH波的散射问题。在直角坐标系X-Y平面内, SH波产生的位移场表示为W(X, Y, t), 该位移场与Z轴无关, 且垂直于X-Y平面。对于稳态问题, 位移场W(X, Y, t)需要满足以下Helmholtz方程:

${\partial ^2}W/\partial {X^2} + {\partial ^2}W/\partial {Y^2} + {k^2}W = 0$

(2)

式中:位移场W(X, Y, t)与时间t的依赖关系为exp(－iωt), 由于本文中研究稳态问题, 因此在以下的分析中略去exp(－iωt)。k=ω/c; 其中ω为位移场W(X, Y, t)的圆频率; c为波速, c²=G/ρ。

在复平面极坐标系下, 应力应变关系表示为:

${\tau _{z\rho }} = G\left[ {\left( {\partial W/\partial z} \right)\left( {z/\left| z \right|} \right) + \left( {\partial W/\partial \bar z} \right)\left( {\left| z \right|/z} \right)} \right]$

(3)

${\tau _{z\varphi }} = {\rm{i}}G\left[ {\left( {\partial W/\partial z} \right)\left( {z/\left| z \right|} \right) - \left( {\partial W/\partial \bar z} \right)\left( {\left| z \right|/z} \right)} \right]$

(4)

1.3 入射波场、散射波场及相应应力

在(z₁, z₁)平面内, 入射波W^(Ⅰ), $\overset\frown{{{T}_{\text{D}}}}$ 在区域Ⅰ和区域Ⅱ内产生的散射波场W^(S1)、W^(S2), $\overset\frown{{{T}_{\text{U}}}}$ 在区域Ⅱ内产生的散射波场W^(S5)及相应的应力可以表示为:

$W_{\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {\rm{I}} \right)} = {W_0}\exp \left[ {{\rm{i}}{k_1}{\mathop{\rm Re}\nolimits} \left( {{z_1}{{\rm{e}}^{ - {\rm{i}}{\alpha _0}}}} \right)} \right]$

(5)

$\tau _{z\rho ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {\rm{I}} \right)} = {\rm{i}}{k_1}{G_1}{W_0}\exp \left[ {{\rm{i}}{k_1}{\mathop{\rm Re}\nolimits} \left( {{z_1}{{\rm{e}}^{ - {\rm{i}}{\alpha _0}}}} \right)} \right]{\mathop{\rm Re}\nolimits} \left[ {\left( {{z_1}{{\rm{e}}^{ - {\rm{i}}{\alpha _0}}}} \right)/\left| {{z_1}} \right|} \right]$

(6)

$\tau _{z\varphi ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {\rm{I}} \right)} = - {\rm{i}}{k_1}{G_1}{W_0}\exp \left[ {{\rm{i}}{k_1}{\mathop{\rm Re}\nolimits} \left( {{z_1}{{\rm{e}}^{ - {\rm{i}}{\alpha _0}}}} \right)} \right]{\mathop{\rm Im}\nolimits} \left[ {\left( {{z_1}{{\rm{e}}^{ - {\rm{i}}{\alpha _0}}}} \right)/\left| {{z_1}} \right|} \right]$

(7)

$W_{\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S1} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{A_n}H_n^{\left( 2 \right)}\left( {{k_1}\left| {{z_1}} \right|} \right){{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(8)

$\tau _{z\rho ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S1} \right)} = 0.5{k_1}{G_1}\sum\limits_{n = - \infty }^{n = + \infty } {{A_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_1}\left| {{z_1}} \right|} \right) - H_{n - 1}^{\left( 2 \right)}\left( {{k_1}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(9)

$\tau _{z\varphi ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S1} \right)} = 0.5{\rm{i}}{k_1}{G_1}\sum\limits_{n = - \infty }^{n = + \infty } {{A_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_1}\left| {{z_1}} \right|} \right) + H_{n - 1}^{\left( 2 \right)}\left( {{k_1}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(10)

$W_{\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S2} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{B_n}H_n^{\left( 1 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right){{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(11)

$\tau _{z\rho ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S2} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{B_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right) - H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(12)

$\tau _{z\varphi ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S2} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{B_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right) + H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(13)

$W_{\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S5} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{E_n}H_n^{\left( 2 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right){{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(14)

$\tau _{z\rho ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S5} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{E_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right) - H_{n + 1}^{\left( 2 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(15)

$\tau _{z\varphi ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S5} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{E_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right) + H_{n + 1}^{\left( 2 \right)}\left( {{k_2}\left| {{z_1}} \right|} \right)} \right]{{\left( {{z_1}/\left| {{z_1}} \right|} \right)}^n}}$

(16)

在(z₂, z₂)平面内, 散射波波场W^(S2), $\overset\frown{{{T}_{\text{C}}}}$ 在区域Ⅱ中产生的散射波场W^(S3)和 $\overset\frown{{{T}_{\text{C}}}}$ 在区域Ⅲ内产生的驻波波场W^(Z4), 散射波波场W^(S5)可分别表示为:

$W_{\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S2} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{B_n}H_n^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^n}}$

(17)

$\begin{array}{*{20}{c}} {\tau _{z\rho ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S2} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{B_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_2}/\left| {{z_2}} \right|} \right) - } \right.} }\\ {\left. {H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_2}/\left| {{z_2}} \right|} \right)} \right]} \end{array}$

(18)

$\begin{array}{*{20}{c}} {\tau _{z\varphi ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S2} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{B_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_2}/\left| {{z_2}} \right|} \right) + } \right.} }\\ {\left. {H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_2}/\left| {{z_2}} \right|} \right)} \right]} \end{array}$

(19)

$W_{\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S3} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{C_n}H_n^{\left( 1 \right)}\left( {{k_2}\left| {{z_2}} \right|} \right){{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(20)

$\tau _{z\rho ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S3} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{C_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_2}} \right|} \right) - H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_2}} \right|} \right)} \right]{{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(21)

$\tau _{z\varphi ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S3} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{C_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_2}} \right|} \right) + H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| {{z_2}} \right|} \right)} \right]{{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(22)

$W_{\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {Z4} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{D_n}{J_n}\left( {{k_3}\left| {{z_2}} \right|} \right){{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(23)

$\tau _{z\rho ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {Z4} \right)} = 0.5{k_3}{G_3}\sum\limits_{n = - \infty }^{n = + \infty } {{D_n}\left[ {{J_{n - 1}}\left( {{k_3}\left| {{z_2}} \right|} \right) - {J_{n + 1}}\left( {{k_3}\left| {{z_2}} \right|} \right)} \right]{{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(24)

$\tau _{z\varphi ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {Z4} \right)} = 0.5{\rm{i}}{k_3}{G_3}\sum\limits_{n = - \infty }^{n = + \infty } {{D_n}\left[ {{J_{n - 1}}\left( {{k_3}\left| {{z_2}} \right|} \right) + {J_{n + 1}}\left( {{k_3}\left| {{z_2}} \right|} \right)} \right]{{\left( {{z_2}/\left| {{z_2}} \right|} \right)}^n}}$

(25)

$W_{\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S5} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{E_n}H_n^{\left( 2 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^n}}$

(26)

$\begin{array}{*{20}{c}} {\tau _{z\rho ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S5} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{E_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_2}/\left| {{z_2}} \right|} \right) - } \right.} }\\ {\left. {H_{n + 1}^{\left( 2 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_2}/\left| {{z_2}} \right|} \right)} \right]} \end{array}$

(27)

$\begin{array}{*{20}{c}} {\tau _{z\varphi ,\left( {{z_2},{{\bar z}_2}} \right)}^{\left( {S5} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{E_n}\left[ {H_{n - 1}^{\left( 2 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_2}/\left| {{z_2}} \right|} \right) + } \right.} }\\ {\left. {H_{n + 1}^{\left( 2 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_2}/\left| {{z_2}} \right|} \right)} \right]} \end{array}$

(28)

在(z₁,z₁)平面内,散射波W^(S3)的位移场和相应应力可以表示为:

$W_{\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S3} \right)} = \sum\limits_{n = - \infty }^{n = + \infty } {{C_n}H_n^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^n}}$

(29)

$\begin{array}{*{20}{c}} {\tau _{z\rho ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S3} \right)} = 0.5{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{C_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_1}/\left| {{z_1}} \right|} \right) - } \right.} }\\ {\left. {H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_1}/\left| {{z_1}} \right|} \right)} \right]} \end{array}$

(30)

$\begin{array}{*{20}{c}} {\tau _{z\varphi ,\left( {{z_1},{{\bar z}_1}} \right)}^{\left( {S3} \right)} = 0.5{\rm{i}}{k_2}{G_2}\sum\limits_{n = - \infty }^{n = + \infty } {{C_n}\left[ {H_{n - 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n - 1}}\left( {{z_1}/\left| {{z_1}} \right|} \right) + } \right.} }\\ {\left. {H_{n + 1}^{\left( 1 \right)}\left( {{k_2}\left| \oplus \right|} \right){{\left( { \oplus /\left| \oplus \right|} \right)}^{n + 1}}\left( {{{\bar z}_1}/\left| {{z_1}} \right|} \right)} \right]} \end{array}$

(31)

式中: ⊗=z₁－i(R_D+h₂), ⊕=z₂+i(R_D+h₂), 下标(z_P, z_P), (P=1, 2)表示所在复平面, 上标(Ⅰ)表示入射波, 上标(S1)表示编号为1的散射波, 上标(Z4)表示编号为4的驻波。A_n、B_n、C_n、D_n、E_n表示波函数的系数。

1.4 连接条件

根据 $\overset\frown{{{T}_{\text{D}}}}$ 和 $\overset\frown{{{T}_{\text{C}}}}$ 位移和径应力连续, $\overset\frown{{{T}_{\text{U}}}}$ 径应力自由, 得到公式(32), 代入相应公式并同乘exp(－imθ)且在(－π, π)上积分, 对m和n截取有限项求出系数A_n~E_n, 便可得到所求的各种未知量了。

$\left\{ \begin{array}{l} {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over T} }_{\rm{D}}}\left( {\left| {{z_1}} \right| = {R_{\rm{D}}}} \right):W_{\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {\rm{I}} \right)} + W_{\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{1}}} \right)} = W_{\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{2}}} \right)} + W_{\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{3}}} \right)} + W_{\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{5}}} \right)}\\ {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over T} }_{\rm{D}}}\left( {\left| {{z_1}} \right| = {R_{\rm{D}}}} \right):\tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {\rm{I}} \right)} + \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{1}}} \right)} = \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{2}}} \right)} + \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{3}}} \right)} + \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{5}}} \right)}\\ {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over T} }_{\rm{C}}}\left( {\left| {{z_2}} \right| = r} \right):W_{\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{2}}} \right)} + W_{\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{3}}} \right)} + W_{\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{5}}} \right)} = W_{\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{4}}} \right)}\\ {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over T} }_{\rm{C}}}\left( {\left| {{z_2}} \right| = r} \right):\tau _{z\rho ,\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{2}}} \right)} + \tau _{z\rho ,\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{3}}} \right)} + \tau _{z\rho ,\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{5}}} \right)} = \tau _{z\rho ,\left( {{z_2}/\left| {{{\bar z}_2}} \right|} \right)}^{\left( {S{\rm{4}}} \right)}\\ {{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over T} }_{\rm{U}}}\left( {\left| {{z_1}} \right| = {R_{\rm{U}}}} \right):\tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{2}}} \right)} + \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{3}}} \right)} + \tau _{z\rho ,\left( {{z_1}/\left| {{{\bar z}_1}} \right|} \right)}^{\left( {S{\rm{5}}} \right)} = 0 \end{array} \right.$

(32)

1.5 动应力集中因子(K_d)

定义 $\tau _{z\varphi , \left( {{z}_{2}}, {{{\bar{z}}}_{2}} \right)}^{*}={{\left| \left( \tau _{z\varphi , \left( {{z}_{2}}, {{{\bar{z}}}_{2}} \right)}^{\left( S2 \right)}+\tau _{z\varphi , \left( {{z}_{2}}, {{{\bar{z}}}_{2}} \right)}^{\left( S3 \right)}+\tau _{z\varphi , \left( {{z}_{2}}, {{{\bar{z}}}_{2}} \right)}^{\left( Z4 \right)}+\tau _{z\varphi , \left( {{z}_{2}}, {{{\bar{z}}}_{2}} \right)}^{\left( S5 \right)} \right)/\left( \text{i}{{k}_{1}}{{G}_{1}}{{W}_{0}} \right) \right|}_{\left| {{z}_{2}} \right|=R}}$ 为圆杂边的动应力集中因子K_d, 最大动应力集中因子表示为K_{d, max}。

2. 算例分析

定义参数:G^*=G₂/G₁, G^#=G₃/G₁, ρ^*=ρ₂/ρ₁, ρ^# =ρ₃/ρ₁, k^*=k₂/k₁, k ^# =k₃/k₁, 其关系为:k^*k^*=ρ ^* /G^*, k^#k^#=ρ^# /G^#。介质越“硬”则波速越快, 因而波数k就越小, 所以当k^*>1时表明区域Ⅰ比区域Ⅱ“硬”, 同理, k^# >1表明区域Ⅰ比区域Ⅲ“硬”。在本算例中, 假定所有k^*>1, 即覆盖层比半空间要“软”, 且假定所有ρ^* = 0.8, r=1, ρ₁ = 1, G₁ = 1, h₁ = h₂=1.5r。

图 2中给出了当α₀ = 90°, G^*=k^*=k^#=ρ^*=1, G^#=ρ^#=0, k₁=0.1, h₁=1.5r、12r时圆杂周边的K_d。此时, 问题退化为图 1(b)中所示的半空间单个圆孔对SH波的散射问题。计算表明, 当R_D≥120r时, 图 2中K_d的分布状况与文献[9]中的结果高度一致, 这说明了大圆弧法的合理性。

图 2 ρ^*=G^*=k^*=k^#=1时圆形夹杂边的动应力集中因子K_d

Figure 2. K_d around circular inclusion (ρ^*=G^*=k^*=k^#=1)

下载: 全尺寸图片幻灯片

图 3描述了当夹杂“最软”时, SH波在不同频段入射时夹杂边K_d的分布情况。G^*=0.355 6, G^#分别为0.273 4、0.242 2、0.216 0、0.193 9。图 3(a)中k₁=0.5, 入射波在低频段, K_d为椭圆形, 随着k^#的增加而不断向两侧变大, 在90°和270°时变化则极为弱小。当k^#以0.1为增量时, K_{d, max}以增量不断减小的方式增大, 但所在角度没有变化, 约在190°和350°两处。图 3(b)中k₁=1, SH波在中频段入射, K_d为蝴蝶形, 图 3(c)中k₁=1.5, SH波在高频段入射, K_d为花瓣形。与图 3(a)类似, K_d也随k^#的增大不断向外扩展, 而K_{d, max}的增量不断减小, 但所在位置与图 3(a)不同, 在图 3(b)中约为20°和160°, 在图 3(c)中约为210°和330°。整体上, K_{d, max}随入射频率的增大而减小。

图 3 ρ^#=0.7时圆形夹杂边的动应力集中因子K_d

Figure 3. K_d around circular inclusion with ρ^#=0.7

下载: 全尺寸图片幻灯片

图 4描述了当夹杂“软硬居中”时, 圆杂边K_d的分布情况。此时G^*=0.355 6, G^#分别为0.743 8、0.625 0、0.532 5、0.459 2。图 4(a)描述了当k₁=0.5时夹杂周边K_d的分布, 与图 3(a)类似, 其形状也为椭圆形, 并随k^#的增加而不断向两侧变大, 但整体上要小于图 3(a)中K_d, 图 3(a)中k^#=1.6时K_{d, max}略大于1.3, 而图 4(a)中k^#=1.4时K_{d, max}≈1。另外与图 3(a)不同的是, 当k^#以0.1为增量增加时, K_{d, max}是以相同的增量(约0.1)不断增大, 但其所在位置(角度)没有变化, 都是在约190°和350°两处。与图 3(b)和图 3(c)类似, 图 4(b)和图 4(c)分别描述了SH波在中频(k₁=1)和高频(k₁=1.5)入射时的情况。与图 3(a)和图 4(a)的关系类似, 图 4(b)~(c)中K_d整体上要比图 3(b)~(c)中K_d小, 而且K_{d, max}也随着k^#的增大而以相同的增量增加。整体而言, 从图 4(a)到图 4(c), K_{d, max}的增量是在不断减小的。

图 4 ρ^#=0.9时圆形夹杂边的动应力集中因子K_d

Figure 4. K_d around circular inclusion with ρ^#=0.9

下载: 全尺寸图片幻灯片

图 5描述了当夹杂“最硬”时, 夹杂周边K_d的分布。G^*=0.355 6, G^#分别为3.055 6、2.244 9、1.718 8、1.358 0。与前面的结果类似, 当k₁分别为0.5、1.0、1.5时, K_d分别为椭圆形、蝴蝶型和花瓣形, 且K_{d, max}所在角度基本没有变化, 但整体上缩小了, 当k^#同样以0.1为增量不断增加时, K_{d, max}却是以增量不断变大的方式增大的, 这与图 3~4的情况都不一样。

图 5 ρ^#=1.1时圆形夹杂边的动应力集中因子K_d

Figure 5. K_d around circular inclusion with ρ^#=1.1

下载: 全尺寸图片幻灯片

图 6描述了当夹杂“最软”、“居中”、“最硬”时, 圆杂的K_{d, max}随k^#的变化情况。与图 3~图 5相同, 都只改变波数k₃, 都是k₁越大则K_{d, max}越小。整体上, 夹杂越“硬”, K_{d, max}越“小”。当夹杂“最软”时, K_{d, max}的增加呈现随k^#的增大而先大后小的变化, 图形为上凸的, 当夹杂“软硬居中”时, K_{d, max}的变化则可认为随着k^#的增大而呈现线性变化, 图形可认为是直线, 当夹杂“最硬”时, K_{d, max}随着k^#的增大而呈现先小后大的变化, 图形是下凸的。这些与图 3~5的结果是相对应的。

图 6 夹杂边K_{d, max}随k^#的变化

Figure 6. Variation of K_{d, max} with k^#

下载: 全尺寸图片幻灯片

图 7描述了夹杂周边K_{d, max}随k₁的变化情况。无论夹杂硬度如何, 只要确定k₃, K_{d, max}先随着k₁的增加而增大, 当k₁≈0.35时达到最大, 而后随着k₁的增加而减小, 当k₁≈0.75时达到极小值, 此后随着k₁的增加而震荡下降。整体上, 夹杂越“软”则K_{d, max}越大。

图 7 夹杂边K_{d, max}随k₁的变化

Figure 7. Variation of K_{d, max} with k₁

下载: 全尺寸图片幻灯片

3. 结论

根据大圆弧法对地表软覆盖层中单个圆杂在SH波作用下的动应力集中问题进行了研究, 将覆盖层边界用大圆弧来近似, 构造散射波场, 得到解析解。算例表明:当SH波垂直入射, 覆盖层“软”, 圆杂位于覆盖层正中时:

(1) 圆杂越“软”, K_d越“大”, 圆杂越“硬”, K_d越小；

(2) 当k₁≈0.35时, K_{d, max}达到最大值, 当k₁≈0.75时出现极小值, 此后随k₁的增加呈震荡下降的变化。

图 1 取样位置及试样制备

Figure 1. Sampling location and specimen preparation

下载: 全尺寸图片幻灯片

图 2 围压SHPB实验系统

Figure 2. SHPB experimental system with confining pressure

下载: 全尺寸图片幻灯片

图 3 不同冲击气压页岩破坏形态

Figure 3. Failure modes of shale under different impact air pressures

下载: 全尺寸图片幻灯片

图 4 冲击气压-循环冲击次数统计图

Figure 4. Relationship between impact pressure and critical cycle impact times

下载: 全尺寸图片幻灯片

图 5 不同冲击气压循环冲击页岩应力-应变曲线

Figure 5. Variation of stress-strain curves of shale with times of cyclic impact under different impact air pressures

下载: 全尺寸图片幻灯片

图 6 一次冲击破坏试样应力-应变曲线及应变损伤曲线

Figure 6. Stress-strain curves and damage-strain curves of specimens failed after a single impact

下载: 全尺寸图片幻灯片

图 7 试样5-1循环冲击应力-应变曲线及应变损伤曲线

Figure 7. Stress-strain and damage-strain curves of specimen 5-1 under cyclic impact

下载: 全尺寸图片幻灯片

图 8 不同载荷下试样损伤随循环冲击次数变化曲线

Figure 8. Variation of specimen damage with cyclic impact times under different loads

下载: 全尺寸图片幻灯片

图 9 各试样循环冲击总入射能统计柱状图

Figure 9. Statistical histogram of total incident energy of cyclic impact for each rock specimen

下载: 全尺寸图片幻灯片

图 10 不同冲击气压梯度循环冲击页岩应力-应变曲线

Figure 10. Variation of stress-strain curves of shale under different impact air pressure gradients

下载: 全尺寸图片幻灯片

图 11 能量吸收比随循环冲击次数的变化曲线

Figure 11. Relationship between the nergy absorption ratios and the times of cyclic impact

下载: 全尺寸图片幻灯片

图 12 各页岩试样能量吸收比统计图

Figure 12. Statistical chart of energy absorption ratios of shale specimens

下载: 全尺寸图片幻灯片

表 1 页岩试样基本物理力学参数

Table 1. Basic physical and mechanical parameters of the shale specimens

密度/(kg·m⁻³)	层理/(°)	纵波波速/(m·s⁻¹)	抗压强度/MPa	弹性模量/GPa	泊松比	抗拉强度/MPa
2619	0	4163	156	4.790	0.2	5.500

下载: 导出CSV

表 2 恒压冲击实验设计

Table 2. Design of constant pressure impact experiments

循环冲击气压/MPa	试样
0.4	1-1, 1-2, 1-3
0.6	2-1, 2-2, 2-3
0.8	3-1, 3-2, 3-3
1.0	4-1, 4-2, 4-3
1.2	5-1, 5-2, 5-3

下载: 导出CSV

表 3 不同气压梯度循环冲击实验设计

Table 3. Design of variable-pressure impact experiments

冲击气压梯度布置	试样	气压梯度/MPa
1.0 MPa→0.9 MPa→0.8 MPa→ 0.7 MPa→0.6 MPa	6-1, 6-2, 6-3	−0.1 MPa
1.2 MPa→1.0 MPa→0.8 MPa→ 0.6 MPa→0.4 MPa	7-1, 7-2, 7-3	−0.2 MPa
0.6 MPa→0.7 MPa→0.8 MPa→ 0.9 MPa→1.0 MPa	8-1, 8-2, 8-3	0.1 MPa
0.4 MPa→0.6 MPa→0.8 MPa→ 1.0 MPa→1.2 MPa	9-1, 9-2, 9-3	0.2 MPa
0.8 MPa→0.8 MPa→0.8 MPa→ 0.8 MPa→0.8 MPa	10-1, 10-2, 10-3	0 MPa

下载: 导出CSV

参考文献(32)

[1]	贾承造, 郑民, 张永峰. 中国非常规油气资源与勘探开发前景 [J]. 石油勘探与开发, 2012, 39(2): 129–136. JIA C Z, ZHENG M, ZHANG Y F. Unconventional hydrocarbon resources in China and the prospect of exploration and development [J]. Petroleum Exploration and Development, 2012, 39(2): 129–136.
[2]	TAYLOUR G B, RIFAI H S, HILDENBRAND Z L, et al. Elucidating hydraulic fracturing impacts on ground water quality using a regional geospatial statistical modeling approach [J]. Science of the Total Environment, 2016, 545: 114–126.
[3]	韩烈祥, 朱丽华, 孙海芳, 等. LPG无水压裂技术 [J]. 天然气工业, 2014, 34(6): 48–54. HAN L X, ZHU L H, SUN H F, et al. LPG waterless fracturing technology [J]. Nature Gas Industry, 2014, 34(6): 48–54.
[4]	翟成, 郑仰峰, 孙勇, 等. 一种页岩储层甲烷原位燃爆压裂与助燃剂安全投放协同控制方法: CN112761588B [P]. 2022-02-08.
[5]	刘厅, 翟成, 赵洋, 等. 基于LF-NMR的页岩多尺度孔裂隙应力敏感性评价 [J]. 煤炭学报, 2021, 46(S2): 887–897. DOI: 10.13225/j.cnki.jccs.2021.0852. LIU T, ZHAI C, ZHAO Y, et al. Evaluation on stress sensitivity of multiscale pore and fracture in shale based on LF-NMR [J]. Journal of China Coal Society, 2021, 46(S2): 887–897. DOI: 10.13225/j.cnki.jccs.2021.0852.
[6]	JUN L, CAO L Y, GUO B Y, et al. Prediction of productivity of high energy gas-fractured oil wells [J]. Journal of Petroleum Science and Engineering, 2018, 160: 510–518. DOI: 10.1016/j.petrol.2017.10.071.
[7]	陈莉静, 冯纪米, 吴小超. 高能气体瞬态破岩特性试验研究 [J]. 岩石力学与工程学报, 2020, 39(S2): 3271–3277. CHEN L J, FENG J M, WU X C. Experimental research on transient rock breaking characteristics of high-energy gas [J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(S2): 3271–3277.
[8]	任山, 黄禹忠, 林永茂, 等. 燃爆诱导及酸处理新技术在川西须家河气藏的应用 [J]. 钻采工艺, 2009, 32(1): 31–32. REN S, HUANG Y Z, LIN Y M, et al. Application of propagated blast and acid treatment technology in Chuanxi Xujiahe gas reservoir [J]. Drilling and production Technology, 2009, 32(1): 31–32.
[9]	任杨, 吴飞鹏, 蒲春生, 等. 长脉冲燃爆压裂复合燃速火药配方优化与应用 [J]. 科学技术与工程, 2014, 14(24): 68–73. REN Y, WU F P, PU C S, et al. The optimization and application of composite burning rate gunpowder formula of long pulse explosive fracturing [J]. Science Technology and Engineering, 2014, 14(24): 68–73.
[10]	吴飞鹏, 徐尔斯, 尉雪梅, 等. 燃爆诱导水力压裂多裂缝耦合起裂规律 [J]. 天然气工业, 2018, 38(11): 65–72. WU F P, XU E S, WEI X M, et al. Laws of multi-fracture coupling initiation during blasting induced hydraulic fracturing [J]. Nature Gas Industry, 2018, 38(11): 65–72.
[11]	吴飞鹏, 蒲春生, 陈德春, 等. 多级脉冲爆燃压裂作用过程耦合模拟 [J]. 石油勘探与开发, 2014, 41(5): 605–611. WU F P, PU C S, CHEN D C, et al. Coupling simulation of multistage pulse conflagration compression fracturing [J]. Petroleum Exploration and Development, 2014, 41(5): 605–611.
[12]	田怡萍. 页岩爆燃压裂下裂缝扩展模式数值模拟研究[D]. 四川绵阳: 西南科技大学, 2019: 1–8. TIAN Y P. Numerical simulation study on crack propagation mode under shale deflagration fracturing[D]. Mianyang, Sichuan, China: Southwest University of Science and Technology,2019:1–8
[13]	刘洪志. 多级燃爆压裂裂缝扩展规律模拟研究[D]. 山东青岛: 中国石油大学(华东), 2017: 2–9. LIU H Z. Simulation on the fracture propagation laws of multi-stage blasting fracturing[D]. Qingdao, Shandong, China: China University of Petroleum (East China), 2017:2–9
[14]	夏昌敬, 谢和平, 鞠杨. 孔隙岩石的SHPB试验研究 [J]. 岩石力学与工程学报, 2006, 25(5): 896–900. XIA C J, XIE H P, JU Y. SHPB test on porous rock [J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(5): 896–900.
[15]	许金余, 吕晓聪, 张军, 等. 循环冲击作用下围压对斜长角闪岩动态特性的影响研究 [J]. 振动与冲击, 2010, 29(8): 60–63. XU J Y, LYU X C, ZHANG J, et al. Research on dynamic mechanical performance of amphibolite under cyclical impact loadings at different confining pressures [J]. Journal of Vibration and Shock, 2010, 29(8): 60–63.
[16]	甘德清, 田晓曦, 刘志义, 等. 循环冲击状态下砂岩力学及损伤特性研究 [J]. 中国矿业, 2021, 30(3): 203–211. GAN D Q, TIAN X X, LIU Z Y, et al. Study on mechanics and damage characteristics of sandstone under cyclic impact state [J]. China Mining Magazine, 2021, 30(3): 203–211.
[17]	SHAN R L, JIANG Y S, LI B Q. Obtaining dynamic complete stress–strain curves for rock using the split Hopkinson pressure bar technique [J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(6): 983–992. DOI: 10.1016/S1365-1609(00)00031-9.
[18]	金解放, 李夕兵, 常军然, 等. 循环冲击作用下岩石应力应变曲线及应力波特性 [J]. 爆炸与冲击, 2013, 33(6): 613–619. DOI: 10.11883/1001-1455(2013)06-0613-07. JIN J F, LI X B, CHANG J R, et al. Stress-strain curve and stress wave characteristics of rock subjected to cyclic impact loadings [J]. Explosion and Shock Waves, 2013, 33(6): 613–619. DOI: 10.11883/1001-1455(2013)06-0613-07.
[19]	谭玉叶, 汪杰, 宋卫东, 等. 循环冲击下胶结充填体动载力学特性试验研究 [J]. 采矿与安全工程学报, 2019, 36(1): 184–190. TAN Y Y, WANG J, SONG W D, et al. Experimental study on mechanical properties of cemented tailings backfill under cycle dynamic loading test [J]. Journal of Mining & Safety Engineering, 2019, 36(1): 184–190.
[20]	金解放, 李夕兵, 王观石, 等. 循环冲击载荷作用下砂岩破坏模式及其机理 [J]. 中南大学学报(自然科学版), 2012, 43(4): 1453–1461. JIN J F, LI X B, WANG G S, et al. Failure modes and mechanisms of sandstone under cyclic impact loadings [J]. Journal of Central South University (Science and Technology), 2012, 43(4): 1453–1461.
[21]	金解放, 李夕兵, 殷志强, 等. 轴压和循环冲击次数对砂岩动态力学特性的影响 [J]. 煤炭学报, 2012, 37(6): 923–930. JIN J F, LI X B, YIN Z Q, et al. Effects of axial pressure and number of cyclic impacts on dynamic mechanical characteristics of sandstone [J]. Journal of China Coal Society, 2012, 37(6): 923–930.
[22]	吕晓聪, 许金余, 赵德辉, 等. 冲击荷载循环作用下砂岩动态力学性能的围压效应研究 [J]. 工程力学, 2011, 28(1): 138–144. LYU X C, XU J Y, ZHAO D H, et al. Research on confining pressure effect of sandstone dynamic mechanical performance under the cyclical impact loadings [J]. Engineering Mechanics, 2011, 28(1): 138–144.
[23]	余永强, 张文龙, 范利丹, 等. 冲击荷载下煤系砂岩应变率效应及能量耗散特征 [J]. 煤炭学报, 2021, 46(7): 2281–2293. YU Y Q, ZHANG W L, FAN L D, er al. Study on strain rate effect and energy dissipation characteristics of coal measures sandstone under impact loading [J]. Journal of China Coal Society, 2021, 46(7): 2281–2293.
[24]	闫雷, 刘连生, 李仕杰, 等. 单轴循环冲击下弱风化花岗岩的损伤演化 [J]. 爆炸与冲击, 2020, 40(5): 053303. DOI: 10.11883/bzycj-2019-0354. YAN L, LIU L S, LI S J, et al. Damage evolution of weakly-weathered granite under uniaxial cyclic impact [J]. Explosion and Shock Waves, 2020, 40(5): 053303. DOI: 10.11883/bzycj-2019-0354.
[25]	杜晶. 不同长径比下岩石冲击动力学特性研究[D]. 长沙: 中南大学, 2011: 51–72. DU J. Size effect on the dynamic mechanical properties under impact loads of rock [D]. Changsha, Hunan, China: Central South University, 2011:51-72.
[26]	孙清佩, 张志镇, 李培超, 等. 黑色页岩动载破坏的层理效应及损伤本构模型研究 [J]. 岩石力学与工程学报, 2019, 38(7): 1319–1331. DOI: 10.13722/j.cnki.jrme.2018.1333. SUN Q P, ZHANG Z Z, LI P C, et al. Study on the bedding effect and damage constitutive model of black shale under dynamic loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(7): 1319–1331. DOI: 10.13722/j.cnki.jrme.2018.1333.
[27]	单仁亮, 薛友松, 张倩. 岩石动态破坏的时效损伤本构模型 [J]. 岩石力学与工程学报, 2003, 22(11): 1771–1776. SHAN R L, XUE Y S, ZHANG Q. Time dependent damage model of rock under dynamic loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(11): 1771–1776.
[28]	杨圣奇, 徐卫亚, 韦立德, 等. 单轴压缩下岩石损伤统计本构模型与试验研究 [J]. 河海大学学报(自然科学版), 2004, 32(3): 200–203. YANG S Q, XU W Y, WEI L D, et al. Statistical constitutive model for rock damage under uniaxial compression and its experimental study [J]. Journal of Hohai University (Natural Sciences), 2004, 32(3): 200–203.
[29]	朱晶晶. 循环冲击载荷下岩石力学特性与损伤模型的试验研究[D]. 长沙: 中南大学, 2012. ZHU J J. Experimental study of rock mechanical properties and damage model under cyclical dynamic loads [D].Changsha, Hunan, China: Central South University, 2012.
[30]	朱晶晶, 李夕兵, 宫凤强, 等. 单轴循环冲击下岩石的动力学特性及其损伤模型研究 [J]. 岩土工程学报, 2013, 35(3): 531–539. ZHU J J, LI X B, GONG F Q, et al. Dynamic characteristics and damage model for rock under uniaxial cyclic impact compressive loads [J]. Chinese Journal of Geotechnical Engineering, 2013, 35(3): 531–539.
[31]	黎立云, 徐志强, 谢和平, 等. 不同冲击速度下岩石破坏能量规律的实验研究 [J]. 煤炭学报, 2011, 36(12): 2007–2011. LI L Y, XU Z Q, XIE H P, et al. Failure experimental study on energy laws of rock under differential dynamic impact velocities [J]. Journal of China Coal Society, 2011, 36(12): 2007–2011.
[32]	黎立云, 谢和平, 鞠杨, 等. 岩石可释放应变能及耗散能的实验研究 [J]. 工程力学, 2011, 28(3): 35–40. LI L Y, XIE H P, JU Y, et al. Experimental investigations of releasable energy and dissipative energy within rock [J]. Engineering Mechanics, 2011, 28(3): 35–40.

施引文献

期刊类型引用(1)
1. 齐辉，陈洪英，张希萌，赵元博，项梦. 半空间内含有部分脱胶的椭圆夹杂及圆孔对SH波的散射. 爆炸与冲击. 2018(06): 1344-1352 . 本站查看
其他类型引用(6)

资源附件(0)

访问统计

图(12) / 表(3)

计量

文章访问数: 714
HTML全文浏览量: 173
PDF下载量: 217
被引次数: 7

1. 理论分析
1.1 问题模型
1.2 控制方程
1.3 入射波场、散射波场及相应应力
1.4 连接条件
1.5 动应力集中因子(Kd)
2. 算例分析
3. 结论

循环冲击载荷作用下页岩动力学响应及能量耗散特征

doi: 10.11883/bzycj-2022-0248

作者简介: 王 宇（1999－ ），男，博士研究生，tb21120024b1@cumt.edu.cn

通讯作者: 翟 成（1978－ ），男，博士，教授，greatzc@126.com

计量

出版历程

Dynamic response and energy dissipating characteristics of shale under cyclic impact loadings

1. 理论分析

1.1 问题模型

1.2 控制方程

1.3 入射波场、散射波场及相应应力

1.4 连接条件

1.5 动应力集中因子(Kd)

2. 算例分析

3. 结论

期刊类型引用(1)

其他类型引用(6)

计量

出版历程

目录

1. 理论分析

1.1 问题模型

1.2 控制方程

1.3 入射波场、散射波场及相应应力

1.4 连接条件

1.5 动应力集中因子(Kd)

2. 算例分析

3. 结论

作者简介:
王　宇（1999－　），男，博士研究生，tb21120024b1@cumt.edu.cn

通讯作者:
翟　成（1978－　），男，博士，教授，greatzc@126.com

1.5 动应力集中因子(K_d)

1.5 动应力集中因子(K_d)