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山东大学学报 (工学版) ›› 2020, Vol. 50 ›› Issue (3): 82-87.doi: 10.6040/j.issn.1672-3961.0.2019.622

• 土木工程 • 上一篇    下一篇

高地应力下砂岩力学参数和波速变化规律试验研究

宫嘉辰1(),陈士海1,2,*()   

  1. 1. 华侨大学土木工程学院，福建 厦门 361021
    2. 福建省隧道与城市地下空间工程技术研究中心, 福建 厦门 361021
  • 收稿日期:2019-10-17 出版日期:2020-06-20 发布日期:2020-06-16
  • 通讯作者: 陈士海 E-mail:836408502@qq.com;cshblast@163.com
  • 作者简介:宫嘉辰(1995—)，男，山东烟台人，硕士研究生，主要研究方向为岩土工程方向研究.E-mail: 836408502@qq.com
  • 基金资助:
    国家自然科学基金资助项目(51974136);华侨大学研究生科研创新基金资助项目(17014086007)

Experimental study on mechanical parameters and wave velocity variation of sandstone under high ground stress

Jiachen GONG1(),Shihai CHEN1,2,*()   

  1. 1. College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian, China
    2. Fujian Research Center for Tunneling and Urban Underground Space Engineering, Xiamen 361021, Fujian, China
  • Received:2019-10-17 Online:2020-06-20 Published:2020-06-16
  • Contact: Shihai CHEN E-mail:836408502@qq.com;cshblast@163.com
  • Supported by:
    国家自然科学基金资助项目(51974136);华侨大学研究生科研创新基金资助项目(17014086007)

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摘要：

基于波动方程，提出一种砂岩的纵波波速与静水围压关系的数学模型。在岩石常规三轴试验的基础上得到不同静水围压下砂岩的静弹性模量、静泊松比和纵波波速，并分别拟合得到静弹性模量-静水围压和静泊松比-静水围压关系的拟合曲线和拟合公式。试验结果表明，砂岩的静弹性模量和静泊松比随静水围压的增大而增加，且静弹性模量增加速率缓慢减少。基于波动方程求解得到纵波波速-静水围压关系的数学模型，利用数学模型计算得到的纵波波速可知，砂岩的纵波波速随静水围压的增大而增大，且增加速率逐渐变缓。计算得到的纵波波速与试验测得的纵波波速进行对比验证，误差范围为7.0%~8.3%，故基于波动方程求解的砂岩纵波波速-静水围压关系的数学模型可靠性和准确性较高，对高地应力下岩石的物理力学参数和波速变化规律的分析判定具有指导意义。

关键词: 高地应力, 波动方程, 砂岩, 纵波波速, 静水围压, 静弹性模量, 静泊松比

Abstract:

A large number of studies showed that high ground stress had a certain influence on the wave velocity of deep buried rock, based on the wave equation, a mathematical model of the relationship between longitudinal wave velocity of sandstone and hydrostatic confining pressure was proposed. Based on the conventional triaxial test of rock, the static elastic modulus, static Poisson's ratio and longitudinal wave velocity of sandstone under different hydrostatic confining pressures were obtained, and the fitting curves and fitting formulas of static elastic modulus-hydrostatic confining pressure and static Poisson's ratio-hydrostatic confining pressure were obtained respectively. The test results showed that the static elastic modulus and static Poisson's ratio of sandstone increased with the increase of hydrostatic pressure, and the rate of increase of static elastic modulus decreased slowly. Based on the wave equation, the mathematical model of the longitudinal wave velocity-hydrostatic confining pressure was obtained, the longitudinal wave velocity calculated by the mathematical model showed that the longitudinal wave velocity of the sandstone increased with the increase of the hydrostatic pressure, and the increasing rate gradually became slower. The calculated longitudinal wave velocity was compared with the measured, the error range was 7.0%-8.3%. Therefore, the mathematical model of sandstone longitudinal wave velocity-hydrostatic confining pressure based on wave equation was reliable and accurate, it was of guiding significance to analyze and judge the physical and mechanical parameters of rock under high ground stress and the variation law of wave velocity.

Key words: high ground stress, wave equation, sandstone, longitudinal wave velocity, hydrostatic confining pressure, static elastic modulus, static Poisson′s ratio

中图分类号: 

  • TD23

图1

试样及设备安装示意图"

图2

砂岩单轴应力-应变曲线"

图3

不同围压下砂岩三轴应力-应变曲线"

表1

不同静水围压下砂岩的静弹性参数"

编组 围压/MPa 静弹性模量/GPa 静泊松比
1-1 6 21.82 0.013
1-2 8 22.64 0.028
1-3 10 23.43 0.046
1-4 12 24.26 0.062
1-5 14 24.96 0.074
1-6 16 25.44 0.089

表2

静弹性参数与静水围压关系拟合公式"

拟合公式 相关系数 a b
静弹性模量 E=a ln σ+b 0.989 91 3.785 30 14.881 30
静泊松比 μ=a ln σ+b 0.981 28 0.073 28 -0.121 02

图4

静弹性模量与静水围压关系的拟合曲线"

图5

静泊松比与静水围压关系的拟合曲线"

表3

不同静水围压下砂岩计算纵波波速"

编组 静水围压/MPa 计算纵波波速/(m·s-1)
1-1 6 3 049
1-2 8 3 114
1-3 10 3 179
1-4 12 3 239
1-5 14 3 289
1-6 16 3 337

图6

计算纵波波速与静水围压关系的拟合曲线"

表4

不同静水围压下砂岩的实测纵波波速"

编组 静水围压/MPa 实测纵波波速/(m·s-1)
1-1 6 2 814
1-2 8 2 886
1-3 10 2 952
1-4 12 3 012
1-5 14 3 066
1-6 16 3 118

表5

实测纵波波速和计算纵波波速对比分析"

静水围压/
MPa		 实测纵波波速/
(m·s-1)		 计算纵波波速/
(m·s-1)		 误差/
%
6 2 814 3 049 8.3
8 2 886 3 114 7.9
10 2 952 3 179 7.7
12 3 012 3 239 7.5
14 3 066 3 289 7.2
16 3 118 3 337 7.0
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