QQ群聊

• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## 基于波速测量的岩石储能量化表征方法研究

1. 中南大学资源与安全工程学院，湖南 长沙 410083

2. 中南大学高等研究中心，湖南 长沙 410083

## Research on Quantitative Characterization Method of Rock Energy Storage Based on Wave Velocity Measurement

GUO Chunzhi,1, MA Chunde,1,2, ZHOU Yanan1, LIU Zelin1, LONG Shan1

1. School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China

2. Advanced Research Center, Central South University, Changsha 410083, Hunan, China

 基金资助: 新疆维吾尔自治区重大科技专项“东天山复杂地质特长公路隧道建设关键工程研究与应用——特长公路隧道机械化安全快速施工技术研究”（编号：2018A03003-2）和国家重点研发计划项目“深部岩体力学与开采理论”之“深部高应力诱导与能量调控理论”.  编号：2016YFC0600706

Received: 2018-05-15   Revised: 2018-09-18   Online: 2019-04-29

Abstract

The underground rock mass stores a large amount of energy，disasters such as rock bursts will occur under certain conditions.The benign application of rock energy storage can not only effectively reduce the sudden release of energy，but also make use of rock energy.But there are still a series of technical problems to be solved in order to make it work.One of the key issues is how to accurately quantify the energy storage of deep rock mass.This study only qualitatively and quantitatively studies the elastic range of rock，using low-intensity red sandstone (sedimentary rock)，medium-strength marble (metamorphic rock) and high-strength granite (magmatic rock).The basic idea of ​​this study is to explore the relationship between wave velocity and stress in the elastic phase of rock.The model is used to characterize the corresponding stress value by wave velocity，and then explore the relationship between stress and the corresponding energy density.The model uses stress to characterize the energy stored in the rock，and then compares the energy value obtained by the model with the actual energy value to verify the method of characterizing energy with wave velocity.The test results show that the longitudinal wave velocity and the compressive stress show a linear relationship in the three typical rock elastic stages，and the compressive stress and the rock energy storage basically conform to the complex power exponential relationship.The results also show that the theoretical value is not much different from the real value，the error is small，and the hard rock is more suitable than soft rock to be quantified the stored energy with this method，with higher precision and accuracy.In this paper，through the uniaxial repeated loading and unloading test and calculation of the typical rock specimens of marble，granite and red sandstone in the elastic range，the following conclusions are drawn: $①$ The three waves exhibit wave velocity with increasing stress.However，when the stress is 30$%$ of the maximum stress，the wave velocity growth of the three rocks is relatively uniform.When the stress exceeds 30$%$ of the maximum stress，the growth rate of marble and granite is still consistent，while the rate of growth of red sandstone is steep.Increase the phenomenon.$②$ The wave velocity and stress of the three rocks accord with the linear model.The accuracy of the red sandstone is lower than that of marble and granite.The total energy and elastic energy of the granite are larger than that of marble and red sandstone.The red sandstone has higher dissipative energy than marble and granite.$③$ According to the function of unloading wave velocity-stress and stress-elasticity，the wave velocity-elastic energy model is constructed and verified，the overall effect is better，and the accuracy and accuracy of hard rock are higher than that of soft rock.

Keywords： typical rock ; rock strength ; unloaded wave velocity ; elastic energy storage ; composite exponential model ; quantitative characterization

GUO Chunzhi, MA Chunde, ZHOU Yanan, LIU Zelin, LONG Shan. Research on Quantitative Characterization Method of Rock Energy Storage Based on Wave Velocity Measurement[J]. Gold Science and Technology, 2019, 27(2): 223-231 doi:10.11872/j.issn.1005-2518.2019.02.223

## 1 实验仪器及方法

### 图1

Fig.1   MTS815 material testing machine with real-time measuring function

Table 1  Physical and mechanical parameters of three kinds of rocks

### 图2

Fig.2   Cover area under stress-strain curve

### 图3

（a）、（b）大理岩；（c）、（d）花岗岩；（e）、（f）红砂岩

4给出了反复加卸载后大理岩、花岗岩和红砂岩的平均相对纵波波速随应力的变化规律。为便于比较，以各个应力值与最大应力值之比作为横坐标，以平均波速值与平均初始波速之比作为纵坐标，绘制其变化曲线如图5所示。

### 图5

（a）大理岩；（b）花岗岩；（c）红砂岩

$v=k1σ+v0$

Table 2  Fitting table of relationship between wave velocity and stress

2-加载14.865 1030.967
3-加载13.385 1000.989

1-卸载14.495 1020.977
2-卸载14.085 1060.976
3-卸载14.145 0880.993

2-加载8.454 6230.978
3-加载8.384 5760.983

1-卸载8.774 6160.974
2-卸载7.974 6790.969
3-卸载8.454 6000.984

2-加载24.822 7200.963
3-加载27.972 6460.986

1-卸载24.052 7460.961
2-卸载25.002 7170.967
3-卸载27.592 6600.986

### 2.2 加卸载后应力与能量的对应关系

$W=k2σα$

Table 3  Fitting table of relationship between stress and energy

2-加载0.0031.7500.997
3-加载0.0031.7880.998

1-卸载0.0031.7600.998
2-卸载0.0031.7570.998
3-卸载0.0031.7940.999

2-加载0.0071.6670.999
3-加载0.0071.6480.999

1-卸载0.0061.6900.999
2-卸载0.0081.6210.998
3-卸载0.0071.6320.998

2-加载0.0191.7000.998
3-加载0.0181.7240.998

1-卸载0.0201.6710.995
2-卸载0.0191.6840.994
3-卸载0.0241.5950.999

### 2.3 弹性能的波速表征方法

$W=k2(v-v0k1)α$

$W=0.003(v-508514.24)1.770$

4所示为大理岩的波速—能量关系对应表。

Table 4  Correspondence table of wave velocity-energy relation of marble

V/（m·s-1W理论值/JW真实值/J相对误差/%
6 213.008.4488.4960.56
6 167.007.0387.5236.45
6 078.006.0976.5937.52
6 049.335.8065.7141.61
6 006.675.3854.9079.74
5 951.004.4564.1367.74
5 878.673.6053.4205.41
5 787.003.2392.76017.36
5 711.332.4582.17513.01
5 666.002.0321.64623.45
5 570.001.7001.17844.31
5 467.001.3120.77768.85
5 312.000.6110.44936.08
5 203.330.2630.21124.64
5 105.330.0640.08020.00

$W=0.007(v-46248.40)1.668$

5所示为花岗岩波速—能量关系对应表。

Table 5  Correspondence table of wave velocity-energy relation of granite

V/（m·s-1W理论值/JW真实值/J相对误差/%
5 385.0013.19613.3511.16
5 306.0011.60111.6810.68
5 274.6710.78910.5532.24
5 241.339.6159.2813.60
5 207.338.0598.3093.01
5 190.007.6477.3703.76
5 138.006.3416.2551.37
5 106.675.5305.2794.75
5 088.004.6084.4224.21
5 063.673.9843.54012.54
5 003.333.1952.9279.16
4 967.002.5552.17617.42
4 889.672.0381.61426.27
4 799.331.4101.10727.37
4 752.330.5890.69715.49
4 694.670.1210.37267.47
4 668.000.0360.14374.83

$W=0.021(v-268825.55)1.648$

6所示为红砂岩的波速—能量关系对应表。

Table 6  Correspondence table of wave velocity-energy relation of red sandstone

V/（m·s-1W理论值/JW真实值/J相对误差/%
3 6108.0888.4994.84
3 5407.3956.8198.45
3 4745.9595.22014.16
3 3624.0813.7119.97
3 2192.3912.3720.80
2 9351.0251.23917.27
2 7730.1670.33650.30

## 4 结论

（1）3种岩石均呈现出波速随应力的增大而增大，当应力值未达到各自最大应力值的30%时，3种岩石的波速增长较一致；当应力值超过最大应力值的30%时，大理岩和花岗岩的波速增长速率仍较一致，而红砂岩的波速增长速率呈现出突增现象。

（2）3种岩石的波速与应力符合线性模型，呈现出红砂岩的精确度低于大理岩和花岗岩；应力与能量符合复合幂函数模型，花岗岩的总能量和弹性能大于大理岩和红砂岩，红砂岩的耗散能高于大理岩和花岗岩。

（3）根据卸载波速—应力与应力—弹性能的函数关系，构建波速—弹性能模型并进行验证，总体效果较好，相比之下硬岩的精度和准确度比软岩高。

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

ZhangZ ZGaoF.

Research on nonlinear characteristics of rock energy evolution under uniaxial compression

［J］.Chinese Journal of Rock Mechanics and Engineering2012316）：1198-1207.

［J］.岩土力学，201637（增2）：129-136.

GuoJianqiangLiuXinrongWangJunbaoet al.

Strength criterion of rock based on elastic strain energy

［J］.Rock and Soil Mechanics2016,

37（Supp

.2）：129-136.

GuoWWangLYangD Y.

Rock damage research based on the energy principles

［J］.Applied Mechanics and Materials201187）：238-242.

TangA JShiC GWangYet al.

Energy characteristics of brittle rock in failure process

［J］.Applied Mechanics and Materials2014,580-583260-263.

［J］.岩石力学与工程学报，20072612）：2437-2443.

GaoHongZhengYingrenFengXiating.

Study on energy yield criterion of rock materials

［J］.Rock Mechanics and Rock Engineering20072612）：2437-2443.

［J］.中南大学学报（自然科学版），2016479）：3140-3147.

CongYuWangZaiquanZhengYingrenet al.

［J］.Journal of Central South University （Science and Technology）2016479）：3140-3147.

［J］.水利水电科技进展，2013333）：77-84.

LiGuoZhouChengjingZhangYonget al.

Review of rockburst in underground engineering

［J］.Advances in Science and Technology of Water Resources2013333）：77-84.

［J］.岩土力学，2017385）：1397-1404.

ZhangChuanqingLuJingjingChenJunet al.

Discussion on rock burst proneness indexes and their relation

［J］.Geomechanics2017385）：1397-1404.

［J］.岩石力学与工程学报，20052420）：3796-3802.

YangJianWangLianjun.

Study on mechanism of rock burst by acoustic emission testing

［J］.Chinese Journal of Rock Mechanics and Engineering20052420）：3796-3802.

CaiMKaiserP KMoriokaH.

FLAC/PEC coupled numerical simulation of AE in large-scale underground excavations

［J］.International Journal of Rock Mechanics and Mining Sciences2007444）：550-564.

［J］.北京交通大学学报，2009331）：99-108.

ChenXiangQiXiaoboCaiXinbinet al.

Application of extension comprehensive evaluation method in rockburst discrimination

［J］.Journal of Beijing Jiaotong University2009331）：99-108.

［J］.岩石力学与工程学报，2013326）：1101-1111.

LiXibingYaoJinruiDuKun.

Preliminary study for induced fracturing and non-explosive continuous mining in high-geostress hard rock mine:A case study of Kaiyang phosphate mine

［J］.Chinese Journal of Rock Mechanics and Engineering2013326）：1101-1111.

［J］.科技创新导报，201615）：173.

LiXibingGongFengqiangDuKunet al.

Rockburst experimental study of rock mass with high stress under dynamic disturbance

［J］.Science and Technology Innovation Herald201615）：173.

［J］.岩石力学与工程学报，2012319）：1830-1938.

LiangChangyuLiXiaoWangShengxinget al.

Experimental investigations on rate-dependent stress-strain characteristics and energy mechanism of rock under uniaxial compression

［J］.Chinese Journal of Rock Mechanics and Engineering2012319）：1830-1938.

［J］.工程力学，2007241）：136-142.

YangShengqiXuWeiyaSuChengdong.

Study on the deformation failure and energy properties of marble specimen under triaxial compression

［J］.Engineering Mechanics2007241）：136-142.

［J］.岩石力学与工程学报，2011301）：141-148.

XuJiangZhangYuanYangHongweiet al.

Energy evolution law of deformation and damage of sandstone under cyclic pore water pressure

［J］.Chinese Journal of Rock Mechanics and Engineering2011301）：141-148.

［J］.岩石力学与工程学报，2001201）：38-42.

CaiMeifengWangJin’anWangShuanghong.

Analysis on energy distribution and prediction of rock burst during deep mining excavation in Linglong gold mine

［J］.Chinese Journal of Rock Mechanics and Engineering2001201）：38-42.

［D］.兰州兰州大学201316-17.

LiGaoyong.

Research on Correlation Between Velocity and Stress in Sandstone in Real Time

［D］.LanzhouLanzhou University201316-17.

［J］.岩石力学与工程学报，2012315）：953-962.

ZhangZhizhenGaoFeng.

Experimental research on energy evolution of red sandstone samples under uniaxial compression

［J］.Chinese Journal of Rock Mechanics and Engineering2012315）：953-962.

/

 〈 〉