Error analysis and discussion of determining the maximum horizontal principal stress by hydraulic fracturing based on the compliance analysis of testing system
YANG Yuehui1，2，SUN Dongsheng1，2，QIN Xianghui1，2，LI Awei1，2，SUN Weifeng1，2，ZHANG Chongyuan1，2，LI Ran1，2，MENG Wen1，2，CHEN Qunce1，2
(1. Institute of Geomechanics，Chinese Academy of Geological Science，Beijing 100081，China；2. Engineering Technology Innovation Center of In-situ Stress，Ministry of Natural Resources，Beijing 100081，China)
Abstract：The large error in the results of the maximum horizontal principal stress is a prominent problem in the in-situ stress measurement by hydraulic fracturing method. In this paper，the differences and applicability of several main formulas used to calculate the maximum horizontal principal stress are compared and analyzed on the basis of the domestic and foreign hydraulic fracturing in-situ stress measurements regulations or suggested methods. Taking the test system compliance as the main influencing factor，the error sources and physical mechanism that affect the calculation accuracy of the maximum horizontal principal stress are analyzed in detail and depth. On this basis，taking the measured hydraulic fracturing data of the deep-hole obtained from the granite borehole in Beishan，Gansu as an example，the fracture reopening process is numerically analyzed based on the KGD theoretical model, and the influence of system compliance on the calculation result of the maximum horizontal principal stress is quantitatively studied. Taking the theoretical calculation value of eliminating the influence factors of compliance as correction value，the measured data and heoretical correction valueof 6 testing intervals in the hole depth range of 18–930 m are given. The results show that the error of the maximum horizontal principal stress measurement results increases gradually with the increase of test depth due to the influence of the test system compliance. When the test depth is 930 m，the relative error of the measurement results is 24.55%. The research results can provide a reference for the error problem of the maximum horizontal principal stress measurement results in relevant engineering applications，also provide a new idea and technical approach for the error analysis and further improvement of the reliability of the hydraulic fracturing in-situ stress measurements.
杨跃辉1，2，孙东生1，2，秦向辉1，2，李阿伟1，2，孙炜锋1，2，张重远1，2，李 冉1，2，孟 文1，2，陈群策1，2. 基于测试系统柔度分析的水压致裂法确定最大水平主应力误差分析与讨论[J]. 岩石力学与工程学报, 2024, 43(S1): 3385-3396.
YANG Yuehui1，2，SUN Dongsheng1，2，QIN Xianghui1，2，LI Awei1，2，SUN Weifeng1，2，ZHANG Chongyuan1，2，LI Ran1，2，MENG Wen1，2，CHEN Qunce1，2. Error analysis and discussion of determining the maximum horizontal principal stress by hydraulic fracturing based on the compliance analysis of testing system. , 2024, 43(S1): 3385-3396.
[1] HAIMSON B C，FAIRHURST C. Initiation and extension of hydraulic fractures in rocks[J]. Journal of Petroleum Science and Engineering，1967，7(3)：310–318.
[2] HAIMSON B C. Hydraulic fracturing in porous and nonporous rock and its potential for determining in situ stress at great depth[Ph. D. Thesis][D]. Minneapolis：University of Minnesota System，1968：1–233.
[3] ZOBACK M L，ZOBACK M. State of stress in the conterminous United States[J]. Journal of Geophysical Research，1980，85(B11)：6 113–6 156.
[4] CORNET F H，VALETTE B. In situ stress determination from hydraulic injection test data[J]. Journal of Geophysical Research，1984，89(B13)：11 527–11 537.
[5] HAIMSON B C. The hydraulic fracturing method of stress measurement：theory and practice[M]. Oxford：Oxford Pergamon Press，1993：395–412.
[6] SCHEIDEGGER A E. On the connection between tectonic stresses and well fracturing data[J]. Pure and Applied Geophysics，1960，46(1)：66–76.
[7] HAYASHI K，SAKURAI I. Interpretation of hydraulic fracturing shut-in curves for tectonic stress measurements[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1989，26(6)：477–482.
[8] HAYASHI K，HAIMSON B C. Characteristics of shut-in curves in hydraulic fracturing stress measurements and determination of in situ minimum compressive stress[J]. Journal of Geophysical Research，1991，96(B11)：311–321.
[9] HAIMSON B C，CORNET F H. ISRM suggested methods for rock stress estimation—part 3：hydraulic fracturing(HF) and/or hydraulic testing of pre-existing fractures(HTPF)[J]. International Journal of Rock Mechanics and Mining Sciences，2003，40(7/8)：1 011–1 020.
[10] 李方全，翟青山，毕尚煦，等. 水压致裂法原地应力测量及初步结果[J]. 地震学报，1986，8(4)：431–438.(LI Fangquan，ZHAI Qingshan，BI Shangxu，et al. In-situ stress measurement by hydraulic fracturing and preliminary results[J]. Acta Seismologica Sinica，1986，8(4)：431–438.(in Chinese))
[11] 刘允芳. 水压致裂法三维地应力测量[J]. 岩石力学与工程学报，1991，10(3)：246–256.(LIU Yunfang. In-situ 3-dimensional stress measurements by hydraulic fracturing technique[J]. Chinese Journal of Rock Mechanics and Engineering，1991，10(3)：246–256.(in Chinese))
[12] 陈群策，孙东生，崔建军，等. 雪峰山深孔水压致裂地应力测量及其意义[J]. 地质力学学报，2019，25(5)：853–865.(CHEN Qunce，SUN Dongsheng，CUI Jianjun，et al. Hydraulic fracturing stress measurements in Xuefengshan deep borehole and its significance[J]. Journal of Geomechanics，2019，25(5)：853–865.(in Chinese))
[13] 邬爱清，韩晓玉，尹健民，等. 一种新型绳索取芯钻杆内置式双管水压致裂地应力测试方法及其应用[J]. 岩石力学与工程学报，2018，37(5)：1 126–1 133.(WU Aiqing，HAN Xiaoyu，YIN Jianmin，et al. A new hydraulic fracturing method for rock stress measurement based on double pressure tubes internally installed in the wire-line core drilling pipes and its application[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(5)：1 126–1 133.(in Chinese))
[14] BREDEHOEFT J D，WOLF R G，KEYS W S，et al. Hydraulic fracturing to determine the regional in situ stress field in the Piceance Basin，Colorado[J]. Geological Society of America Bulletin，1976，87(2)：250–258.
[15] HAIMSON B C，ZHAO Z. Effect of borehole size and pressurization rate on hydraulic fracturing breakdown pressure[C]// Rock Mechanics as a Multidisciplinary Science. [S. l.]：[s. n.]，1991：191–199.
[16] CUISIA T F D，HAIMSON B C. Scale effects in rock mass stress measurements[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1992，29(2)：99–117.
[17] 王成虎，宋成科，邢博瑞. 水压致裂应力测量系统柔性分析及其对深孔测量的影响[J]. 现代地质，2012，26(4)：808–816.(WANG Chenghu，SONG Chengke，XING Borui. Compliance of drilling-rod system for hydro-fracturing in situ stress measurement and its effect on measurements at great depth[J]. Geoscience，2012，26(4)：808–816.(in Chinese))
[18] 王成虎，王仁涛，王春权. 多直径岩芯液压致裂岩石抗拉强度快速试验机研发[J]. 岩石力学与工程学报，2017，36(增1)：3 321–3 331. (WANG Chenghu，WANG Rentao，WANG Chunquan. Development of multiple-diameter core hydraulic fracturing machine to test tensile strength of rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(Supp.1)：3 321–3 331.(in Chinese))
[19] CHANG C D，JO Y G，OH Y K，et al. Hydraulic fracturing in situ stress estimations in a potential geothermal site，Seokmo island，South Korea[J]. Rock Mechanics and Rock Engineering，2014，47(5)：1 793–1 808.
[20] 王春权，王成虎，江英豪，等. 基于不同岩石抗拉强度值确定最大水平主应力的对比分析[J]. 地下空间与工程学报，2017，13(1)：41﹣47.(WANG Chunquan，WANG Chenhu，JIANG Yinghao，et al. Comparative analysis of determinating the maximum horizontal principal stress based on different tensile strength of rocks[J]. Chinese Journal of Underground Space and Engineering，2017，13(1)：41﹣47.(in Chinese))
[21] 贾 晋，王成虎，高桂云，等. 2种方法优选确定易县紫荆关最大水平主应力量值[J]. 岩石力学与工程学报，2018，37(增2)：4 142﹣4 150. (JIA Jin，WANG Chenghu，GAO Guiyun，et al. Utilizing two methods to determine the horizontal principal stresses of Zijingguan region，Yixian County，Heibei Province[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(Supp.2)：4 142﹣4 150.(in Chinese))
[22] 尤明庆，苏承东. 平台巴西圆盘劈裂和岩石抗拉强度的试验研究[J].岩石力学与工程学报，2004，23(18)：3 106﹣3 112.(YOU Mingqing，SU Chengdong. Experimental study on split test with flattened disk and tensile strength of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(18)：3 106﹣3 112.(in Chinese))
[23] 喻 勇. 质疑岩石巴西圆盘拉伸强度试验[J]. 岩石力学与工程学报，2005，24(7)：1 150﹣1 157.(YU Yong. Questioning the validity of the Brazilian test for determing tensile strength of rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(7)：1 150﹣ 1 157.(in Chinese))
[24] 刘运思，傅鹤林，饶军应，等. 不同层理方位影响下板岩各向异性巴西圆盘劈裂试验研究[J]. 岩石力学与工程学报，2012，31(4)：785﹣791.(LIU Yunsi，FU Heling，RAO Junying，et al. Research on Brazili and iscsplitting tests for an isotropy of slate under influence different bedding origientations[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(4)：785﹣791.(in Chinese))
[25] 高桂云，王成虎，王春权. 双圆环直接拉伸试验试验最有尺寸范围研究[J]. 岩土力学，2018，39(增1)：191﹣202.(GAO Guiyun，WANG Chenghu，WANG Chunquan. Optimal size range study of rock specimen for double concen tricannular core direct tensile test[J]. Rock and Soil Mechanics，2018，39(Supp.1)：191﹣202.(in Chinese))
[26] EVANS K，ENGELDER T，PLUMB R A. Appalachian stress study，1. A detailed description of in situ stress variations in Devonian shales of the Appalachian plateau[J]. Journal of Geophysical Research，1989，94(B6)：7 129–7 154.
[27] LEE M Y，HAIMSON B C. Statistical evaluation of hydraulic fracturing stress measurement parameters[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1989，26(6)：447–456.
[28] ZOBACK M D，TSUKAHARA H，HICKMAN S. Stress measurements at depth in the vicinity of the San Andreas fault：Implications for the magnitude of shear stress at depth[J]. Journal of Geophysical Research，1980，85(B11)：6 157–6 173.
[29] BRÖKER K，MA X D. Estimating the least principal stress in a granitic rock mass：Systematic mini-frac tests and elaborated pressure transient analysis[J]. Rock Mechanics and Rock Engineering，2022，55：1 931–1 954.
[30] ITO T，IGARASHI A，KATO H，et al. Crucial effect of system compliance on the maximum stress estimation in the hydrofracturing method：Theoretical considerations and field-test verification[J]. Earth，planets and space，2006，58(8)：963–971.
[31] ITO T，EVANS K，KAWAI K，et al. Hydraulic fracture reopening pressure and the estimation of maximum horizontal stress[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1999，36(6)：811–826.
[32] KLEE G，RUMMEL F，WILLIAMS A. Hydraulic fracturing stress measurements in Hong Kong[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(6)：731–741.
[33] ITO T，SA TOH T，KA TO H. Deep rock stress measurement by hydraulic fracturing method taking account of system compliance effect[C]// ISRM International Symposium on In-situ Rock Stress. Beijing：Taylor and Francis Group，2010：43–49.
[34] PINE R J，LEDINGHAM P，MERRIFIELD C M. In situ stress measurement in the Carnmenellis granite–II. Hydrofracture tests at Rosemanowes Quarry to depths of 2 000 m[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1983，20(2)：63–72.
[35] HARDY M P，ASGIAN M I. Fracture reopening during hydraulic fracturing stress determinations[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1989，26(6)：489–497.
[36] RUTQVIST J，TSANG C F，STEPHANSSON O. Uncertainty in the maximum principal stress estimated from hydraulic fracturing measurements due to the presence of the induced fracture[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，2000，37(1/2)：107–120.
[37] Japanese Geotechnical Society(JGS). JGS3761–2017 Method for initial stress measurement by hydraulic fracturing technique[S]. [S. l.]：[s. n.]，2017.
[38] ITO T，YOKOYAMA T. Effect of system compliance on pressure-time curve at reopening and new standard in Japan[C]// Proceedings of the 55th US Rock Mechanics/Geomechanics Symposium. Houston：ARMA，2021：1–7.
[39] ECONOMIDES M J，NOLTE K G. Reservoir stimulation[M]. Wiley：Chichester，2000：70–198.
[40] 高建理，丁健民，梁国平，等. 龙羊峡水电站水压致裂应力测量[J]. 岩石力学与工程学报，1990，21(2)：134–146.(GAO Jianli，DING Jianmin，LIANG Guoping，et al. Hydraulic fracturing stress measurements at the Longyangxia water-power station[J]. Chinese Journal of Rock Mechanics and Engineering，1990，21(2)：134–146.(in Chinese))
[41] 孙世宗，高建理，丁健民，等. 广州抽水蓄能电站水压致裂应力测量[J]. 岩石力学与工程学报，1991，10(4)：374–381.(SUN Shizong，GAO Jianli，DING Jianmin，et al. Hydrofracturing geostress measurement at the Guangzhou pumped storage powerplant[J]. Chinese Journal of Rock Mechanics and Engineering，1991，10(4)：374–381.(in Chinese))
[42] 李方全，刘 鹏，张 钧，等. 原地应力测量对某核废料处置场场地评价的应用[J]. 岩石力学与工程学报，1993，12(1)：55–62.(LI Fangquan，LIU Peng，ZHANG Jun，et al. Application of in situ stress measurements to the assessment of a site for nuclear waste disposal[J]. Chinese Journal of Rock Mechanics and Engineering，1993，12(1)：55–62.(in Chinese))
[43] 祁英男，李方全，毛吉震，等. 万家寨水利枢纽水压致裂应力测量结果和分析[J]. 岩石力学与工程学报，1999，18(2)：70–73.(QI Yingnan，LI Fangquan，MAO Jizhen，et al. The hydro-fracturing in-situ stress measurement and analysis for Wanjiazhai key water control project[J]. Chinese Journal of Rock Mechanics and Engineering，1999，18(2)：70–73.(in Chinese))
[44] 刘允芳，何建华. 地应力研究与西部大开发[J]. 岩石力学与工程学报，2001(增1)：1 638–1 644.(LIU Yunfang，HE Jianhua. The great development in west China and geostress study[J]. Chinese Journal of Rock Mechanics and Engineering，2001(Supp.1)：1 638–1 644.(in Chinese))
[45] 尹建民，刘元坤，罗超文，等. 原生裂隙水压法三维地应力测量原理及应用[J]. 岩石力学与工程学报，2001，20(增1)：1 706– 1 709.(YIN Jianmin，LIU Yuankun，LUO Chaowen，et al. 3-dimesional geostress determination by hydraulic test on preexisting fractures and application[J]. Chinese Journal of Rock Mechanics and Engineering，2001，20(Supp.1)：1 706–1 709.(in Chinese))
[46] 郭启良，安其美，赵仕广. 水压致裂应力测量在广州抽水蓄能电站设计中的应用研究[J]. 岩石力学与工程学报，2002，21(6)：828–832.(GUO Qiliang，AN Qimei，ZHAO Shiguang. Application of hydraulic fracturing test in the design of Guangzhou pump storage project[J]. Chinese Journal of Rock Mechanics and Engineering，2002，21(6)：828–832.(in Chinese))
[47] 肖本职，罗超文，刘元坤. 鄂西地应力测量与隧道岩爆预测分析[J]. 岩石力学与工程学报，2005，24(24)：4 472–4 477.(XIAO Benzhi，LUO Chaowen，LIU Yuankun. In-situ stress measurement and prediction analysis of tunnel rock burst in West Hubei[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(24)：4 472– 4 477.(in Chinese))
[48] 蔡美峰，陈长臻，彭 华，等. 万福煤矿深部水压致裂地应力测量[J]. 岩石力学与工程学报，2006，25(5)：1 069–1 074.(CAI Meifeng，CHEN Changzhen，PENG Hua，et al. In-situ stress measurement by hydraulic fracturing technique in deep position of Wanfu coal mine[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(5)：1 069–1 074.(in Chinese))
[49] 周春华，艾 凯，尹健民，等. 布西水电站坝址边坡地应力场及岩体力学特性的试验研究[J]. 岩石力学与工程学报，2006，25(增2)：3 959–3 964.(ZHOU Chunhua，AI Kai，YIN Jianmin，et al. Experimental study on geostress field and rock mass mechanical characters in dam site slope of Buxi hydropower station[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(Supp.2)：3 959–3 964.(in Chinese))
[50] 王建新，高成玉，郭啟良，等. 尼泊尔上塔马克西水电站三维地应力测试分析[J]. 岩石力学与工程学报，2012，31(增1)：3 339–3 344. (WANG Jianxin，GAO Chengyu，GUO Qiliang，et al. Measurement and analysis of 3d geostress at upper Tamakoshi hydropower station in Nepal[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.1)：3 339–3 344.(in Chinese))
[51] 郑红霞，张训华，赵铁虎，等. 渤海海峡及周边地应力分布规律与应力积累研究[J]. 岩石力学与工程学报，2017，36(2)：357–369.(ZHENG Hongxia，ZHANG Xunhua，ZHAO Tiehu，et al. Geostress distribution and stress accumulation in Bohai strait and adjacent area[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(2)：357–369.(in Chinese))
[52] 牛琳琳，陈群策，丰成君，等. 新疆某高放废物预选处置库区地应力测量研究[J]. 岩石力学与工程学报，2017，36(4)：917–927.(NIU Linlin，CHEN Qunce，FENG Chengjun，et al. In-situ stress measurement of candidate area for high level radioactive waste repository in Xinjiang[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(4)：917–927.(in Chinese))
[53] 秦向辉，陈群策，赵星光，等. 水压致裂地应力测量中系统柔度影响试验研究[J]. 岩石力学与工程学报，2020，39(6)：1 189–1 202. (QIN Xianghui，CHEN Qunce，ZHAO Xingguang，et al. Experimental study on the crucial effect of test system compliance on hydraulic fracturing in-situ stress measurements[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(6)：1 189–1 202.(in Chinese))
[54] TADA H，PARIS P，IRWIN G. The stress analysis of cracks handbook[M]. New York：American Society of Mechanical Engineers Press，2000：82–332.
2024, Vol. 43 
