热应力和天然裂缝影响下干热岩水力裂缝扩展机制研究

doi:10.3724/1000-6915.jrme.2024.0664

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Abstract Understanding the mechanism of hydraulic fracture propagation in hot-dry-rock(HDR) reservoirs，particularly under the influence of thermal stress and natural fractures，is crucial for effectively guiding hydraulic fracturing design and enhancing geothermal energy development. First，an independently developed high-temperature true triaxial hydraulic fracturing simulation experiment system is utilized to conduct high-temperature true triaxial hydraulic fracturing tests on granite samples，examining how variations in temperature influence rock fractures. And a 3D thermo-hydro-mechanical coupling model for fracture propagation simulation is created based on the continuum-discontinuum element method. The model's accuracy is verified through comparison with a 3D theoretical model of fracture propagation and high-temperature hydraulic fracturing experiments. Subsequently，numerical simulations of hydraulic fracturing in HDR reservoirs are performed to study the effects of thermal stress and natural fractures on the hydraulic fractures propagation. The results indicate that the induced thermal stress caused by the injected cold water can reduce the reservoir fracture pressure and fracture extension pressure，increase the fracture width and decrease the fracture length. As the temperature of the rock sample rises，the induced thermal stress increases considerably，leading to a significant decrease in the rock fracture pressure observed in both experiments and the numerical simulations. When accounting for the effect of induced thermal stress，hydraulic fracturing can active the natural fractures even when there are significant horizontal geostress differences and large approach angles. Compared with the HDR reservoir without natural fractures，the stimulation reservoir volume of the reservoir with 200 randomly distributed natural fractures increases by 63.8%. As the thermal expansion coefficient of the reservoir rises，the influence of thermal stress becomes increasingly pronounced，leading to the formation of secondary fractures that develop perpendicular to the main fracture surface，and the stimulation reservoir volume increases significantly.

Key words： soil mechanics hot dry rock fracture propagation high-temperature hydraulic fracturing experiment numerical simulation thermo-hydro-mechanical coupling continuum-discontinuum element method

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	Articles by authors
	GUO Tiankui1
	WANG Jiwei1
	2
	3
	ZHAI Cheng2
	3
	CHEN Ming1
	DAI Caili1
	QU Zhanqing1
	ZHANG Bo1

Cite this article:

GUO Tiankui1,WANG Jiwei1,2, et al. Mechanism of hydraulic fracture propagation in hot dry rocks under the influence of thermal stress and natural fractures[J]. , 2025, 44(4): 810-826.

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https://rockmech.whrsm.ac.cn/EN/10.3724/1000-6915.jrme.2024.0664 OR https://rockmech.whrsm.ac.cn/EN/Y2025/V44/I4/810

[14]	申林方，苏威，张家明，等. 考虑流体热物理性质动态演化的高温岩石粗糙裂隙渗流传热效应研究[J]. 岩石力学与工程学报，2024，43(6)：1 359-1 370.(SHEN Linfang，SU Wei，ZHANG Jiaming，et al. Study on the seepage and heat transfer effect of rough fractures in hot matrix considering dynamic thermophysical properties of fluid[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(6)：1 359-1 370.(in Chinese))
[20]	LI N，MA X F，ZHANG S C，et al. Thermal effects on the physical and mechanical properties and fracture initiation of Laizhou granite during hydraulic fracturing[J]. Rock Mechanics and Rock Engineering，2020，53：2 539-2 556.
[1]	赵阳升，王瑞凤，胡耀青，等. 高温岩体地热开发的块裂介质固流热耦合三维数值模拟[J]. 岩石力学与工程学报，2002，21(12)： 1 751-1 755.(ZHAO Yangsheng，WANG Ruifeng，HU Yaoqing，et al. 3D numerical simulation for coupled THM of rock matrix-fractured media in heat extraction in HDR[J]. Chinese Journal of Rock Mechanics and Engineering，2002，21(12)：1 751-1 755.(in Chinese))
[15]	GUO T K，TANG S J，SUN J，et al. A coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extraction in the enhanced geothermal system based on analytic hierarchy process and fuzzy comprehensive evaluation[J]. Applied Energy，2020，258：113981.
[16]	郤保平，吴阳春，王帅，等. 青海共和盆地花岗岩高温热损伤力学特性试验研究[J]. 岩石力学与工程学报，2020，39(1)：69-83.(XI Baoping，WU Yangchun，WANG Shuai，et al. Experimental study on mechanical properties of granite taken from Gonghe basin，Qinghai province after high temperature thermal damage[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(1)：69-83.(in Chinese))
[21]	FRASH L P，GUTIERREZ M，HAMPTON J. Laboratory-scale-model testing of well stimulation by use of mechanical-impulse hydraulic fracturing[J]. SPE Journal，2015，20(3)：536-549.
[2]	汪集旸，胡圣标，庞忠，等. 中国大陆干热岩地热资源潜力评估[J]. 科技导报，2012，30(32)：25-31.(WANG Jitang，HU Shengbiao，PANG Zhong，et al. Estimate of geothermal resources potential for hot dry rock in the continental area of China[J]. Science and Technology Review，2012，30(32)：25-31.(in Chinese))
[17]	阴伟涛. 裂缝后期充填花岗岩体裂缝分布特征研究[J]. 岩石力学与工程学报，2023，42(9)：2 203-2 211.(YIN Weitao. Experimental research on the fracture distribution characteristics of fractured-subsequently-filled granite[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(9)：2 203-2 211.(in Chinese))
[22]	KUMARI W G P，RANJITH P G，PERERA M S A，et al. Hydraulic fracturing under high temperature and pressure conditions with microCT applications：Geothermal energy from hot dry rocks[J]. Fuel，2018，230：138-154.
[3]	谢和平，熊伦，谢凌志，等. 中国CO2地质封存及增强地热开采一体化的初步探讨[J]. 岩石力学与工程学报，2014，33(增1)：3 077-3 086.(XIE Heping，XIONG Lun，XIE Lingzhi，et al. Preliminary study of CO2 geological sequestration and enhancement of geothermal exploitation integration in China[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(Supp.1)：3 077-3 086.(in Chinese))
[18]	XIE J Y，CAO H，WANG D，et al. A comparative study on the hydraulic fracture propagation behaviors in hot dry rock and shale formation with different structural discontinuities[J]. Journal of Energy Engineering，2022，148(6)：04022040.
[23]	ZHUANG D D，YIN T B，LI Q，et al. Effect of injection flow rate on fracture toughness during hydraulic fracturing of hot dry rock(HDR)[J]. Engineering Fracture Mechanics，2022，260：108207.
[4]	NORBECK J H，MCCLURE M W，HORNE R N. Field observations at the Fenton Hill enhanced geothermal system test site support mixed-mechanism stimulation[J]. Geothermics，2018，74(7)：135-149.
[19]	李庭樑，曹文炅，王亦伟，等. 增强型地热系统水力压裂与声发射监测室内实验研究[J]. 新能源进展，2019，7(3)：241-248.(LI Tingliang，CAO Wenjiong，WANG Yiwei，et al. Laboratory study on hydraulic fracturing and acoustic emission monitoring of enhanced geothermal system[J]. Advances in New and Renewable Energy，2019，7(3)：241-248.(in Chinese))
[24]	周舟，金衍，曾义金，等. 青海共和盆地干热岩地热储层水力压裂物理模拟和裂缝起裂与扩展形态研究[J]. 吉林大学学报：地球科学版，2019，49(5)：1 425-1 430.(ZHOU Zhou，JIN Yan，ZENG Yijin，et al. Experimental study on hydraulic fracturing physics simulation，crack initiation and propagation in hot dry rock geothermal reservoir in Gonghe basin，Qinghai[J]. Journal of Jilin University：Earth Science，2019，49(5)：1 425-1 430.(in Chinese))
[5]	RINALDI A P，RUTQVIST J. Joint opening or hydroshearing Analyzing a fracture zone stimulation at Fenton Hill[J]. Geothermics，2019，77：83-98
[20]	LI N，MA X F，ZHANG S C，et al. Thermal effects on the physical and mechanical properties and fracture initiation of Laizhou granite during hydraulic fracturing[J]. Rock Mechanics and Rock Engineering，2020，53：2 539-2 556.
[25]	CHENG Y X，ZHANG Y J，YU Z W，et al. An investigation on hydraulic fracturing characteristics in granite geothermal reservoir[J]. Engineering Fracture Mechanics，2020，237：107252.
[6]	李根生，武晓光，宋先知，等. 干热岩地热资源开采技术现状与挑战[J]. 石油科学通报，2022，7(3)：343-364.(LI Gensheng，WU Xiaoguang，SONG Xianzhi，et al. Status and challenges of hot dry rock geothermal resource exploitation[J]. Petroleum Science Bulletin，2022，7(3)：343-364.(in Chinese))
[21]	FRASH L P，GUTIERREZ M，HAMPTON J. Laboratory-scale-model testing of well stimulation by use of mechanical-impulse hydraulic fracturing[J]. SPE Journal，2015，20(3)：536-549.
[26]	ZHANG W，GUO T K，QU Z Q，et al. Research of fracture initiation and propagation in HDR fracturing under thermal stress from meso-damage perspective[J]. Energy，2019，178：508-521.
[7]	OKABE T. Analysis in preparation for Hijiori long term circulation test[C]// World Geothermal Congress. Morioka：[s. n.]，2000：3 823-3 828.
[22]	KUMARI W G P，RANJITH P G，PERERA M S A，et al. Hydraulic fracturing under high temperature and pressure conditions with microCT applications：Geothermal energy from hot dry rocks[J]. Fuel，2018，230：138-154.
[27]	林海飞，李博涛，李树刚，等. 液氮致裂层理煤体热-流-固-损伤耦合模型及数值模拟研究[J]. 岩石力学与工程学报，2024，43(5)：1 110-1 123.(LIN Haifei，LI Botao，LI Shugang，et al. A thermal-hydraulic-mechanical-damage coupling model of layer coal fracturing by liquid nitrogen[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(5)：1 110-1 123.(in Chinese))
[8]	PARKER R. The rosemanowes HDR project 1983-1991[J]. Geothermics，1999，28(4/5)：603-615.
[23]	ZHUANG D D，YIN T B，LI Q，et al. Effect of injection flow rate on fracture toughness during hydraulic fracturing of hot dry rock(HDR)[J]. Engineering Fracture Mechanics，2022，260：108207.
[28]	GUO T K，TANG S J，LIU S，et al. Numerical simulation of hydraulic fracturing of hot dry rock under thermal stress[J]. Engineering Fracture Mechanics，2020，240：107350.
[9]	GENTER A，EVANS K，CUENOT N，et al. Contribution of the exploration of deep crystalline fractured reservoir of Soultz to the knowledge of enhanced geothermal systems(EGS)[J]. Comptes Rendus Geoscience，2010，342(7/8)：502-516.
[24]	周舟，金衍，曾义金，等. 青海共和盆地干热岩地热储层水力压裂物理模拟和裂缝起裂与扩展形态研究[J]. 吉林大学学报：地球科学版，2019，49(5)：1 425-1 430.(ZHOU Zhou，JIN Yan，ZENG Yijin，et al. Experimental study on hydraulic fracturing physics simulation，crack initiation and propagation in hot dry rock geothermal reservoir in Gonghe basin，Qinghai[J]. Journal of Jilin University：Earth Science，2019，49(5)：1 425-1 430.(in Chinese))
[29]	WU X T，LI Y C，TANG C A. Fracture spacing in horizontal well multi-perforation fracturing optimized by heat extraction[J]. Geothermics，2022，101：102376.
[10]	MOSKA R，LABUS K，KASZA P. Hydraulic fracturing in enhanced geothermal systems—field，tectonic and rock mechanics conditions—a review[J]. Energies，2021，14(18)：5 725.
[25]	CHENG Y X，ZHANG Y J，YU Z W，et al. An investigation on hydraulic fracturing characteristics in granite geothermal reservoir[J]. Engineering Fracture Mechanics，2020，237：107252.
[30]	ZENG Q D，YAO J，SHAO J F. An extended finite element solution for hydraulic fracturing with thermo-hydro-elastic-plastic coupling[J]. Computer Methods in Applied Mechanics and Engineering，2020，364：112967.
[11]	单丹丹，李玮，闫铁，等. 增强型地热系统采热性能评价——以共和盆地恰卜恰地区干热岩储层为例[J]. 天然气工业，2022，42(10)：150-160.(SHAN Dandan，LI Wei，YAN Tie，et al. Evaluation on heat extraction performance of enhanced geothermal system：A case study of hot-dry rock reservoirs in the Qiabuqia area of the Gonghe Basin[J]. Natural Gas Industry，2022，42(10)：150-160.(in Chinese))
[26]	ZHANG W，GUO T K，QU Z Q，et al. Research of fracture initiation and propagation in HDR fracturing under thermal stress from meso-damage perspective[J]. Energy，2019，178：508-521.
[31]	LI S，ZHANG D. Three‐dimensional thermoporoelastic modeling of hydrofracturing and fluid circulation in hot dry rock[J]. Journal of Geophysical Research：Solid Earth，2023，128(2)：e2022JB025673.
[12]	蔺文静，王凤元，甘浩男，等. 福建漳州干热岩资源选址与开发前景分析[J]. 科技导报，2015，33(19)：28-34.(LIN Wenjing，WANG Fengyuan，GAN Haonan，et al. Site selection and development prospect of a hot dry rock resource project in Zhangzhou geothermal field，Fujian province[J]. Science and Technology Review，2015，33(19)：28-34.(in Chinese))
[27]	林海飞，李博涛，李树刚，等. 液氮致裂层理煤体热-流-固-损伤耦合模型及数值模拟研究[J]. 岩石力学与工程学报，2024，43(5)：1 110-1 123.(LIN Haifei，LI Botao，LI Shugang，et al. A thermal-hydraulic-mechanical-damage coupling model of layer coal fracturing by liquid nitrogen[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(5)：1 110-1 123.(in Chinese))
[32]	TOMACI I，GUTIERREZ M. Micro-mechanics of hydro-thermo-mechanical fracture propagation in granite[C]// 48th U.S. Rock Mechanics/Geomechanics Symposium. Minneapolis，Minnesota：[s. n.]，2014：1-7.
[13]	郭建春，肖勇，蒋恕，等. 深层干热岩水力剪切压裂认识与实践[J]. 地质学报，2021，95(5)：1 582-1 593.(GUO Jianchun，XIAO Yong，JIANG Shu，et al. Understanding and practice of hydraulic shearing in deep hot dry rocks[J]. Acta Geologica Sinica，2021，95(5)：1 582-1 593.(in Chinese))
[28]	GUO T K，TANG S J，LIU S，et al. Numerical simulation of hydraulic fracturing of hot dry rock under thermal stress[J]. Engineering Fracture Mechanics，2020，240：107350.
[33]	HU Z X，XU T F，MOORE J，et al. Investigation of the effect of different injection schemes on fracture network patterns in hot dry rocks-A numerical case study of the FORGE EGS site in Utah[J]. Journal of Natural Gas Science and Engineering，2022，97：104346.
[14]	申林方，苏威，张家明，等. 考虑流体热物理性质动态演化的高温岩石粗糙裂隙渗流传热效应研究[J]. 岩石力学与工程学报，2024，43(6)：1 359-1 370.(SHEN Linfang，SU Wei，ZHANG Jiaming，et al. Study on the seepage and heat transfer effect of rough fractures in hot matrix considering dynamic thermophysical properties of fluid[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(6)：1 359-1 370.(in Chinese))
[29]	WU X T，LI Y C，TANG C A. Fracture spacing in horizontal well multi-perforation fracturing optimized by heat extraction[J]. Geothermics，2022，101：102376.
[34]	ZHU X G，FENG C，CHENG P D，et al. A novel three-dimensional hydraulic fracturing model based on continuum-discontinuum element method[J]. Computer Methods in Applied Mechanics and Engineering，2021，383：113887.
[15]	GUO T K，TANG S J，SUN J，et al. A coupled thermal-hydraulic-mechanical modeling and evaluation of geothermal extraction in the enhanced geothermal system based on analytic hierarchy process and fuzzy comprehensive evaluation[J]. Applied Energy，2020，258：113981.
[16]	郤保平，吴阳春，王帅，等. 青海共和盆地花岗岩高温热损伤力学特性试验研究[J]. 岩石力学与工程学报，2020，39(1)：69-83.(XI Baoping，WU Yangchun，WANG Shuai，et al. Experimental study on mechanical properties of granite taken from Gonghe basin，Qinghai province after high temperature thermal damage[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(1)：69-83.(in Chinese))
[30]	ZENG Q D，YAO J，SHAO J F. An extended finite element solution for hydraulic fracturing with thermo-hydro-elastic-plastic coupling[J]. Computer Methods in Applied Mechanics and Engineering，2020，364：112967.
[35]	REN Q S，ZHAO Y X，ZHU X G，et al. CDEM-based simulation of the 3D propagation of hydraulic fractures in heterogeneous Coalbed Methane reservoirs[J]. Computers and Geotechnics，2022，152：104992.
[17]	阴伟涛. 裂缝后期充填花岗岩体裂缝分布特征研究[J]. 岩石力学与工程学报，2023，42(9)：2 203-2 211.(YIN Weitao. Experimental research on the fracture distribution characteristics of fractured-subsequently-filled granite[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(9)：2 203-2 211.(in Chinese))
[31]	LI S，ZHANG D. Three‐dimensional thermoporoelastic modeling of hydrofracturing and fluid circulation in hot dry rock[J]. Journal of Geophysical Research：Solid Earth，2023，128(2)：e2022JB025673.
[36]	柳贡慧，庞飞，陈治喜. 水力压裂模拟实验中的相似准则[J]. 石油大学学报：自然科学版，2000，24(5)：45-48.(LIU Gonghui，PANG Fei，CHEN Zhixi. Development of scaling laws for hydraulic fracture simulation tests[J]. Journal of University of Petroleum：Natural Science，2000，24(5)：45-48.(in Chinese))
[18]	XIE J Y，CAO H，WANG D，et al. A comparative study on the hydraulic fracture propagation behaviors in hot dry rock and shale formation with different structural discontinuities[J]. Journal of Energy Engineering，2022，148(6)：04022040.
[32]	TOMACI I，GUTIERREZ M. Micro-mechanics of hydro-thermo-mechanical fracture propagation in granite[C]// 48th U.S. Rock Mechanics/Geomechanics Symposium. Minneapolis，Minnesota：[s. n.]，2014：1-7.
[37]	郭天魁，刘晓强，顾启林. 射孔井水力压裂模拟实验相似准则推导[J]. 中国海上油气，2015，27(3)：108-112.(GUO Ttiankui，LIU Xiaoqiang，GU Qilin. Deduction of similarity laws of hydraulic fracturing simulation experiments for perforated wells[j]. China Offshore Oil and Gas，2015，27(3)：108-112.(in Chinese))
[19]	李庭樑，曹文炅，王亦伟，等. 增强型地热系统水力压裂与声发射监测室内实验研究[J]. 新能源进展，2019，7(3)：241-248.(LI Tingliang，CAO Wenjiong，WANG Yiwei，et al. Laboratory study on hydraulic fracturing and acoustic emission monitoring of enhanced geothermal system[J]. Advances in New and Renewable Energy，2019，7(3)：241-248.(in Chinese))
[33]	HU Z X，XU T F，MOORE J，et al. Investigation of the effect of different injection schemes on fracture network patterns in hot dry rocks-A numerical case study of the FORGE EGS site in Utah[J]. Journal of Natural Gas Science and Engineering，2022，97：104346.
[38]	LEI Z H，ZHANG Y J，ZHANG S K，et al. Numerical study of hydraulic fracturing treatments and geothermal energy extraction from a naturally fractured granitic formation[J]. Geothermics，2023，111：102692.
[20]	LI N，MA X F，ZHANG S C，et al. Thermal effects on the physical and mechanical properties and fracture initiation of Laizhou granite during hydraulic fracturing[J]. Rock Mechanics and Rock Engineering，2020，53：2 539-2 556.
[34]	ZHU X G，FENG C，CHENG P D，et al. A novel three-dimensional hydraulic fracturing model based on continuum-discontinuum element method[J]. Computer Methods in Applied Mechanics and Engineering，2021，383：113887.
[39]	王理想，唐德泓，李世海，等. 基于混合方法的二维水力压裂数值模拟[J]. 力学学报，2015，47(6)：973-983.(WANG Lixiang，TANG Dehong，LI Shihai，et al. Numerical simulation of hydraulic fracturing by a mixed method in two dimensions[J]. Chinese Journal of Theoretical and Applied Mechanics，2015，47(6)：973-983.(in Chinese))
[21]	FRASH L P，GUTIERREZ M，HAMPTON J. Laboratory-scale-model testing of well stimulation by use of mechanical-impulse hydraulic fracturing[J]. SPE Journal，2015，20(3)：536-549.
[35]	REN Q S，ZHAO Y X，ZHU X G，et al. CDEM-based simulation of the 3D propagation of hydraulic fractures in heterogeneous Coalbed Methane reservoirs[J]. Computers and Geotechnics，2022，152：104992.
[40]	WANG J W，GUO T K，CHEN M，et al. Numerical simulation of fracture propagation morphology in hydraulic fracturing development of geothermal reservoirs based on the CDEM-THM3D[J]. Computers and Geotechnics，2024，172：106444.
[22]	KUMARI W G P，RANJITH P G，PERERA M S A，et al. Hydraulic fracturing under high temperature and pressure conditions with microCT applications：Geothermal energy from hot dry rocks[J]. Fuel，2018，230：138-154.
[36]	柳贡慧，庞飞，陈治喜. 水力压裂模拟实验中的相似准则[J]. 石油大学学报：自然科学版，2000，24(5)：45-48.(LIU Gonghui，PANG Fei，CHEN Zhixi. Development of scaling laws for hydraulic fracture simulation tests[J]. Journal of University of Petroleum：Natural Science，2000，24(5)：45-48.(in Chinese))
[41]	冯春，李世海，周东，等. 爆炸载荷作用下岩石损伤破裂过程的数值分析[J]. 岩土工程学报，2014，36(7)：1 262-1 270.(FENG Chun，LI Shihai，ZHOU Dong，et al. Numerical analysis of damage and crack process of rock under explosive loading[J]. Chinese Journal of Geotechnical Engineering，2014，36(7)：1 262-1 270.(in Chinese))
[23]	ZHUANG D D，YIN T B，LI Q，et al. Effect of injection flow rate on fracture toughness during hydraulic fracturing of hot dry rock(HDR)[J]. Engineering Fracture Mechanics，2022，260：108207.
[37]	郭天魁，刘晓强，顾启林. 射孔井水力压裂模拟实验相似准则推导[J]. 中国海上油气，2015，27(3)：108-112.(GUO Ttiankui，LIU Xiaoqiang，GU Qilin. Deduction of similarity laws of hydraulic fracturing simulation experiments for perforated wells[j]. China Offshore Oil and Gas，2015，27(3)：108-112.(in Chinese))
[42]	DONTSOV E V. An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness，fluid viscosity and leak-off[J]. Royal Society Open Science，2016，3(12)：160737.
[24]	周舟，金衍，曾义金，等. 青海共和盆地干热岩地热储层水力压裂物理模拟和裂缝起裂与扩展形态研究[J]. 吉林大学学报：地球科学版，2019，49(5)：1 425-1 430.(ZHOU Zhou，JIN Yan，ZENG Yijin，et al. Experimental study on hydraulic fracturing physics simulation，crack initiation and propagation in hot dry rock geothermal reservoir in Gonghe basin，Qinghai[J]. Journal of Jilin University：Earth Science，2019，49(5)：1 425-1 430.(in Chinese))
[38]	LEI Z H，ZHANG Y J，ZHANG S K，et al. Numerical study of hydraulic fracturing treatments and geothermal energy extraction from a naturally fractured granitic formation[J]. Geothermics，2023，111：102692.
[25]	CHENG Y X，ZHANG Y J，YU Z W，et al. An investigation on hydraulic fracturing characteristics in granite geothermal reservoir[J]. Engineering Fracture Mechanics，2020，237：107252.
[39]	王理想，唐德泓，李世海，等. 基于混合方法的二维水力压裂数值模拟[J]. 力学学报，2015，47(6)：973-983.(WANG Lixiang，TANG Dehong，LI Shihai，et al. Numerical simulation of hydraulic fracturing by a mixed method in two dimensions[J]. Chinese Journal of Theoretical and Applied Mechanics，2015，47(6)：973-983.(in Chinese))
[26]	ZHANG W，GUO T K，QU Z Q，et al. Research of fracture initiation and propagation in HDR fracturing under thermal stress from meso-damage perspective[J]. Energy，2019，178：508-521.
[40]	WANG J W，GUO T K，CHEN M，et al. Numerical simulation of fracture propagation morphology in hydraulic fracturing development of geothermal reservoirs based on the CDEM-THM3D[J]. Computers and Geotechnics，2024，172：106444.
[27]	林海飞，李博涛，李树刚，等. 液氮致裂层理煤体热-流-固-损伤耦合模型及数值模拟研究[J]. 岩石力学与工程学报，2024，43(5)：1 110-1 123.(LIN Haifei，LI Botao，LI Shugang，et al. A thermal-hydraulic-mechanical-damage coupling model of layer coal fracturing by liquid nitrogen[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(5)：1 110-1 123.(in Chinese))
[41]	冯春，李世海，周东，等. 爆炸载荷作用下岩石损伤破裂过程的数值分析[J]. 岩土工程学报，2014，36(7)：1 262-1 270.(FENG Chun，LI Shihai，ZHOU Dong，et al. Numerical analysis of damage and crack process of rock under explosive loading[J]. Chinese Journal of Geotechnical Engineering，2014，36(7)：1 262-1 270.(in Chinese))
[28]	GUO T K，TANG S J，LIU S，et al. Numerical simulation of hydraulic fracturing of hot dry rock under thermal stress[J]. Engineering Fracture Mechanics，2020，240：107350.
[42]	DONTSOV E V. An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness，fluid viscosity and leak-off[J]. Royal Society Open Science，2016，3(12)：160737.
[29]	WU X T，LI Y C，TANG C A. Fracture spacing in horizontal well multi-perforation fracturing optimized by heat extraction[J]. Geothermics，2022，101：102376.
[30]	ZENG Q D，YAO J，SHAO J F. An extended finite element solution for hydraulic fracturing with thermo-hydro-elastic-plastic coupling[J]. Computer Methods in Applied Mechanics and Engineering，2020，364：112967.
[31]	LI S，ZHANG D. Three‐dimensional thermoporoelastic modeling of hydrofracturing and fluid circulation in hot dry rock[J]. Journal of Geophysical Research：Solid Earth，2023，128(2)：e2022JB025673.
[32]	TOMACI I，GUTIERREZ M. Micro-mechanics of hydro-thermo-mechanical fracture propagation in granite[C]// 48th U.S. Rock Mechanics/Geomechanics Symposium. Minneapolis，Minnesota：[s. n.]，2014：1-7.
[33]	HU Z X，XU T F，MOORE J，et al. Investigation of the effect of different injection schemes on fracture network patterns in hot dry rocks-A numerical case study of the FORGE EGS site in Utah[J]. Journal of Natural Gas Science and Engineering，2022，97：104346.
[34]	ZHU X G，FENG C，CHENG P D，et al. A novel three-dimensional hydraulic fracturing model based on continuum-discontinuum element method[J]. Computer Methods in Applied Mechanics and Engineering，2021，383：113887.
[35]	REN Q S，ZHAO Y X，ZHU X G，et al. CDEM-based simulation of the 3D propagation of hydraulic fractures in heterogeneous Coalbed Methane reservoirs[J]. Computers and Geotechnics，2022，152：104992.
[36]	柳贡慧，庞飞，陈治喜. 水力压裂模拟实验中的相似准则[J]. 石油大学学报：自然科学版，2000，24(5)：45-48.(LIU Gonghui，PANG Fei，CHEN Zhixi. Development of scaling laws for hydraulic fracture simulation tests[J]. Journal of University of Petroleum：Natural Science，2000，24(5)：45-48.(in Chinese))
[37]	郭天魁，刘晓强，顾启林. 射孔井水力压裂模拟实验相似准则推导[J]. 中国海上油气，2015，27(3)：108-112.(GUO Ttiankui，LIU Xiaoqiang，GU Qilin. Deduction of similarity laws of hydraulic fracturing simulation experiments for perforated wells[j]. China Offshore Oil and Gas，2015，27(3)：108-112.(in Chinese))
[38]	LEI Z H，ZHANG Y J，ZHANG S K，et al. Numerical study of hydraulic fracturing treatments and geothermal energy extraction from a naturally fractured granitic formation[J]. Geothermics，2023，111：102692.
[39]	王理想，唐德泓，李世海，等. 基于混合方法的二维水力压裂数值模拟[J]. 力学学报，2015，47(6)：973-983.(WANG Lixiang，TANG Dehong，LI Shihai，et al. Numerical simulation of hydraulic fracturing by a mixed method in two dimensions[J]. Chinese Journal of Theoretical and Applied Mechanics，2015，47(6)：973-983.(in Chinese))
[40]	WANG J W，GUO T K，CHEN M，et al. Numerical simulation of fracture propagation morphology in hydraulic fracturing development of geothermal reservoirs based on the CDEM-THM3D[J]. Computers and Geotechnics，2024，172：106444.
[41]	冯春，李世海，周东，等. 爆炸载荷作用下岩石损伤破裂过程的数值分析[J]. 岩土工程学报，2014，36(7)：1 262-1 270.(FENG Chun，LI Shihai，ZHOU Dong，et al. Numerical analysis of damage and crack process of rock under explosive loading[J]. Chinese Journal of Geotechnical Engineering，2014，36(7)：1 262-1 270.(in Chinese))
[42]	DONTSOV E V. An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness，fluid viscosity and leak-off[J]. Royal Society Open Science，2016，3(12)：160737.