Micromechanisms of borehole instability leading to breakouts in rocks

This paper reviews the different borehole breakout failure micromechanisms observed during a multiyear laboratory research effort at the University of Wisconsin. Vertical borehole drilling experiments were conducted in a variety of granites, limestones, and sandstones under a wide range of pre-existing stress fields. Test samples that developed breakouts during drilling were analyzed under optical and scanning electron microscopes to establish the micromechanics of failure. All rocks tested, except for the quartz-rich sandstones, develop dog-eared breakouts along the minimum horizontal far-field stress springline, even though the grain-scale mechanisms leading to the final appearance may differ considerably. The common denominator is the incipient failure in the form of dilatant microcracking in the zones of the highest compressive stress concentration around the borehole. Dependent on rock type, these microcracks could be tensile or shear openings, extending inter- or intra-granularly. A type of failure not hitherto recognized was discovered in quartz-rich sandstones, which develop tabular slot-shaped breakouts that maintain a constant very narrow width over an extensive length, resulting in a fracture-like appearance. Such breakouts are the result of a largely non-dilatant micromechanism consisting of localized grain debonding and repacking leading to the formation of an apparent reduced-porosity compaction band along the minimum horizontal far-field stress springline. Breakouts are produced by the removal, with the help of the circulating drilling fluid, of loose grains and grain fragments that were debonded in the process of compaction band forming.     

Experimental observations of the mechanics of borehole failure in porous sandstone

To investigate borehole failure under hydrostatic stress in sandstone of varying porosity, experiments were conducted on three sandstone varieties with 2–5 mm bores. Tennessee, Darley Dale, and Penrith sandstone-types were selected to represent most of the spectrum of sandstone porosity variations (respectively, 0.07, 0.12 and 0.28). Confining pressures ranged up to 500 MPa, and pore fluid volumometry was used to detect bore failure. Failed samples were studied microstructurally using optical and scanning electron microscopy.Each rock type failed with the development of oriented breakout features normally seen to develop around boreholes loaded under non-hydrostatic stress, and in Tennessee sandstone at least, these developed in a consistent orientation with respect to an external reference frame (dip-direction of foreset beds). All of the rock types showed strength and/or elastic anisotropy, thus the formation of oriented breakouts under hydrostatic loading is attributed to the effects of anisotropy.Two modes of breakout development were observed. In Darley Dale and Penrith sandstones, a combination of intergranular shear and extensional fracture produced broad and shallow features with breakout width unaltered during growth. In Tennessee sandstone a purely extensional mode of intragranular fracture was observed, leading to deeper breakout features.The samples tested showed higher failure pressures for smaller bore sizes. When failure pressure is normalized with respect to grain crushing pressure P^*_i, and bore diameter with the product of porosity with grain size, all data lie on a single master curve, with bore failure pressure approximately 0.15 P^*_i in the regime of bore size-independent behaviour.     

Effects of borehole stress concentration on elastic wave velocities in sandstones

The stress redistribution that occurs in the vicinity of a borehole may lead to damage or failure of the rock. If the vertical stress is a principal stress, the principal stresses at the wall of a vertical well are the hoop, radial, and vertical stresses. The hoop stress varies with position around the wellbore and takes its maximum compressive value at the azimuth of the far-field minimum horizontal stress. This may lead to compressive failure at this azimuth if the compressive strength of the rock is exceeded. Recent developments in sonic logging allow the variation in elastic wave velocities with radius and azimuth around a borehole to be characterized. Since elastic wave velocities in sandstones are sensitive to changes in stress, owing to the presence of stress-sensitive grain boundaries within the rock, this allows the changes in stress to be monitored. An expansion of the elastic compliance of the grain boundaries to first order in stress shows that a radially polarized, vertically propagating shear wave is more sensitive to radial stress than to hoop stress. Close to the wellbore, however, large changes in stress occur, and any nonlinearity in the variation in compliance of the grain boundaries as a function of stress becomes important. This nonlinearity increases the sensitivity to the wellbore pressure, and can cause significant reductions in the velocity of compressional and shear waves in the vicinity of the wellbore.     

南水北调西线工程区地应力测量及地应力场特征分析

基于对南水北调西线一期工程场区现场水压致裂地应力测试工作,得出如下初步结论:(1)各线路孔中最大水平主应力值最高约为25 MPa,最大水平主应力方向均为NNE或NEE;(2)各坝址孔中最大水平主应力值最高约为17 MPa,最大水平主应力方向受局部地形地势影响变化较大,但大多数孔方向仍为NNE或NEE;(3)在试验深度范围内,线路孔侧压系数随着钻孔深度的增加逐渐减小;当测试深度在200 m以下时,侧压系数值基本维持在2左右;(4)各测孔侧压系数均大于1,表明工程场区地应力以构造应力为主导;(5)在测试深度范围内,各测孔的最大、最小水平主应力随岩层深度的增加均有增大趋势;(6)回归分析结果表明线路孔的最大水平主应力值随深度呈现良好的线性关系;(7)由于隧洞洞室埋深较深,且穿越高应力区,存在中等强度岩爆或流变的可能性。     

Evolution granulométrique des sols sablo-argileux soumis à des compactages dynamique et statique

The compaction of a quartz sand by the modified Proctor test involves the production of fines produced by the breaking of the grains of the sand. This production of fines is measured by the grain size analysis before and after compaction. The adding of clay to the sand diminishes the evolution of the grain size. The process is proportional to the quantity of clay added to the sand. If the dynamic compaction of the Proctor test is substituted by the static compaction, one notes the same occurrences: static or dynamic compaction breaks the grains of sand and the clay added to the sand protects the grains from the breaking induced by the compaction stresses.     

Practical application of failure criteria in determining safe mud weight windows in drilling operations简

Wellbore instability is reported frequently as one of the most significant incidents during drilling operations. Analysis of wellbore instability includes estimation of formation mechanical properties and the state of in situ stresses. In this analysis, the only controllable parameter during drilling operation is the mud weight. If the mud weight is larger than anticipated, the mud will invade into the formation, causing tensile failure of the formation. On the other hand, a lower mud weight can result in shear failures of rock, which is known as borehole breakouts. To predict the potential for failures around the wellbore during drilling, one should use a failure criterion to compare the rock strength against induced tangential stresses around the wellbore at a given mud pressure. The Mohr–Coulomb failure criterion is one of the commonly accepted criteria for estimation of rock strength at a given state of stress. However, the use of other criteria has been debated in the literature. In this paper, Mohr–Coulomb, Hoek–Brown and Mogi–Coulomb failure criteria were used to estimate the potential rock failure around a wellbore located in an onshore field of Iran. The log based analysis was used to estimate rock mechanical properties of formations and state of stresses. The results indicated that amongst different failure criteria, the Mohr–Coulomb criterion underestimates the highest mud pressure required to avoid breakouts around the wellbore. It also predicts a lower fracture gradient pressure. In addition, it was found that the results obtained from Mogi–Coulomb criterion yield a better comparison with breakouts observed from the caliper logs than that of Hoek–Brown criterion. It was concluded that the Mogi–Coulomb criterion is a better failure criterion as it considers the effect of the intermediate principal stress component in the failure analysis.     

Borehole breakout evolution through acoustic emission location analysis

A series of thick-wall cylinder tests were performed on Bentheim sandstone to investigate the nucleation and propagation of borehole breakouts. Isotropic compression tests showed a significant decrease of the critical pressure required to nucleate breakouts with increasing borehole diameter. Advanced analysis of acoustic emission radiation and optical microstructures indicate a three stage process of breakout nucleation and growth. Relatively few acoustic emissions are observed during the elastic loading stage of the specimens. Once breakout nucleation has occurred at the borehole wall a drastic increase of acoustic emission activity is observed. A close spatial correspondence between located acoustic events and the breakout indicates formation of two symmetric cusp-shaped breakouts on opposite sides of the borehole. With increasing isotropic pressure the breakouts grow forming parallel-sided slots that are surrounded by a process zone revealing grain crushing and pore collapse as typically observed in experimentally produced compaction bands. We apply a simple fracture mechanics approach to predict the observed size effect of the critical pressure required to initiate breakouts.     

横观各向同性地层水平井井壁拟三维应力场计算模型

 针对横观各向同性地层,基于各向异性材料力学理论,运用应力叠加原理和坐标变换方法,考虑井筒流体压力、最大水平主应力、最小水平主应力和上覆岩层压力作用,推导横观各向同性地层中,水平井沿任意方向钻进时井壁应力场的拟三维解析解。进而分析了页岩和砂岩水平井井壁上任意岩石质点3个主应力的分布规律,分析表明,与地层力学性质各向同性条件相比,力学性质各向异性时,井壁上任意岩石质点的第一主应力 没有改变,而第二主应力 和第三主应力 发生了改变,岩石力学性质各向异性度越大,主应力 和 改变越大,岩石力学性质高各向异性度增加了井壁可能发生张性破裂的点数。研究成果可为横观各向同性地层水平井水力裂缝起裂以及井壁稳定性分析提供参考。     

Evidence of thermally induced borehole elongation: a case study at Soultz, France

When they occur, borehole breakouts are considered strong markers of principal stress directions at depth. An innovative processing method for automatically identifying breakouts from ultrasonic borehole wall images has been developed. It has been applied to data sets from two deep, sub-vertical wells (GPK1 and GPK2) at the Soultz geothermal site in eastern France. In well GPK1, below 3 km depth, compression breakouts, with a 95°±7° azimuth, increasingly occur with depth. They result from time dependent compression failure at sub-critical stress levels and are indicators of the minimum horizontal principal stress orientation. However, in the uppermost logged section of well GPK2 (1.6–2.9 km depth), continuous borehole elongations share roughly the same azimuth with so called drilling-induced fractures (164°±18° and 175°±17° azimuth, respectively). Both features concomitantly vanish with depth, together with the amplitude of the thermal perturbation induced by drilling. It is proposed that these latter borehole elongations result from a pervasive, cooling-induced, tensile micro-cracking process prior to macroscopic failure localization. They are termed thermal elongations and are indicators of the maximum horizontal principal stress orientation. Had a simple logging caliper tool been used for this work, these thermal elongations might have been confused with classical compression breakouts. A simple criterion for differentiating compression breakouts from thermal elongation is proposed.     

Anhydrite cementation and compaction in geothermal reservoirs: Interaction of pore-space structure with flow, transport, P–T conditions, and chemical reactions

In order to analyze local clogging phenomena due to the precipitation of anhydrite in the pore-space we performed a petrophysical study on cores and data from three boreholes probing the Rhaetian hydrothermal aquifer in northern Germany (Allermöhe, Neuruppin 1/88, Neuruppin 2/87). The pore size geometry of sandstones was studied using, among other methods, pulsed field gradient-nuclear magnetic resonance (PFG-NMR). We found two facies types with clearly different diagenetic history: (1) a fine-grained sand with small pores, mechanically compacted during diagenesis into an average sandstone of fractal pore geometry; (2) a coarser sand with larger pores, almost completely cemented by anhydrite after compaction had reduced the pore-space to a porosity of 30%; thus no further mechanical compaction occurred and the pores remained smooth. In contrast, the fine-grained facies was not cemented, possibly because anhydrite crystal nuclei are unstable in pores of insufficient size. With regard of these two facies types we developed: (1) an approach for calculating vertical logs of anhydrite and permeability content from gamma density measurements in boreholes or on core; (2) a chemical reaction model to calculate the amount of precipitation and dissolution of each mineral species at high temperature and salinity. These petrophysical and geochemical models are integrated into the numerical simulation tool SHEMAT for simulating coupled flow, heat and species transport, and chemically induced permeability changes. A comparison of the diagenesis of the cemented and un-cemented facies types yields an improved understanding of the geological conditions required for anhydrite cementation. Specifically, with regard to the studied Rhaetian sandstones, numerical reactive flow simulations demonstrate that intense, local anhydrite cementation may occur when saline formation waters mix with hot brines ascending on faults.     

内蒙古海拉尔盆地乌尔逊及贝尔凹陷南屯组致密砂岩储层微观结构表征

为了明确海拉尔盆地南屯组致密砂岩储层微观孔隙结构与储层物性的相关关系,本次研究通过铸体薄片观察、物性测试及恒速压汞实验,明确储层微观特征及孔隙结构参数,包括孔隙及喉道类型、大小、分布、连通性,并讨论了储层微观孔隙结构与储层物性的相关关系。研究结果表明:南屯组储层主要矿物颗粒为石英、长石、火山碎屑岩及凝灰岩岩屑,压实作用较强烈,颗粒排列紧密,胶结类型多为接触式胶结及镶嵌胶结,并以长石溶蚀现象最为普遍。储层多发育溶蚀孔,同含有少量粒间孔,喉道多为片状、管束状及缩颈型喉道。储层孔隙半径大多分布在110~170μm,孔径分布曲线形态呈单峰态,孔隙半径与孔隙度、渗透率无明显相关性;喉道半径分布在0.508~4.069μm。受控于孔隙结构的差异,孔喉半径比与渗透率呈一定相关性。综上所述,南屯组致密砂岩储层孔隙结构是其物性差异的主控因素,决定流体渗流能力。     

新疆某高放废物预选处置库区地应力测量研究

 为了获得预选处置库区现今地应力的赋存特征,在该区花岗岩体内的4个深钻孔中采用水压致裂方法进行地应力测量。基于钻孔岩芯编录结果,在0～700 m深度范围内,成功取得地应力量值和最大水平主应力方向数据。依据获取的地应力实测资料,结合拜尔利定律和断层摩擦库伦准则,对预选区的地应力状态及断层活动性进行分析。结果表明：(1) 3个主应力随深度呈现出较好的线性关系;(2) 测试深度范围内,水平应力普遍高于垂向应力,预选区构造应力占主导地位,且随深度的增加逐渐减弱,岩体北部的水平力作用强于中部及南部,南部最弱;(3) 最大水平应力优势方位为NEE,与区域构造应力场方向基本吻合,自青藏高原内部及边缘到东天山地区,现今最大主应力的作用方向表现为由NE～NEE的变化规律;(4) 预选区地应力量值未达到断层摩擦滑动临界值,断层活动性较弱;(5) 研究成果为处置库的开挖设计和稳定性评价提供科学的指导,实测资料填补了该区域地应力数据的空白,为我国西部地区地应力场分布规律研究提供重要参考资料。     

Petrophysics studies of sedimentary rocks from a cross-hole seismic test site

In order to provide a site for studying in detail seismic wave propagation over a large range of frequencies through layered sedimentary rocks, four vertical boreholes of approximately 260 m depth and maximum distance apart of 95 m have been drilled through five cyclical sequences of shallow-dipping sandstone, mudrock and limestone formations in the Carboniferous Limestone series in northern England. Two of the boreholes were fully cored and a number of core samples from these were carefully preserved, at 1 m intervals in the first and at selected intervals in the second. Bulk density, porosity and P- and S-wave velocities and attenuation in the vertical and horizontal directions have been made on a total of 180 specimens from the preserved core samples. Permeability and electrical properties have been measured for the sandstone samples. Multiple linear regression equations have been derived relating the P- and S-wave velocities to porosity and clay content. These equations indicate the relative importance of increases in porosity and in clay content on decreases in all velocities, and the relative insensitivity to changes in clay content of PH- and SH-wave velocities. For the samples tested, the average anisotropy observed under in situ stress conditions is approximately 0.5% for limestones (porosities to 12%) and 5% for sandstones (porosities in the range 2 to 18%). For mudrocks (porosities in the range 2 to 15%), the average anisotropy is 21% for P waves and 27% for S waves. The results have been used to confirm the magnitudes of anisotropy observed in cross-hole seismic tomography at the site, in modelling the seismic response of sedimentary rocks with an appreciable clay content, and in modelling velocity dispersion and attenuation for rocks at the site over a wide range of frequencies.     

Micromechanics of compressive failure and spatial evolution of anisotropic damage in Darley Dale sandstone

The micromechanics of compressive failure in Darley Dale sandstone (with initial porosity of 13%) was investigated by characterizing quantitatively the spatial evolution of anisotropic damage under the optical and scanning electron microscopes. Two series of triaxial compression experiments were conducted at the fixed pore pressure of 10 MPa and confining pressures of 20 and 210 MPa, respectively. For each series, three samples deformed to different stages were studied. Failure in the first series was by brittle faulting. In contrast, failure in the second series was ductile, involving shear-enhanced compaction and distributed cataclastic flow. In the ductile series, crack density and acoustic emission activity both increased with the development of strain hardening. The stress-induced cracking was relatively isotropic. In the brittle series, crack density increased with the progressive development of dilatancy, with spatial distributions indicative of clustering of damage at the peak stress and shear localization in the strain softening stage. Dilatancy was associated with significant anisotropy in stress-induced cracking, that was primarily due to intragranular and intergranular cracking with a preferred orientation parallel to the maximum principal stress. Compared with published data for Westerly granite and San Marcos gabbro (with porosities of the order of 1%) and for Berea sandstone (with porosity of 21%), there is an overall trend for the stress-induced anisotropy (in a sample deformed to near the peak stress) to decrease with increasing porosity. The sliding wing crack model was adopted to analyze the evolution of anisotropic damage, using a friction coefficient and fracture toughness inferred from stress states at the onset of dilatancy. Significant discrepancy exists between the model prediction and microstructural data on stress-induced anisotropy, which is possibly due to limitations intrinsic to the microscopy technique as well as the sliding wing crack model.     

Orientation and magnitude of in situ stress to 6.5 km depth in the Baltic Shield

Understanding the state of stress in the earth is important for a broad range of engineering and geological problems. To obtain the state of stress in boreholes where conditions are such that conventional stress measurement techniques are impossible, we have used recent developments in the analysis of compressive and tensile wellbore failure in an integrated stress measurement strategy, involving also direct measurement of the least principal stress. The analysis is carried out in the two deep boreholes in the Siljan Ring area of the Baltic Shield. The Gravberg-1 borehole reached 6779 m true vertical depth (TVD) in the Siljan region, central Sweden, and the Stenberg-1 borehole, drilled 10 km to the south of Gravberg-1, was completed at 6529 m TVD. Analysis of vertical, drilling-induced tensile fractures in the nondeviating part of the Gravberg-1 well indicated that one principal stress is vertical and thus could be calculated from density estimates. Borehole breakouts and tensile fractures indicated that the average direction of the maximum horizontal stress, S_H, is N72°W±7° in Gravberg-1 and N53°W±9° in the Stenberg-1 well. The direction of S_H is on average very stable in both wells. Lower bound limits on the magnitude of the minimum horizontal stress, S_h, in the Gravberg-1 well were obtained from controlled and uncontrolled hydraulic fracturing and formation integrity tests. At 5 km depth in the Gravberg-1 borehole the minimum horizontal stress is approximately two-thirds of the vertical stress. We estimated the magnitude of the maximum horizontal stress in Gravberg-1 on the basis of drilling-induced tensile fractures identified in the borehole. S_H was estimated by calculating the stress at the borehole wall necessary to cause tensile failure of the formation, incorporating our lower bound S_h estimates, corrections for the cooling of the wellbore by drilling fluids and differential fluid pressures. Our results indicate a strike-slip faulting regime in the Siljan area and that the state of stress is in frictional equilibrium with a coefficient of friction in the range 0.5 to 0.6.     

A microstructural analysis of the compaction of claystone aggregates at high temperatures

The compaction behavior of rock aggregates at high temperatures and under intermediate stresses is investigated. A series of compaction experiments is performed in the laboratory on well-sorted claystone grain aggregates at temperatures up to 1000°C and under stresses up to 10 MPa. In order to investigate the mechanisms controlling the compaction process, we have developed a microstructural model based on the compaction of monosized spherical grains. In the model, compaction occurs through changes in the packing of the grains and by the indentation of grains. The grain contacts are assumed to be at yield stress, which is controlled by creep. We have analyzed the compaction-induced microstructural changes of the tested grain aggregates by using image analysis techniques. The spatial characteristics measured were used to make the model assumptions plausible. We found that the compaction model describes well the permanent volumetric strain in terms of microstructural parameters for relatively large strains. The model does not apply to the tested aggregates in the lower temperature range (550°C<T<650°C) probably because the main assumption, that the grain contacts are at yield stress, was not satisfied. A quantitative comparison of the compaction results of this study with results obtained from triaxial experiments on cores leads to the conclusion that the micromechanical model describes satisfactorily the compaction of the claystone aggregates in the high-temperature range (T>650°C).     

Numerical simulation of pore space clogging in geothermal reservoirs by precipitation of anhydrite

Anhydrite cementation in hydrothermal reservoirs can decrease porosity and permeability significantly. In these cases, the amount of hot water produced by hydrothermal heat mining installations is far too low for an economical use of the resource. We study two such cases in the North German sedimentary basin where a secondary anhydrite cementation drastically reduced the original high permeability of a Rhaetian sandstone reservoir. Core-flooding experiments under reservoir conditions indicate that in contrast to the instant dissolution of anhydrite in saline reservoirs, the nucleation probability of anhydrite and the speed of epitaxy on anhydrite crystals ( and , respectively) are very low. We performed numerical simulations of reactive flow on the local and regional scale in order to understand the apparent conflict between constricted nucleation, observed in laboratory experiments, and a complete filling of the pore space by anhydrite cementation found in core samples from boreholes at Neuruppin and Allermöhe. A highly resolved cylindrical reservoir model was used to simulate a chemical stimulation of the Allermöhe reservoir, i.e. the forced increase in porosity and permeability around the borehole in response to the injection of cold brines. Studying the dissolution process for different brine temperatures and salinities, we found that an injection of cold, highly saline brines will break through a cemented barrier of a radius of 5 m around the borehole after 10 days of stimulation. An additional study of the combined effect of hydraulic fracturing and chemical stimulation showed that both types of borehole stimulation increase the permeability by approximately the same amount if dissolution can act directly on the fracture walls. On the reservoir scale, numerical simulations indicate that strata-bound convective flow in the Rhaetian reservoir, driven by temperature differences due to the topography of the aquifer, is insufficient to explain the observed high degree of cementation. However, it can be shown that Ca²⁺ and dissolved in the reservoir brine are forced to precipitate around the fracture zone, if additional hot fluids flow up along faults, heat up the aquifer, and mix with the colder reservoir brine.     

利用地应力实测数据讨论地形对地应力的影响

首先详细描述了研究区域内2个钻孔的水压致裂地应力测试结果，包括测试段深度、最大和最小水平主应力的量值以及诱发破裂的印模定向试验结果。此外，还对测区内地质构造、地形地貌条件以及地层岩性进行了简要的介绍。经过对地应力测试结果以及相关数据的初步分析，发现对于相距仅280m左右的2个钻孔，其地应力状态及其分布规律存在较大的差异。为此，结合三维有限元数值模拟技术，对研究区域的地应力赋存状态和分布规律进行了更为详尽的分析，进一步研究和讨论了地形条件对地应力状态的影响和控制作用。     

陕北永宁山丹霞地貌造景地层地质特征

永宁山作为陕北地区丹霞地貌典型代表,其造景地层下白垩统洛河组(K₁l)在岩性、岩石特征、物源、沉积环境等方面的研究较少。通过剖面测量,抗压强度、薄片鉴定、X衍射分析、常量元素与稀土微量元素测试,对洛河组岩性岩相、地球化学特征进行了分析、总结。洛河组岩性主要为沙漠相风力作用沉积的一套紫红、灰红色细—中粗粒长石砂岩、石英砂岩、岩屑长石石英砂岩,岩石呈颗粒支撑,胶结类型为孔隙式、连生胶结,岩石次生变化较强,分选性好,抗压强度较大;岩层发育产状较统一的中大型板状、楔状斜层理,指示沉积作用主要受单向西北风控制。洛河组风成砂岩地球化学岩石类型为亚长石砂岩、长石砂岩和砂屑砂岩;物源区位于被动大陆边缘,砂岩的成分成熟度高,遭受风化程度很低;古气候条件表现为干燥、炎热。通过本次研究探讨永宁山一带洛河组砂岩地质特征、古气候、古环境变迁与变化,对陕北地区丹霞地貌成因机理研究,科学保护、合理利用具有重要意义。     

煤矿井下地质构造对地应力分布的影响

采用小孔径水压致裂地应力测量装置,在典型的急倾斜、特厚煤层矿区——甘肃华亭矿区的大型向斜构造附近进行14个测站地应力测量,以分析向斜构造不同部位的地应力变化。实测数据表明:华亭煤矿、砚北煤矿井下构造应力占绝对优势;在向斜翼部,水平应力较小;在向斜轴部,水平应力急剧增加,增加幅度远大于垂直应力;向斜构造对矿区地应力分布产生严重影响。基于山西晋城矿区的地应力实测数据,分析断层对地应力值与方向的影响。断层附近某些区域水平应力有所减小,大型断层会引起最大水平主应力方向的扭转。在实测数据基础上,采用FLAC3D数值计算软件,分析华亭矿区大型向斜构造周围地应力场分布,并与地应力实测数据进行对比。将地应力实测与数值模拟有机结合,是全面了解煤矿井下地应力场分布特征的有效途径。