Pulp health and calcific healing of a complicated crown–root fracture with additional root fracture in a maxillary incisor: A case report

BACKGROUND Complicated crown–root fracture (CRF) involves severe injury to the crown, root,and pulp, and may be accompanied by multiple root fractures. The loss of a toothhas lifelong consequences for children and teenagers, but the maintenance of pulphealth and the calcific healing of multiple root fractures are rarely reported in theliterature.CASE SUMMARY This case reports healing of a permanent tooth with complicated crown–root andadditional root fractures, in which pulp health was maintained. A 10-year-old girlfell and fractured the root of her maxillary left central incisor at the cervical level.After the coronal fragment was repositioned, the tooth was splinted until thetooth was no longer mobile, 2 years later. Eight years after treatment, the toothhas remained asymptomatic with vital pulp and localized gingival overgrowth.Cone-beam computed tomography revealed not only calcified healing of the CRFbut also spontaneous healing in an additional undiagnosed root fracture. Thefracture line on the enamel could not be healed by hard tissue and formed agroove in the cervical crown. It was speculated that the groove was related to thelocalized gingival overgrowth.CONCLUSION This case provides a clinical perspective of the treatment of a tooth with acomplicated CRF and an additional root fracture.

Factors Influencing Fracture Propagation in Collaborative Fracturing ofMultiple HorizontalWells

Horizontal well-stimulation is the key to unconventional resource exploration and development.The development mode of the well plant helps increase the stimulated reservoir volume.Nevertheless,fracture interference between wells reduces the fracturing effect.Here,a 2D hydro-mechanical coupling model describing hydraulic fracture(HF)propagation is established with the extended finite element method,and the effects of several factors on HF propagation during multiple wells fracturing are analyzed.The results show that with an increase in elastic modulus,horizontal principal stress difference and injection fluid displacement,the total fracture area and the reservoir stimulation efficiency are both improved in all three fracturing technologies.After a comparison of the three technologies,the method of improved zipper fracturing is proposed,which avoids mutual interference between HFs,and the reservoir stimulation effect is improved significantly.The study provides guidance for optimizing the fracturing technology of multiple horizontal wells.

Healing time, calcium and phosphorus contents as well as bone metabolism evaluation after Xianling Gubao-assisted surgical treatment of Colles fracture in elderly women

Objective:To study the effect of Xianling Gubao-assisted surgical treatment on postoperative healing, calcium and phosphorus contents as well as bone metabolism in elderly women with Colles fracture.Methods:A total of 96 elderly female patients with Colles fracture treated in our hospital between June 2013 and December 2015 were selected and randomly divided into two groups, the observation group of patients received Xianling Gubao capsule combined with manual reduction and plaster external fixation therapy, and control group of patients only received reduction and external fixation therapy. The fracture healing time was followed up after treatment, and 3 months after treatment, serum was collected to determine the content of calcium-phosphorus metabolism indexes and bone metabolism indexes.Results:The fracture healing time of observation group was significantly shorter than that of control group;1 month and 3 months after treatment, serum Ca, P, ALP, IGF-1, PDGF, BGP and PICP levels of both groups were significantly higher than those before treatment while CTX-1, tPINP and TRACP-5b levels were significantly lower than those before treatment;serum Ca, P, ALP, IGF-1, PDGF, BGP and PICP levels of observation group after treatment were significantly higher than those of control group while CTX-1, tPINP and TRACP-5b levels were significantly lower than those of control group.Conclusion:Adjuvant Xianling Gubao capsule therapy can promote the Colles fracture healing in elderly women, also improve calcium-phosphorus metabolism, promote bone formation and inhibit bone resorption.

Retrospective Epidemiological Analysis of Colles’ Fracture in Patients Admitted in Fernandes Távora Hospital

Background: Colles’ fracture is a type of fracture of the distal third of the radius and its most common cause is falling from patient’s own height and, epidemiologically, it is more common in the elderly. Objectives: The main objective of this study is to analyze the epidemiology of Colles’ fracture retrospectively, in patients admitted to Fernandes Távora Hospital. Materials and Methods: This retrospective study conducted at the Fernandes Távora Hospital used 1030 radiographic images of patients with wrist fractures. Results: (After a careful analysis) It was found that this type of fracture occurred with a greater frequency in age groups of 50 to 69, 60 to 69, and 40 to 49 years old, which corresponds to 59.5% of patients and the most affected sex were females (51.1%). Conclusion: The study concluded that this type of bone injury is more common in people aged 40 to 69 years old, especially in women, because of their geometry and bone composition. It is evident that Colles’ fracture impacts the life of the affected person, therefore, an adequate diagnosis and treatment having utmost importance.

Effect of the Jintiange capsule-assisted internal fixation on fracture healing and bone metabolism activity of patients with Colles fracture

Objective:To study the effect of the Jintiange capsule-assisted internal fixation on fracture healing and bone metabolism activity of patients with Colles fracture.Methods:A total of 120 patients with Colles fracture who received internal fixation in the hospital between July 2014 and May 2016 were collected and divided into control group and observation group according to the random number table method, 60 cases in each group. The control group received regular open reduction and internal fixation, and the observation group received Jintiange capsule-assisted internal fixation. The fracture healing quality as well as calcium phosphorus metabolism index and bone metabolism index levels were compared between the two groups before and after the operation.Results: Before operation, the differences in fracture end parameter levels, peripheral blood calcium and phosphorus metabolism index contents and serum bone metabolism index contents were not statistically significant between the two groups of patients;differences in fracture end radial incline, ulnar inclination and processus styloideus radii height were not statistically significant between the two groups of patients 6 weeks after surgery;peripheral blood Ca, P and ALP contents of observation group 6 weeks after surgery were significantly higher than those of control group, and serum bone formation indexes BGP and OPG contents were higher than those of control group while bone resorption indexes TRACP and CTX contents were significantly lower than those of control group. Conclusions: Jintiange capsule-assisted internal fixation can effectively improve the calcium and phosphorus metabolism, optimize bone formation/bone resorption balance and promote fracture healing in patients with Colles fracture.

FRACTURE序列在中轴型脊柱关节炎骶髂关节结构性病变中的诊断价值

目的:评估限制回波间隔的快速梯度回波类CT成像(FRACTURE)序列在检测中轴型脊柱关节炎(SpA)骶髂关节结构病变中的诊断价值。方法:回顾性分析83例确诊中轴型SpA患者在2021年12月-2022年8月进行骶髂关节MRI和CT检查的影像资料。评估图像包括FRACTURE、T_(1)WI序列和CT平扫图像。对骶髂关节的影像图像进行结构性病变评分:关节间隙变化(0~5分)、骨质侵蚀(0~3分)和骨质硬化(0~2分)。根据修改后的纽约标准评分系统对骶髂关节炎进行综合评分。结果:总共有166个骶髂关节图像(83名受试者)可供分析。以CT图像作为参考标准,FRACTURE序列在关节间隙改变、骨质侵蚀、骨质硬化和骶髂关节炎综合评分与CT结果表现出较高的一致性,AUC分别为0.908、0.943、0.918和0.944。与T_(1)WI相比,FRACTURE在关节间隙变化(91.8%vs.70.5%)、骨质侵蚀(93.3%vs.56.4%)、骨质硬化(94%vs.77.6%)和骶髂关节炎综合评分(98.9%vs.75.3%)方面具有更高的诊断准确性。结论:FRACTURE成像可以评估中轴型SpA患者骶髂关节的结构性病变,并显示出良好的诊断性能。

分阶段使用石膏、夹板对老年Colles骨折腕关节功能的影响

目的:探讨分阶段使用石膏、夹板对老年Colles骨折患者腕关节功能的影响。方法:选取2021年5月~2022年11月江西中医药大学附属医院90例老年Colles骨折患者,按照治疗方式,分为夹板组、石膏组、石膏夹板组,各30例,比较各项指标。结果:相较于复位前,三组掌倾角角度、尺偏角角度均得到提升,差异有统计学意义(P<0.05);复位后,三组掌倾角角度、尺偏角角度比较,差异无统计学意义(P>0.05);固定2周时,石膏夹板组优于夹板组,差异有统计学意义(P<0.05),石膏夹板组与石膏组比较,差异无统计学意义(P>0.05);固定6周时,石膏夹板组优于夹板组、石膏组,差异有统计学意义(P<0.05)。固定6周后,石膏夹板组Dienst腕关节功能评分高于夹板组、石膏组,差异有统计学意义(P<0.05);夹板组与石膏组Dienst腕关节功能评分比较,差异无统计学意义(P>0.05);固定6周后,石膏夹板组PRWE腕关节功能评分低于夹板组,差异有统计学意义(P<0.05);石膏夹板组PRWE腕关节功能评分低于石膏组,差异有统计学意义(P<0.05);夹板组与石膏组PRWE腕关节功能评分比较,差异无统计学意义(P>0.05)。结论:保守治疗老年Colles骨折患者时,单一使用夹板、石膏固定方式,均能获得良好效果,然而分阶段使用石膏、夹板固定方式,其疗效优于单一方式,有助于促进手腕功能康复。

Production induced fracture closure of deep shale gas well under thermo-hydro-mechanical conditions

Deep shale gas reservoirs have geological characteristics of high temperature,high pressure,high stress,and inferior ability to pass through fluids.The multi-stage fractured horizontal well is the key to exploiting the deep shale gas reservoir.However,during the production process,the effectiveness of the hydraulic fracture network decreases with the closure of fractures,which accelerates the decline of shale gas production.In this paper,we addressed the problems of unclear fracture closure mechanisms and low accuracy of shale gas production prediction during deep shale gas production.Then we established the fluid—solid—heat coupled model coupling the deformation and fluid flow among the fracture surface,proppant and the shale matrix.When the fluid—solid—heat coupled model was applied to the fracture network,it was well solved by our numerical method named discontinuous discrete fracture method.Compared with the conventional discrete fracture method,the discontinuous discrete fracture method can describe the three-dimensional morphology of the fracture while considering the effect of the change of fracture surface permeation coefficient on the coupled fracture—matrix flow and describing the displacement discontinuity across the fracture.Numerical simulations revealed that the degree of fracture closure increases as the production time proceeds,and the degree of closure of the secondary fractures is higher than that of the primary fractures.Shale creep and proppant embedment both increase the degree of fracture closure.The reduction in fracture surface permeability due to proppant embedment reduces the rate of fluid transfer between matrix and fracture,which has often been overlooked in the past.However,it significantly impacts shale gas production,with calculations showing a 24.7%cumulative three-year yield reduction.This study is helpful to understand the mechanism of hydraulic fracture closure.Therefore,it provides the theoretical guidance for maintaining the long-term effectiveness of hydraulic fractures.

Study of hydro-mechanical behaviours of rough rock fracture with shear dilatancy and asperities using shear-flow model

The geometric properties of fracture surfaces significantly influence shear-seepage in rock fractures,introducing complexities to fracture modelling.The present study focuses on the hydro-mechanical behaviours of rough rock fractures during shear-seepage processes to reveal how dilatancy and fracture asperities affect these phenomena.To achieve this,an improved shear-flow model(SFM)is proposed with the incorporation of dilatancy effect and asperities.In particular,shear dilatancy is accounted for in both the elastic and plastic stages,in contrast to some existing models that only consider it in the elastic stage.Depending on the computation approaches for the peak dilatancy angle,three different versions of the SFM are derived based on Mohr-Coulomb,joint roughness coefficient-joint compressive strength(JRC-JCS),and Grasselli’s theories.Notably,this is a new attempt that utilizes Grasselli’s model in shearseepage analysis.An advanced parameter optimization method is introduced to accurately determine model parameters,addressing the issue of local optima inherent in some conventional methods.Then,model performance is evaluated against existing experimental results.The findings demonstrate that the SFM effectively reproduces the shear-seepage characteristics of rock fracture across a wide range of stress levels.Further sensitivity analysis reveals how dilatancy and asperity affect hydraulic properties.The relation between hydro-mechanical properties(dilatancy displacement and hydraulic conductivity)and asperity parameters is analysed.Several profound understandings of the shear-seepage process are obtained by exploring the phenomenon under various conditions.

Numerical modeling of fracture propagation of supercritical CO_(2)compound fracturing

The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical CO_(2)(SC-CO_(2))compound fracturing which is expected to be an efficient and environmentally friendly way to develop shale gas.The coupling model is solved by the finite element method,and the results are in good agreement with the analytical solutions and fracturing experiments.Based on this model,the fracture propagation characteristics at the two stages of compound fracturing are studied and the influence of pressurization rate,in situ stress,bedding angle,and other factors are considered.The results show that at the SC-CO_(2)fracturing stage,a lower pressurization rate is conducive to formation of the branches around main fractures,while a higher pressurization rate inhibits formation of the branches around main fractures and promotes formation of the main fractures.Both bedding and in situ stress play a dominant role in the fracture propagation.When the in situ stress ratio(δ_(x)/δ_(y))is 1,the presence of bedding can reduce the initiation pressure and failure pressure.Nevertheless,it will cause the fracture to propagate along the bedding direction,reducing the fracture complexity.In rocks without bedding,hydraulic fracturing has the lengthening and widening effects for SC-CO_(2)induced fracture.In shale,fractures induced at the hydraulic fracturing stage are more likely to be dominated by in situ stresses and have a shorter reorientation radius.Therefore,fracture branches propagating along the maximum principal stress direction may be generated around the main fractures induced by SC-CO_(2)at the hydraulic fracturing stage.When the branches converge with the main fractures,fracture zones are easily formed,and thus the fracture complexity and damage area can be significantly increased.The results are instructive for the design and application of SC-CO_(2)compound fracturing.

Shared genetic architecture highlights the bidirectional association between major depressive disorder and fracture risk

Background There is limited evidence suggesting that osteoporosis might exacerbate depressive symptoms,while more studies demonstrate that depression negatively affects bone density and increases fracture risk.Aims To explore the relationship between major depressive disorder(MDD)and fracture risk.Methods We conducted a nested case-control analysis(32670 patients with fracture and 397017 individuals without fracture)and a matched cohort analysis(16496 patients with MDD and 435492 individuals without MDD)in the same prospective UK Biobank data set.Further,we investigated the shared genetic architecture between MDD and fracture with linkage disequilibrium score regression and the MiXeR statistical tools.We used the conditional/conjunctional false discovery rate approach to identify the specific shared loci.We calculated the weighted genetic risk score for individuals in the UK Biobank and logistic regression was used to confirm the association observed in the prospective study.Results We found that MDD was associated with a 14%increase in fracture risk(hazard ratio(HR)1.14,95%CI 1.14 to 1.15,p<0.001)in the nested case-control analysis,while fracture was associated with a 72%increase in MDD risk(HR 1.72,95%CI 1.64 to 1.79,p<0.001)in the matched cohort analysis,suggesting a longitudinal and bidirectional relationship.Further,genetic summary data suggested a genetic overlap between MDD and fracture.Specifically,we identified four shared genomic loci,with the top signal(rs7554101)near SGIP1.The protein encoded by SGIP1 is involved in cannabinoid receptor type 1 signalling.We found that genetically predicted MDD was associated with a higher risk of fracture and vice versa.In addition,we found that the higher expression level of SGIP1 in the spinal cord and muscle was associated with an increased risk of fracture and MDD.Conclusions The genetic pleiotropy between MDD and fracture highlights the bidirectional association observed in the epidemiological analysis.The shared genetic components(such as SGIP1)between the diseases suggest that modulating the endocannabinoid system could be a potential therapeutic strategy for both MDD and bone loss.

Management and classification of the fracture of lateral process of talus:An overview and literature update

Fracture of the lateral process of the talus(FLPT)is uncommon in clinical practice and can be easily missed or misdiagnosed.In recent years,as researchers from all over the world have further deepened their research on FLPT,there has been a breakthrough in the classification,and the methods and principles of clinical management have changed accordingly;however,there is still no standardized guideline for the diagnosis and management of FLPT,and there have been few relevant literature review articles related to this kind of fracture in the past at least 5 years.In this article,we review the clinical classification,classification-based therapeutic recommendations,and prognosis of FLPT,with the aim of providing a reference for the clinical diagnosis and management of this infrequent fracture.

Effect of fracture fluid flowback on shale microfractures using CT scanning

The field data of shale fracturing demonstrate that the flowback performance of fracturing fluid is different from that of conventional reservoirs,where the flowback rate of shale fracturing fluid is lower than that of conventional reservoirs.At the early stage of flowback,there is no single-phase flow of the liquid phase in shale,but rather a gas-water two-phase flow,such that the single-phase flow model for tight oil and gas reservoirs is not applicable.In this study,pores and microfractures are extracted based on the experimental results of computed tomography(CT)scanning,and a spatial model of microfractures is established.Then,the influence of rough microfracture surfaces on the flow is corrected using the modified cubic law,which was modified by introducing the average deviation of the microfracture height as a roughness factor to consider the influence of microfracture surface roughness.The flow in the fracture network is simulated using the modified cubic law and the lattice Boltzmann method(LBM).The results obtained demonstrate that most of the fracturing fluid is retained in the shale microfractures,which explains the low fracturing fluid flowback rate in shale hydraulic fracturing.

Complication rates after direct anterior vs posterior approach for hip hemiarthroplasty in elderly individuals with femoral neck fractures

BACKGROUND Dislocation rates after hemiarthroplasty reportedly vary from 1%to 17%.This serious complication is associated with increased morbidity and mortality rates.Approaches to this surgery are still debated,with no consensus regarding the superiority of any single approach.AIM To compare early postoperative complications after implementing the direct anterior and posterior approaches(PL)for hip hemiarthroplasty after femoral neck fractures.METHODS This is a comparative,retrospective,single-center cohort study conducted at a university hospital.Between March 2008 and December 2018,273 patients(a total of 280 hips)underwent bipolar hemiarthroplasties(n=280)for displaced femoral neck fractures using either the PL(n=171)or the minimally invasive direct anterior approach(DAA)(n=109).The choice of approach was related to the surgeons’practices;the implant types were similar and unrelated to the approach.Dislocation rates and other complications were reviewed after a minimum followup of 6 mo.RESULTS Both treatment groups had similarly aged patients(mean age:82 years),sex ratios,patient body mass indexes,and patient comorbidities.Surgical data(surgery delay time,operative time,and blood loss volume)did not differ significantly between the groups.The 30 d mortality rate was higher in the PL group(9.9%)than in the DAA group(3.7%),but the difference was not statistically significant(P=0.052).Among the one-month survivors,a significantly higher rate of dislocation was observed in the PL group(14/154;9.1%)than in the DAA group(0/105;0%)(P=0.002).Of the 14 patients with dislocation,8 underwent revision surgery for recurrent instability(posterior group),and one of them had 2 additional procedures due to a deep infection.The rate of other complications(e.g.,perioperative and early postoperative periprosthetic fractures and infection-related complications)did not differ significantly between the groups.CONCLUSION These findings suggest that the DAA to bipolar hemiarthroplasty for patients with femoral neck fractures is associated with a lower dislocation rate(<1%)than the PL.

Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

Systemic modulation of skeletal mineralization by magnesium implant promoting fracture healing: Radiological exploration enhanced with PCA-based machine learning in a rat femoral model

The clinical application of magnesium(Mg)and its alloys for bone fractures has been well supported by in vitro and in vivo trials.However,there were studies indicating negative effects of high dose Mg intake and sustained local release of Mg ions on bone metabolism or repair,which should not be ignored when developing Mg-based implants.Thus,it remains necessary to assess the biological effects of Mg implants in animal models relevant to clinical treatment modalities.The primary purpose of this study was to validate the beneficial effects of intramedullary Mg implants on the healing outcome of femoral fractures in a modified rat model.In addition,the mineralization parameters at multiple anatomical sites were evaluated,to investigate their association with healing outcome and potential clinical applications.Compared to the control group without Mg implantation,postoperative imaging at week 12 demonstrated better healing outcomes in the Mg group,with more stable unions in 3D analysis and high-mineralized bridging in 2D evaluation.The bone tissue mineral density(TMD)was higher in the Mg group at the non-operated femur and lumbar vertebra,while no differences between groups were identified regarding the bone tissue volume(TV),TMD and bone mineral content(BMC)in humerus.In the surgical femur,the Mg group presented higher TMD,but lower TV and BMC in the distal metaphyseal region,as well as reduced BMC at the osteotomy site.Principal component analysis(PCA)-based machine learning revealed that by selecting clinically relevant parameters,radiological markers could be constructed for differentiation of healing outcomes,with better performance than 2D scoring.The study provides insights and preclinical evidence for the rational investigation of bioactive materials,the identification of potential adverse effects,and the promotion of diagnostic capabilities for fracture healing.

Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Experimental investigation on coal pore-fracture variation and fractal characteristics synergistically affected by solvents for improving clean gas extraction

Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy

With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions.Compared with the traditional connectivity indexes based on the statistics of fracture geometry,the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks.According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks,the hydraulic conductivities and entropic scales in different directions both increase with spatial order(i.e.,trace length decreasing and spacing increasing)and are independent of the dip angle.As a result,the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function,which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.