Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position

The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.

Numerical Analysis on Displacement Law of Discontinuous Rock Mass in Broken Rock Zone for Deep Roadways

On the basis of the characteristics of broken rock zone, using the program of "discontinuous deformation analysis(DDA)", the changing law of influential factors of discontinuous rock mass in large broken rock zone was researched quantitatively for the first time. Based on the results of computation, the concept of "key part"of roadways and its stability criterion were brought forward, and it was pointed out that in inclined coal and rock seams the"key parts"of roadways are the upper side and the floor of surrounding rocks, especially the former.

Pull-apart Basins and the Total Lateral Displacement Along the Haiyuan Fault Zone in Cenozoic

Pull-apart basins of three scales were found along the Haiyuan fault zone. The largest one is more than 50km long, named Laolongwan basin developed in Miocene. A model was built to calculate the amount of pull-apart of an extensional basin. Parameters used in calculation include thickness and length of deposition and depth of detachment. The results of calculation show that the amount of pull-apart of the Laolongwan Basin is about 30 km. Based on previous studies and calculating by using the average slip rate method, amount of pull-apart of the other two smaller basins are 22 km and 8 km, respectively. Thus, the total displacement of strike-slip along the Haiyuan fault zone is about 60 km, which is close to the offset of the Yellow River from Jingtai to Jingyuan.

Ground Surface Ruptures and Near-Fault,Large-Scale Displacements Caused by the Wenchuan Ms8.0 Earthquake Derived from Pixel Offset Tracking on Synthetic Aperture Radar Images

The 12 May 2008 Wenchuan Ms8.0 earthquake produced surface displacements along the causative fault, the Yingxiu-Beichuan Fault, which are up to several meters near the fault. Because of the large gradient, satellite synthetic aperture radar （SAR） interferometric data are strongly incoherent; the usual SAR interferometry method does not allow such displacements to be measured. In the present study, we employed another approach, the technique based on pixel offset tracking, to solve this problem. The used image data of six tracks are from the Advanced Land Observing Satellite, Phased Array type L-band Synthetic Aperture Radar （ALOS/PALSAR） dataset of Japan. The results show that the entire surface rupture belt is 238 km long, extending almost linearly in a direction of 42°north-east. It is offset left laterally by a north-west-striking fault at Xiaoyudong, and turns at Gaochuan, where the rupture belt shifts toward the south by 5 km, largely keeping the original trend. In terms of the features of the rupture traces, the rupture belt can be divided into five sections and three types. Among them, the Beichuan-Chaping and Hongkou-Yingxiu sections are relatively complex, with large widths and variable traces along the trend. The Pingtong-Nanba and Qingping-Jingtang sections appear uniform, characterized by straight traces and small widths. West of Yingxiu, the rupture traces are not clear. North of the rupture belt, surface displacements are 2.95 m on average, mostly 2-3.5 m, with 7-9 m the maximum near Beichuan. South of the rupture belt, the average displacement is 1.75 m, dominated by 1-2 m, with 3-4 m at a few sites. In the north, the displacements in the radar line of sight are of subsidence, and in the south, they are uplifted, in accordance with a right-slip motion that moves the northern wall of the fault to the east, and the southern wall to the west, respectively. Along the Guanxian-Jiangyou Fault, there is a uplift zone in the radar line of sight, which is 66 km long, 1.5-6 km wide, and has vertical displacements of approximately 2 m, but no observable rupture traces.

Estimation of earth pressure against retaining walls with different limited displacement modes based on elastic theory

The earth pressure acting on retaining walls due to creep and consolidation is under limited equilibrium conditions(limited displacement). Linear elastic constitutive theory can be applied to determine earth pressure distribution along retaining walls under limited displacement condition. In addition,tangent modulus in Duncan-Chang nonlinear elastic model was introduced to reflect the variations of soil modulus with confining pressure, and boundary strains were derived from Rankine active earth pressure, Rankine passive earth pressure, static earth pressure and principal stress direction deflection.According to the above four boundary strains, earth pressure on retaining walls was divided into five state zones. By comparing the calculation results obtained from the equations proposed in this paper with those of experimental tests, the following conclusions can be drawn: earth pressure distribution was always nonlinear along retaining walls for translation displacement(T mode), rotation displacement around wall base(RB mode), and translation + rotation displacement around wall base(RBT mode). Also,calculated earth pressure distributions along with the depth of wall were found to be consistent with measured values under three displacement modes.Additionally, a parametric study was carried out to evaluate the effects of internal friction angle and backfill soil cohesion on earth pressure. It could be seen from the above series of studies that the earth pressure equations derived in this work could be well applied in practical engineering in designing retaining walls.

Analysis of horizontal displacement distribution caused by single advancing longwall panel excavation

The paper presents an analysis of the horizontal displacement of surfaces induced by exploitation in a longwall panel. The panel under discussion is No. 698 of Prosper Haniel coal mine, Germany. The author discusses both the distribution of displacement vectors, according to the theory assuming surface point displacement towards the center of gravitation （COG） zone of a selected deposit element, and the analysis of horizontal displacement measurements, based on the assumption that the value of horizontal displacement is proportional to the slope of the subsidence trough. Finally, the value of horizontal displacement coefficient B is estimated for particular longitudinal and transverse measurement section of the analyzed longwall No. 698.

THE APPLICATION OF MOIRE INTERFEROMETRY IN THE MEASUREMENT OF DISPLACEMENT FIELD AND STRAIN FIELD AT NOTCH-TIP AND CRACK-TIP

This paper presents the application of Moire interferometry in measuring the displacement and strain field at notch-tip and crack-tip before and after crack propagation.The experiment is carried out using a three point bending beam with a notch.The N_x and N_y fringe patterns representing displacement field,and the ΔN_x/Δx and ΔN_y/Δy fringe patterns representing the strain field are obtained.The sensitivity of the meas- ured displacement is 0.417μm per fringe order.The displacement and strain distribution along the section x=0 have been worked out according to N_x and N_y fringe patterns.

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.

CHARACTERISTICS OF CLIMATE WARMING AND IMPACT ON CLIMATE ZONES CHANGE IN GUANGDONG

Based on temperature data in Guangdong in the past 50years, statistical methods are used to analyze the characteristics of temperature in spatial and temporal variation. The results show that land surface temperature warms by 0.16℃/1 0a in Guangdong. The range of warming was lower than the average of nationwide and global land surface. Furthermore, the temperature has a larger increase tendency in winter and spring and coastal areas than in summer and autumn and inland areas. Climate zones move towards the north obviously. North tropical zone is expanding, south subtropical zone is reducing and central subtropical zone is relatively stable. Under the global climate warming, characteristics of climate warming in Guangdong were influenced by atmosphere general circulation, sea surface temperature and human activities etc.

An alternative interpretation for the map expression of "abrupt" changes in lateral stratigraphic level near transverse zones in fold-thrust belts

The map expression of ＂abrupt＂ changes in lateral stratigraphic level of a thrust fault has been traditionally interpreted to be a result of the presence of （1） a lateral （or oblique） thrust-ramp, or （2） a frontal ramp with displacement gradient, and/or （3） a combination of these geometries. These geometries have been used to interpret the structures near transverse zones in fold-thrust belts （FTB）. This contribution outlines an alternative explanation that can result in the same map pattern by lateral variations in stratigraphy along the strike of a low angle thrust fault. We describe the natural example of the Leamington transverse zone, which marks the southern margin of the Pennsylvanian-Permian Oquirrh basin with genetically related lateral stratigraphic variations in the North American Sevier FTB. Thus, the observed map pattern at this zone is closely related to lateral stratigraphic variations along the strike of a horizontal fault. Even though the present-day erosional level shows the map pattern that could be interpreted as a lateral ramp, the observed structures along the Leamington zone most likely share the effects of the presence of a lateral （or oblique） ramp, lateral stratigraphic variations along the fault trace, and the displacement gradient.

Moving line crack accompanied with damage zone subject to remote tensile loading

In the 1920s, a closed-form solution of the moving Criffith crack was first obtained by Yoffe. Based on Yoffe＇s solution, the Dugdale model for the moving crack case gives a good result. However, the Dugddle model fails when the crack speed is closed to the Rayleigh wave speed because of the discontinuity occurred in the crack opening displacement （COD）. The problem is solved in this paper by introducing a restraining stress zone ahead of the crack tip and two velocity functions. The restraining stresses are linearly distributed and related to the velocity of the moving crack. An analytical solution of the problem is obtained by use of the superposition principle and a complex function method. The final result of the COD is continuous while the crack moves at a Rayleigh wave speed. The characteristics of the strain energy density （SED） and numerical results are discussed, and conclusions are given.

The Study of Paleoearthquakes on the Weihe Fault Zone

It is indicated by historical records and the exploratory trench on the Weihe fault that the Yaodian-Zhangjiawan segment of the Weihe fault zone has experienced a historical earthquake and 3 paleoearthquake events in the past 9110a. The historical earthquake, namely, event Ⅳ, occurred between 1487 and 1568 AD. The date of paleoseismic event Ⅰ is （9110 ＋ 90） a, and the ages of events Ⅱ and Ⅲ are unknown. The coseismic vertical displacement of events Ⅰ, Ⅱ and Ⅲ is 0.5m, 0.5m and 0.2m, respectively. The exploratory trench also indicates that the Yaodian-Zhangjiawan segment of the Weihe fault was active in the Holocene.

Analysis on the Observation Data of Three Profiles across the Qilian Mountain-Haiyuan Fault Zone

By analyzing GPS, leveling and gravity observation data from the Minle, Huazangsi and Shagouhe profiles across the Qilian Mountain-Haiyuan fault during 2005 - 2009, the changes of these data and activity characteristics of the main faults in different time are obtained. The results show that the Changma-Erbo, Maomaoshan, Zhunglanghe and Haiyuan faults have been active in recent years. The relationship between the vertical displacement and mobile gravity data is analyzed, and the results reveal the gravity changes are mainly due to mass transfer. The results of GPS observation show that the direction of the horizontal movement velocity was almost along the fault strike in 2006 - 2007, while the horizontal velocity deviated from the fault direction in 2007 - 2008, characterized by increased eastward displacement. Further analysis upon removal of the linear trend on the time series of the N and E coordinate values of the continuous observation stations of the Crustal Movement Observation Network of China near the three profiles reveals that the Wenchuan earthquake had an effect on the observations in 2007 - 2008. Comparing the gravitational changes in 2008 - 2009 with the Bouguer gravity anomaly background, we find that the area near Minle profile is in the stage of adjustment and recovery, while the anomaly is not completely recovered around Huazangsi and Shagouhe profiles.

基于地质分区的伊犁河谷黄土滑坡滑移特征研究

滑坡给人类生命、财产和基础设施带来了极高风险。在阿拉尔村附近发现了一处潜在不稳定滑坡。本文通过ArcGIS软件对潜在滑坡进行高程、坡度和坡向3方面分析,依据这3个地质因子对边坡进行了地质分区;再运用颗粒流软件PFC^(2D)建立潜在滑坡数值模型,模拟潜在不稳定滑坡位移过程,分析其颗粒应变规律,通过双轴试验模型对滑坡土体的细观参数进行标定,使其和实际相符;最后将数值模型的位移结果与地质分区相结合,得到该潜在滑坡的位移分析结果。结果表明:该潜在滑坡的位移主要集中在高高程、中等坡度区域,而该滑坡在此区域面积占比最大,研究为后续边坡治理提供了一定理论依据。

基于桩-土界面剪切特性的单桩沉降和承载问题研究

近年来,西北地区出现了许多高填方场地,为减小建筑物基础的不均匀沉降,基础类型广泛使用桩基础。与一般场地不同,黄土填方场地中的单桩桩周土受力后仍会产生较大的变形,该类场地单桩沉降机制复杂。桩顶总沉降计算是桩基设计的重要依据,为此,建立了高填方黄土场地单桩桩顶总沉降计算模型。基于传统的荷载传递法和剪切位移法,分别考虑桩-土界面的桩-土相互作用和桩-土界面外剪切带土体的剪切变形。依据桩端边界,将单桩类型分为摩擦桩和端承摩擦桩,分别建立桩周土弹性阶段和塑性阶段的桩身位移控制微分方程,结合边界条件进行求解,得到桩身位移、轴力、侧摩阻力,并通过弹塑性理论求解了桩周土剪切带土体剪切变形,进而通过叠加原理求得桩顶总沉降。用桩长与桩周土塑性发展深度的比值,定义了桩基承载力安全系数K。通过算例分析与现场试验数据对比分析,研究结果表明:使用新的模型计算得到的桩顶总沉降与现场试验结果相近;当桩顶荷载较小、桩周土处于弹性阶段时,桩端边界对桩身轴力、位移和侧摩阻力影响很小,但桩周土进入塑性滑移阶段后,桩端边界的影响开始变大,考虑桩端土的承载能力会极大提高单桩极限承载力;建立了将荷载传递法和剪切位移法综合起来的计算模型,不仅可以考虑桩-土界面的相对滑移,还可以计算桩-土界面外土体剪切带的剪切变形,使得桩顶总沉降计算更加精确,可为类似场地中单桩沉降的分析与控制提供一定的参考。

基于位移等代法的深部直墙半圆拱形隧洞松动圈厚度预测

【目的】位移等代法是在工程实践中被广泛应用的一种等效圆法。为进一步探索该方法在深部非均匀应力场下预测松动圈厚度的工程效果,并建立具有工程适用性的等效圆半径计算公式,【方法】选取深部隧洞常采用的直墙半圆拱形断面为研究对象,根据位移等代法基本原理,利用FLAC~(3D)数值模拟和理论计算相结合的方式,建立了侧压系数λ为1.1~1.5,跨高比b_0/h为1.3~1.5条件下的等效圆半径函数关系式,并应用到江西曲江某煤矿水仓围岩的松动圈厚度预测。【结果】结果显示:根据等效圆公式计算出的水仓围岩松动圈的纵轴厚度为1.41 m,横轴为1.20 m,呈椭圆形;现场实测的松动圈也呈椭圆形,厚度平均值在1.15~1.45 m,其中最大均值在纵轴1.45 m,最小均值在横轴为1.15 m。理论预测值与实测值相吻合。【结论】结果表明:位移等代法适用于深部软岩松动圈厚度预测;所建等效圆半径公式具有良好的工程适用性,可为评价和预测类似隧洞工程松动圈厚度提供一种简化的、可借鉴的方法和思路。

滩涂地区预压作用下人工硬壳层对桥梁桩基的影响分析: 以浙江省十一塘高速为例

滩涂地区深厚的软土地质条件给现浇箱梁的施工带来了较大挑战,依托浙江省十一塘高速公路一期工程,研究预压荷载作用下人工就地固化硬壳层对桥梁桩基的影响。基于土体硬化模型建立三维数值计算模型,对比不同硬壳层深度下桩身轴力、侧摩阻力和水平位移的变化规律,结果表明:当硬壳层厚度为2 m时,桩身轴力减少约16%且硬壳层的厚度会改变负摩阻力的传递深度,表现为硬壳层厚度越厚桩侧阻力中性点越往上移。此外,在一定深度影响范围内,硬壳层能够有效控制桩顶和不同深度处桩身水平位移,硬壳层厚度越大,桩顶水平位移越小。最后通过分析土体模量对桩身水平位移的影响发现,桩身水平位移会随该层土压缩模量的增大而减小且土体卸载/再加载刚度模量E_(ur)的影响高于土体偏量加载刚度模量E_(50)及土体侧限压缩刚度模量E_(eod)的影响。

油气沿断层垂向运移特征及主控因素分析——以东海盆地西湖凹陷平湖斜坡为例

东海盆地西湖凹陷平湖斜坡油气纵向富集差异受断层控制作用明显,但断层活动期与成藏期匹配关系差,油气成藏时断层处于不活跃期(简称静止断层),明确油气沿静止断层垂向运移特征及影响因素,可以为西湖凹陷或相似地区油气勘探提供理论依据。为此,综合测井、录井、地震等资料和包裹体均一温度及盐度、岩石热解等分析测试数据,研究平湖斜坡油气供烃层系与成藏期次,确定油气沿静止断层垂向运移特征及影响因素。结果表明,平湖斜坡供烃层系为宝石组和平湖组好—优质的成熟烃源岩,油气纵向上主要富集于平中段—平上段,具有下生上储的运聚特征。存在玉泉组—柳浪组沉积期和三潭组沉积期至今两期油气充注,断层主要活动时间为宝石组—龙井组沉积期,与成藏期匹配关系差,油气晚期沿静止断裂带发生了垂向运移。油气能够沿静止断层垂向运移的影响因素包括断裂带宽度、烃源岩层压力和断裂带排替压力。研究区断裂带宽度分布在138~288m之间,与油气垂向运移距离呈正相关关系。烃源岩层压力经历了复杂的演化过程,成藏期压力略低于现今,但已发育弱超压或超压,现今和成藏期压力系数越高,油气垂向运移距离越大。断裂带排替压力主要分布在0.2~3.5MPa之间,与油气垂向运移距离呈负相关关系。基于3个影响因素与油气垂向运移距离的相关关系,建立了断层垂向输导能力定量评价公式,评价结果与油气最大运移距离具有明显的正相关性,据此确定了平湖斜坡有利勘探层系为F2和F5断层附近的平湖组和花下段。

无底柱分段崩落法进路宽度对其围岩稳定性的影响

增加回采进路宽度,能够改善无底柱分段崩落法的放矿效果,但也存在着进路稳定性降低的风险。采用数值分析方法,分析了某铁矿西矿段开采时5组进路宽度下的围岩应力分布规律、位移量变化和塑性区分布特征,研究了进路宽度对围岩稳定性的影响。结果表明:①围岩中最大与最小主应力在进路顶板、底板与侧帮处的应力集中区呈不同形态分布,其范围差异也较大,而且两相邻进路之间受应力叠加作用影响,存在1个“圆角矩形”应力集中区。②随着进路宽度和围岩深度增加,围岩中的最大与最小主应力也随之增大,各应力集中区范围大小产生了不同的变化,其中顶底板处的应力集中区范围增幅较大,5组进路宽度下的顶板围岩均易发生张拉破坏。③在进路宽度为7 m和8 m时,最小主应力变化受到了相邻进路围岩应力叠加作用影响,侧帮围岩发生张拉破坏的可能性较大。④进路顶板位移量呈现出了“中间大、两侧小”的特征,顶板下沉量及其增幅远大于侧帮下沉量与增幅,增加进路宽度易造成进路顶板垮落事故。⑤顶底板围岩中塑性区以剪切塑性区和张拉塑性区的混合区为主,两帮围岩中以剪切塑性区为主,进路宽度越大,塑性区总体积增长越快,进路宽度增加过大不利于顶板的稳定性。建议该矿山西矿段进路宽度应以6 m为宜,并对进路两帮采取支护措施,若大于6 m时,则需对顶板围岩采取适当支护措施。

深部厚煤层回采巷道支护设计及围岩控制研究

为研究深部厚煤层回采巷道支护设计问题,基于唐阳煤矿432运输巷道,从安全及支护成本角度出发提出3种支护设计方案;采用理论分析、数值模拟和工程实践的方法分别研究了各方案支护参数的取值、位移变形量、塑性区及支护方案实际支护效果。理论分析结果表明:3种支护方案选取的锚杆锚索参数及间排距均符合理论计算值。数值模拟结果表明:支护方案Ⅰ顶底板及两帮相对位移变形量分别为77.6、103.4 mm,支护方案Ⅱ为79.7、105.5 mm,与支护方案Ⅰ相近且塑性破坏单元最少,支护方案Ⅲ位移变形量最大分别为83.8、111.1 mm;在支护效果相近的情况下,支护方案Ⅱ的支护成本仅为方案Ⅰ的64.7%。工程实践结果表明:支护方案Ⅱ的实际支护效果能实现巷道的安全支护。