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.

Source parameters and aftershock pattern of the October 7,2021,M5.9 Harnai earthquake,Pakistan

On October 7,2021,a magnitude 5.9 earthquake struck the Harnai(Baluchistan)region of Pakistan,causing several fatalities and injuries within the epicentral area.First-order tectonic deformation in this region is caused by the convergence of the Indian Plate with respect to the Eurasian Plate.The Katwaz Block hinders the motion of the Indian Plate,resulting in the formation of strike-slip faults.In this study,the P-wave first-motion polarity technique was used to determine the mainshock faulting style.Cyclic scanning of the polarity solutions was applied to determine the most suitable focal mechanism solution among the available solutions generated by the FOCMEC(focal mechanism)software.The nodal planes correspond to different faulting styles(i.e.,thrust and strike-slip faulting).A nodal plane oriented in the NW-SE direction corresponded to a strike-slip mechanism,which was considered to be the fault plane.Tectonically,this earthquake was associated with the Harnai-Karahi strike-slip fault zone owing to the fault strike and direction of slip.The apparent stress drop,fault length,and moment magnitude of the Harnai earthquake were 35.4 bar,6.1 km,and 5.9,respectively.A lower b-value for the Gutenberg-Richter law was observed prior to the earthquake.Higherα-than b-values(α>b)indicate that this earthquake was governed by large events as opposed to small-magnitude events.The Harnai sequence had a decay exponent close to unity,lasted for 145 days,and produced few aftershocks.The study will help the future hazard mitigation in the region.

Fault plane parameters of Tancheng M81/2 earthquake on the basis of present-day seismological data

The great Tancheng earthquake of M81/2 occurred in 1668 was the largest seismic event ever recorded in history in eastern China. This study determines the fault geometry of this earthquake by inverting seismological data of present-day moderate-small earthquakes in the focal area. We relocated those earthquakes with the double-difference method and found focal mechanism solutions using gird test method. The inversion results are as follows： the strike is 21.6°, the dip angle is 89.5°, the slip angle is 170°, the fault length is about 160 km, the lower-boundary depth is about 32 km and the buried depth of upper boundary is about 4 km. This shows that the seismic fault is a NNE-trending upright right-lateral strike-slip fault and has cut through the crust. Moreover, the surface seismic fault, intensity distribution of the earthquake, earthquake-depth distribution and seismic-wave velocity profile in the focal area all verified our study result.

Tunnel effect of fractal fault and transient S-wave velocity rupture (TSVR) of in-plane shear fault

Transient S wave velocity rupture (TSVR) means the velocity of fault rupture propagation is between S wave velocity α and P wave velocity β . Its existing in the rupture of in plane ( i.e . strike slip) fault has been proved, but in 2 dimensional classical model, there are two difficulties in transient S wave velocity rupture, i.e ., initialization difficulty and divergence difficulty in interpreting the realization of TSVR. The initialization difficulty means, when v ↑ v R (Rayleigh wave velocity), the dynamic stress strength factor K 2(t) →+0, and changes from positive into negative in the interval ( v R, β ). How v transit the forbidden of ( v R, β )? The divergence difficulty means K 2(t) →+∞ when v ↓ β . Here we introduce the concept of fractal and tunnel effect that exist everywhere in fault. The structure of all the faults is fractal with multiple cracks. The velocity of fault rupture is differentiate of the length of the fault respect to time, so the rupture velocity is also fractal. The tunnel effect means the dynamic rupture crosses over the interval of the cracks, and the coalescence of the intervals is slower than the propagation of disturbance. Suppose the area of earthquake nucleation is critical or sub critical propagation everywhere, the arriving of disturbance triggers or accelerates the propagation of cracks tip at once, and the observation system cannot distinguish the front of disturbance and the tip of fracture. Then the speed of disturbance may be identified as fracture velocity, and the phenomenon of TSVR appears, which is an apparent velocity. The real reason of apparent velocity is that the mathematics model of shear rupture is simplified of complex process originally. The dual character of rupture velocity means that the apparent velocity of fault and the real velocity of micro crack extending, which are different in physics, but are unified in rupture criterion. Introducing the above mentioned concept to the calculation of K 2 (t) , the difficulty of initialization can be overcome, and the integral equation of triggering the initialization of TSVR is given quantitatively. By solving this integral equation, the lower limit of TSVR is 1.105 3 β , not β , and the divergence difficulty is overcome. TSVR is unstable solution, and may degenerate to sub Rayleigh wave velocity rupture immediately where the non critical condition can be measured. The results of this paper show that the initialization and continuum depends on the condition of earthquake nucleation in seismogenic area.

Application of fuzzy clustering method to determining sub-fault planes of earthquake from aftershocks sequence

Earthquake rupture process generally involves several faults activities instead of a single fault A new method using both fuzzy clustering and principal component analysis makes it possible to reconstruct three dimensional structure of involved faults in earthquake if the aftershocks around the active fault planes distribute uniformly. When seismic events are given, the optimal faults structures can be determined by our new method. Each of sub-fault planes is fully characterized by its central location, length, width, strike and dip. The resolution determines the number of fault segments needed to describe the earthquake catalog. The higher the resolution, the finer the structure of the reconstructed fault segments. The new method successfully reconstructs the fault segments using synthetic earthquake catalogs. By taking the 28 June 1992 Landers earthquake oceured in southern California as an example, the reconstructed fault segments are consistent with the faults already known on geological maps or blind faults that appeared quite frequently in longer-term catalogs.

Study on the distribution characteristics of faults and their control over petroliferous basins in the China seas and its adjacent areas

As one of the main controlling factors of oil and gas accumulation,faults are closely related to the distribution of oil and gas reservoirs.Studying how faults control petroliferous basins is particularly important.In this work,we investigated the plane positions of major faults in the China seas and its adjacent areas using the normalized vertical derivative of the total horizontal derivative(NVDR-THDR)of the Bouguer gravity anomaly,the fusion results of gravity and magnetic anomalies,and the residual Bouguer gravity anomaly.The apparent depths of major faults in the China seas and its adjacent areas were inverted using the Tilt-Euler method based on the Bouguer gravity anomaly.The results show that the strikes of the faults in the China seas and its adjacent areas are mainly NE and NW,followed by EW,and near-SN.Among them,the lengths of most ultra-crustal faults are in the range of 1000–3000 km,and their apparent depths lie between 10 km and 40 km.The lengths of crustal faults lie between 300 km and 1000 km,and their apparent depths are between 0 km and 20 km.According to the plane positions and apparent depths of the faults,we put forward the concept of fault influence factor for the first time.Based on this factor,the key areas for oil and gas exploration were found as follows:the east of South North China Basin in the intracontinental rift basins;the southeast region of East China Sea Shelf Basin,the Taixinan and Qiongdongnan basins in the continental margin rift basins;Zhongjiannan Basin in the strike-slip pull-apart basins;the Liyue,Beikang,and the Nanweixi basins in the rifted continental basins.This work provides valuable insights into oil and gas exploration,mineral resource exploration,and deep geological structure research in the China seas and its adjacent areas.

Applications of seismic moment tensor inversion in fast response to earthquakes

Using the technique of seismic moment tensor inversion, the source mechanisms of 10 earthquakes with Ms5.2that occurred in China from November 1996 to January 1998 were determined rapidly. The determined resultswere sent as 'Bulletins of Source Mechanism Parameters of Earthquakes' to the Seismic Regime Guards' Office,China Seismological Bureau, and the relevant provincial seismological bureaus. These bulletins have played rolein the fast response to large earthquakes.

Is Ziarat a Potential Site for Conventional or Unconventional Energy Resources?

A structural interpretation of the Ziarat block in the Balochistan region （a part of the Suleiman Fold and Thrust Belt） has been carried out using seismic and seismological data. Seismic data consists of nine 2.5D pre-stack migrated seismic lines, whereas the seismological data covers the Fault Plane Solution and source parameters. Structural interpretation describes two broad fault sets of fore and back thrusts in the study area that have resulted in the development of pop-up structures, accountable for the structural traps and seismicity pattern in terms of seismic hazard. Seismic interpretation includes time and depth contour maps of the Dungan Formation and Ranikot group, while seismological interpretation includes Fault Plane Solution, that is correlated with a geological and structural map of the area for the interpretation of the nature of the subsurface faults. Principal stresses are also estimated for the Ranikot group and Dungan Formation. In order to calculate anisotropic elastic properties, the parameters of the rock strength of the formations are first determined from seismic data, along with the dominant stresses （vertical, minimum horizontal, and maximum horizontal）. The differential ratio of the maximum and minimum horizontal stresses is obtained to indicate optimal zones for hydraulic fracturing, and to assess the potential for geothermal energy reservoir prospect generation. The stress maps indicate high values towards the deeper part of the horizon, and low towards the shallower part, attributed to the lithological and structural variation in the area. Outcomes of structural interpretation indicate a good correlation of structure and tectonics from both seismological and seismic methods.

Stress value in 2003 Dayao Ms6.1 earthquake source region

The Ms6.2 Dayao, Yunnan, earthquake occurred on July 21, 2003, followed by a major Ms6.1 earthquake about 88 days later in the same region. Hypocenters of the two earthquakes are almost in the same place. Based on the P wave first motion polarities of the two aftershock sequences recorded by temporary stations, we have studied the stress field in the aftershock zone and obtained the two stress field directions in Dayao region using the new version of PKU_Grid^Test Software provided by Chunquan Yu. Assuming that the rotation of the stress field is caused by the second main shock, we estimated the crustal stress value in the focal region by using the stress value calculation method proposed by Yongge Wan. The estimated maximum, intermediate and minimum principal stresses are 166.3 MPa, 158.7 MPa and 151 MPa, respectively, before the second main shock. The normal and shear stresses projected on the fault plane of the second main shock before it occurred are 157.3 MPa, 7.4 MPa, and are 158.8 MPa, 0.2 MPa after it occurred, respectively. The perturbed input parameters experiments attest the stability of the solution. The result shows that the preseismic shear stress is larger than the post-seismic one, and their difference corresponds to the stress drop approximately. The estimated compressive stress level is very high, but the differential stress is low. The result is helpful for friction coefficient estimation, plate motion simulation and related studies.

Study on the Triggering Effect of the October, 2005 Pakistan M_W7.6 Earthquake on Its Aftershocks

The influences upon aftershocks of Coulomb failure stress change (CFSC) generated by the main-shock of the October 8, 2005, Pakistan earthquake are calculated and analyzed. The following factors are included in the calculation: (1) the difference between the pore fluid pressure and the medium elastic constant in the fault plane area and those of its surrounding medium; (2) the tectonic stress direction of the seismic source area; (3) the aftershock failure mechanism of aftershocks is calculated by stacking the tectonic stress with the stress change generated by the main-shock. Our study, which includes many factors, fits fairly well with the aftershock distribution. It indicates that most of the aftershocks were triggered by the Pakistan main-shock that occurred on October 8, 2005.