Fault rupture propagation in soil with intercalation using nonlocal model and softening modulus modification

Fault rupture propagation is more complex in the overlying soil with intercalation than in homogeneous soil,and it is challenging to simulate this phenomenon accurately using the finite element method.To address this issue,an improved nonlocal model that incorporates softening modulus modification is proposed.The methodology has the advantage that the solutions are independent of both mesh sizes and characteristic lengths,while maintaining objective softening rates of materials.Using the proposed methodology,a series of numerical simulations are conducted to investigate the effects of different mechanical parameters,such as elastic modulus,friction angle and dilation angle of the soil within the intercalation,as well as the impact of geometries,such as the depth and thickness of the intercalation,on the fault rupture progress.This study not only provides significant insights into the mechanisms of fault rupture propagation,specifically in relation to intercalations,but also shows a great value in promoting the current research on fault rupture.

Simplified approach for design of raft foundations against fault rupture.Part II:soil-structure interaction

This is the second paper of two, which describe the results of an integrated research effort to develop a four-step simplified approach for design of raft foundations against dip-slip （normal and thrust） fault rupture. The first two steps dealing with fault rupture propagation in the free-field were presented in the companion paper. This paper develops an approximate analytical method to analyze soil-foundation-structure interaction （SFSI）, involving two additional phenomena： （i） fault rupture diversion （Step 3）; and （ii） modification of the vertical displacement profile （Step 4）. For the first phenomenon （Step 3）, an approximate energy-based approach is developed to estimate the diversion of a fault rupture due to presence of a raft foundation. The normalized critical load for complete diversion is shown to be a function of soil strength, coefficient of earth pressure at rest, bedrock depth, and the horizontal position of the foundation relative to the outcropping fault rupture. For the second phenomenon （Step 4）, a heuristic approach is proposed, which ＂scans＂ through possible equilibrium positions to detect the one that best satisfies force and moment equilibrium. Thus, we account for the strong geometric nonlinearities that govern this interaction, such as uplifting and second order （P-△） effects. Comparisons with centrifuge-validated finite element analyses demonstrate the efficacy of the method. Its simplicity makes possible its utilization for preliminary design.

Simplified approach for design of raft foundations against fault rupture.Part I:free-field

Over the past few decades, earthquake engineering research mainly focused on the effects of strong seismic shaking. After the 1999 earthquakes in Turkey and Taiwan, and thanks to numerous cases where fault rupture caused substantial damage to structures, the importance of faulting-induced deformation has re-emerged. This paper, along with its companion （Part Ⅱ）, exploits parametric results of finite element analyses and centrifuge model testing in developing a four-step semi-analytical approach for analysis of dip-slip （normal and thrust） fault rupture propagation through sand, its emergence on the ground surface, and its interaction with raft foundations. The present paper （Part Ⅰ） focuses on the effects of faulting in the absence of a structure （i.e., in the free-field）. The semi-analytical approach comprises two-steps： the first deals with the rupture path and the estimation of the location of fault outcropping, and the second with the tectonically- induced displacement profile at the ground surface. In both cases, simple mechanical analogues are used to derive simplified semi-analytical expressions. Centrifuge model test data, in combination with parametric results from nonlinear finite element analyses, are utilized for model calibration. The derived semi-analytical expressions are shown to compare reasonably well with more rigorous experimental and theoretical data, thus providing a useful tool for a first estimation of near-fault seismic hazard.

A new method to calculate near-field radiation excited by heterogeneous fault rupture

This paper derives from the representation theory the formula for calculating the radiation excited by heterogeneous fault rupture based on box-like discretization scheme. Preliminary validation indicates that our algorithm has very high computation precision and efficiency; therefore, it is a very practical tool to investigate strong ground motion problems. Additionally, the equations given in this study can also be used to invert the fault rupture process.

A novel mitigation measure for normal fault-induced deformations on pile-raft systems

Evidence from recent earthquakes has shown destructive consequences of fault-induced permanent ground movement on structures.Such observations have increased the demand for improvements in the design of structures that are dramatically vulnerable to surface fault ruptures.In this study a novel connection between the raft and the piles is proposed to mitigate the hazards associated with a normal fault on pile-raft systems by means of 3D finite element(FE)modeling.Before embarking on the parametric study,the strain-softening constitutive law used for numerical modeling of the sand has been validated against centrifuge test results.The exact location of the fix-head and unconnected pile-raft systems relative to the outcropping fault rupture in the free-field is parametrically investigated,revealing different failure mechanisms.The performance of the proposed connection for protecting the pile-raft system against normal fault-induced deformations is assessed by comparing the geotechnical and structural responses of both types of foundation.The results indicate that the pocket connection can relatively reduce the cap rotation and horizontal and vertical displacements of the raft in most scenarios.The proposed connection decreases the bending moment response of the piles to their bending moment capacity,verging on a fault offset of 0.6 m at bedrock.

3D simulation of near-fault strong ground motion: comparison between surface rupture fault and buried fault

In this paper, near-fault strong ground motions caused by a surface rupture fault （SRF） and a buried fault （BF） are numerically simulated and compared by using a time-space-decoupled, explicit finite element method combined with a multi-transmitting formula （MTF） of an artificial boundary. Prior to the comparison, verification of the explicit element method and the MTF is conducted. The comparison results show that the final dislocation of the SRF is larger than the BF for the same stress drop on the fault plane. The maximum final dislocation occurs on the fault upper line for the SRF; however, for the BE the maximum final dislocation is located on the fault central part. Meanwhile, the PGA, PGV and PGD of long period ground motions （≤ 1 Hz） generated by the SRF are much higher than those of the BF in the near-fault region. The peak value of the velocity pulse generated by the SRF is also higher than the BE Furthermore, it is found that in a very narrow region along the fault trace, ground motions caused by the SRF are much higher than by the BF. These results may explain why SRFs almost always cause heavy damage in near-fault regions compared to buried faults.

Evaluation of crustal deformation and associated strong motions induced by the 2022 Paktika earthquake,Afghanistan

The 2022 Paktika earthquake(moment magnitude:6.2) occurred on June 22,2022,near the border between the Khost and Paktika Provinces of Afghanistan,causing heavy damage and casualties in Paktika Province.This study evaluated the crustal deformation and associated strong motions induced by the Paktika earthquake.Crustal deformations were determined using the Differential Interferometric Synthetic Aperture Radar(DInSAR) technique and three-dimensional finite element method(3DFEM) and the results were compared.The permanent ground displacements obtained from the DInSAR and 3D-FEM analyses were similar in terms of amplitude and areal distribution.Strong motions were estimated using the 3D-FEM with and without considering regional topography.The estimations of maximum ground acceleration,velocity,and permanent ground deformations were compared among each other as well as with those inferred from failures of some simple structures in the Spera and Gayan districts.The inferred maximum ground acceleration and velocity from the failed adobe structures were more than 300 Gal and 50 cm/s,respectively,nearly consistent with the estimates obtained using empirical methods.The empirical method yielded a maximum ground acceleration of 347 Gal,whereas the maximum ground velocity was approximately50 cm/s.In light of these findings,some surface expressions of crustal deformations and strong ground motions,such as failures of soil and rock slopes and rockfalls,have been presented.The rock slope failures in the epicentral area were consistent with those observed during various earthquakes in Afghanistan and worldwide.

Fault activation and induced seismicity in geological carbon storage--Lessons learned from recent modeling studies

In the light of current concerns related to induced seismicity associated with geological carbon sequestration(GCS),this paper summarizes lessons learned from recent modeling studies on fault activation,induced seismicity,and potential for leakage associated with deep underground carbon dioxide(CO2) injection.Model simulations demonstrate that seismic events large enough to be felt by humans require brittle fault properties and continuous fault permeability allowing pressure to be distributed over a large fault patch to be ruptured at once.Heterogeneous fault properties,which are commonly encountered in faults intersecting multilayered shale/sandstone sequences,effectively reduce the likelihood of inducing felt seismicity and also effectively impede upward CO2leakage.A number of simulations show that even a sizable seismic event that could be felt may not be capable of opening a new flow path across the entire thickness of an overlying caprock and it is very unlikely to cross a system of multiple overlying caprock units.Site-specific model simulations of the In Salah CO2storage demonstration site showed that deep fractured zone responses and associated microseismicity occurred in the brittle fractured sandstone reservoir,but at a very substantial reservoir overpressure close to the magnitude of the least principal stress.We conclude by emphasizing the importance of site investigation to characterize rock properties and if at all possible to avoid brittle rock such as proximity of crystalline basement or sites in hard and brittle sedimentary sequences that are more prone to injection-induced seismicity and permanent damage.

Study on anti-faulting design process of Urumqi subway line 2 tunnel crossing reverse fault

For the tunnel crossing active fault,the damage induced by fault movement is always serious.To solve such a problem,a detailed anti-faulting tunnel design process for Urumqi subway line 2 was introduced,and seven three-dimensional elastic-plastic finite element models were established.The anti-faulting design process included three steps.First,the damage of tunnel lining from different locations of fault rupture surfaces was analyzed.Then,the analysis of the effect on tunnel buried depth was given.Finally,the effect of the disaster mitigation method on the flexible joint was verified and the location of the flexible joint was discussed.The results show that when the properties of surrounding rock at the tunnel bottom grows soft,the tunnel deformation curve is smoother and tunnel damage induced by fault movement is less serious.The vertical displacement change ratio of secondary linings along the tunnel axis may be the main factor to cause shear damage to the tunnel.The interface between the hanging wall and fracture zone is defined as the most adverse fault rupture surface.The tunnel damage was reduced with the decrease in the tunnel buried depth as more energy was dissipated by overburden soil and the differential uplift zone of soil became more diffuse.The method of the flexible joint can reduce the tunnel damage significantly and the disaster mitigation effect of different locations on the flexible joint is different.The tunnel damage is reduced by the greatest degree when the flexible joint is located on the fault rupture surface.

Soil bentonite wall protects foundation from thrust faulting: analyses and experiment

When seismic thrust faults emerge on the ground surface, they are particularly damaging to buildings, bridges and lifelines that lie on the rupture path. To protect a structure founded on a rigid raft, a thick diaphragm-type soil bentonite wall （SBW） is installed in front of and near the foundation, at sufficient depth to intercept the propagating fault rupture. Extensive numerical analyses, verified against reduced-scale （1 g） split box physical model tests, reveal that such a wall, thanks to its high deformability and low shear resistance, ＂absorbs＂ the compressive thrust of the fault and forces the rupture to deviate upwards along its length. As a consequence, the foundation is left essentially intact. The effectiveness of SBW is demonstrated to depend on the exact location of the emerging fault and the magnitude of the fault offset. When the latter is large, the unprotected foundation experiences intolerable rigid-body rotation even if the foundation structural distress is not substantial.

Potential rupture surface model and its ap-plication on probabilistic seismic hazard analysis

Potential sources are simplified as point sources or linear sources in current probabilistic seismic hazard analysis （PSHA） methods. Focus size of large earthquakes is considerable, and fault rupture attitudes may have great influence upon the seismic hazard of a site which is near the source. Under this circumstance, it is unreasonable to use the simplified potential source models in the PSHA, so a potential rupture surface model is proposed in this paper. Adopting this model, we analyze the seismic hazard near the Chelungpu fault that generated the Chi-Chi （Jiji） earthquake with magnitude 7.6 and the following conclusions are reached. （1） This model is reasonable on the base of focal mechanism, especially for sites near potential earthquakes with large magnitude; （2） The attitudes of potential rupture surfaces have great influence on the results of probabilistic seismic hazard analysis and seismic zoning.

Recent advances in imaging crustal fault zones: a review

Crustal faults usually have a fault core and surrounding regions of brittle damage, forming a low-velocity zone （LVZ） in the immediate vicinity of the main slip interface. The LVZ may amplify ground motion, influence rupture propagation, and hold important information of earthquake physics. A number of geophysical and geodetic methods have been developed to derive high-resolution structure of the LVZ. Here, I review a few recent approaches, including ambient noise cross-correlation on dense across-fault arrays and GPS recordings of fault-zone trapped waves. Despite the past efforts, many questions concerning the LVZ structure remain unclear, such as the depth extent of the LVZ. High-quality data from larger and denser arrays and new seismic imaging technique using larger portion of recorded waveforms, which are currently under active development, may be able to better resolve the LVZ structure. In addition, effects of the alongstrike segmentation and gradational velocity changes across the boundaries between the LVZ and the host rock on rupture propagation should be investigated by conducting comprehensive numerical experiments. Furthermore, high-quality active sources such as recently developed large-volume airgun arrays provide a powerful tool to continuously monitor temporal changes of fault-zone properties, and thus can advance our understanding of fault zone evolution.

Source rupture process of the 2015 Gorkha, Nepal Mw7.9 earthquake and its tectonic implications

On 25 April, 2015, an Mw7.9 earthquake occurred in Nepal, which caused great economic loss and casualties. However, almost no surface ruptures were observed. Therefore, in order to interpret the phenomenon, we study the rupture process of the earthquake to seek answers. Inversion of teleseismic body-wave data is applied to estimate the rupture process of the 2015 Nepal earthquake. To obtain stable solutions, smoothing and non-negative constraints are introduced. 48 teleseismic stations with good coverage are chosen. Finite fault model is established with length and width of 195 km and 150 km, and we set the initial seismic source parameters referring to CMT solutions. Inversion results indicate that the focal mechanism of this earthquake is a thrust fault type, and the strike, dip and rake angle are in accordance with CMT results. The seismic moment is 0.9195 ×10^（21）Nm（Mw7.9）, and source duration is about 70s. The rupture nucleated near the hypocenter and then propagated along the dip direction to the southeast, and the maximum slip amounts to 5.2 m. Uncertainties on the amount of slip retrieved by different inversion methods still exist, the overall characteristics are inconsistent. The lack of shallow slip during the 2015 Gorkha earthquake implies future seismic hazard and this region should be paid more attention to.

Far-field analysis of effects of unilateral rupturing fault on the space correlation of strong ground motion

On the assumption that seismic source is simplified as linear rupture fault with finite length, this paper qualitatively studies the seismic source effects on space correlation of strong ground motion. Based on expanding expression of Fourier spectrum of strong ground motion with space coordinate variables, this paper also gives a expression of describing correlation of strong ground motion field. According to far-field condition, the theoretical formula of the expression can be obtained. Furthermore, this paper presents a theoretical formula of estimation the radius of strong ground motion field, which depends on expansion condition of Fourier spectrum of strong ground motion, with space variables. At last, taking one earthquake as an example, this paper gives three-dimension patterns of radius of the field with epicenter distance and azimuth as well as frequency.

Design of bridges against large tectonic deformation

The engineering community has devoted much effort to understanding the response of soil-structure systems to seismic ground motions, but little attention to the effects of an outcropping fault offset. The 1999 earthquakes of Turkey and Taiwan, offering a variety of case histories of structural damage due to faulting, have （re）fueled the interest on the subject. This paper presents a methodology for design of bridges against tectonic deformation. The problem is decoupled in two analysis steps： the first （at the local level） deals with the response of a single pier and its foundation to fault rupture propagating through the soil, and the superstructure is modeled in a simplified manner; and the second （at the global level） investigates detailed models of the superstructure subjected to the support （differential） displacements of Step 1. A parametric study investigates typical models of viaduct and overpass bridges, founded on piles or caissons. Fixed-head piled foundations are shown to be rather vulnerable to faulting-dnduced deformation. End-bearing piles in particular are unable to survive bedrock offsets exceeding 10 cm. Floating piles perform better, and if combined with hinged pile-to-cap connections, they could survive much larger offsets. Soil resilience is beneficial in reducing pile distress. Caisson foundations are almost invariably successful. Statically-indeterminate superstructures are quite vulnerable, while statically-determinate are insensitive （allowing differential displacements and rotations without suffering any distress）. For large-span cantilever-construction bridges, where a statically determinate system is hardly an option, inserting resilient seismic isolation bearings is advantageous as long as ample seating can prevent the deck from falling off the supports. An actual application of the developed method is presented for a major bridge, demonstrating the feasibility of design against tectonic deformation.

The Doppler effect induced by earthquakes:A case study of the Wenchuan MS8.0 earthquake

Seismologists have found that the first arrival frequencies of P waves at different seismic stations have different widths,that is,different periods or frequencies,and they think that this phenomenon can be used to identify whether a Doppler effect is induced by earthquakes.However,the fault rupture process of a real earthquake is so complex that it is difficult to identify a frequency shift similar to the Doppler effect.A method to identify whether a Doppler effect is induced by an earthquake is proposed here.If a seismic station is in the direction of fault rupture propagation,this station could observe a Doppler effect induced by the earthquake.The Doppler effect causes the frequency of the seismic wave to shift from low frequency to high frequency,and the high frequency amplitudes become mutually superimposed.Under the combined influences of the absorption effect,geometric spreading effect and Doppler effect,the high frequency amplitude of the seismic wave will gradually become higher than the low frequency amplitude with increasing epicentral distance.If we find that the high frequency amplitude is higher than the low frequency amplitude with increasing epicentral distance in the direction of fault rupture propagation,then there is a Doppler effect.The fault that generated the Wenchuan earthquake is a reverse fault,and its horizontal rupture propagation velocity was low.To link fault rupture propagation velocity with the Doppler effect and identify the Doppler effect more easily,we decompose three-component records into two directions:the direction of fault rupture propagation and the direction perpendicular to the fault rupture propagation along the fault plane.The initial components of the two directions are processed by wavelet transform.Several seismic stations in the direction of fault rupture propagation of the Wenchuan earthquake were selected,and it was found that with increasing epicentral distance,the high frequency amplitudes of the wavelet spectra become obviously higher than the low frequency amplitudes.It can be concluded that due to the existence of the Doppler effect,high frequency amplitudes can overcome the influences of the absorption and geometric spreading effects on seismic waves in the fault rupture propagation process.

The May 23 and 24, 1994 Taiwan earth quakes: comparison of source process between the two events

Inversion for the seismic fault rupture history is an important way to study the nature of the earthquake source. Inthis paper, we have selected two Taiwan earthquakes that occurred closely in time and located in the same region,inversed the distribution of the slip amplitudes, rakes, risetimes and the rupture times on the fault planes by usingGDSN broad-band and long-period records and the adaptive hybrid global search algorithm, and compared the twoevents. The slip rate of every subfault calculated provides information about the distribution of tectonic stress andfault strength. To the former event (Ms=6.0), the maximum slip amplitude 2.4 m and the minimum risetime 1.2 sare both located at the hypocentre. The latter earthquake (Ms=6.6) consisted of two subevents and the second source has 4 s delay. The maximum slip amplitUde 0.9 m located near hypocentre is corresponding to the minimumrisetime l.4 s, and the corresponding maximum slip rate 0.7 m.s~-1 is similar to the peak value of other large sliprate areas. We consider that the latter event has more complicated temporal-spatial distribution than the former.

A Simple Model for Earthquake Instability

Based on the heterogeneity of fault plane strength,the macro rupture process of a fault plane can be treated as the rupture accumulation process of local micro-elements in the fault surface.Assuming that the strength of the local micro-elements follows the Weibull probability distribution,the macro-fault constitutive relationship of the complete load-deformation process is derived from a statistical mechanics viewpoint.Applying a one-dimensional earthquake mechanics model and using far-field displacement a as the control variable,the problem of earthquake instability is investigated by employing the stability theory.The results show that the system stiffness ratio(stiffness ratio of fault to surroun-ding rock) β is the important parameter that affects the occurrence of earthquakes.Earthquake instability occurs only when β < 1,and the sudden stress jump appears at the displacement turning point of the equilibrium path curve.The expression of three important parameters for earthquakes(fault half-dislocation distance after earthquake,earthquake stress drop and elastic energy release) is also given.When β≥1,the earthquake does not occur and the fault only slips slowly without an earthquake.

Source models for the 2016 Mw6.0 Hutubi earthquake, Xinjiang,China: A possible reverse event

South and north-dipping nodal planes from the U.S. Geological Survey moment tensor solution were used to invert global teleseismic body waves to reveal the source rupture process of the December 8, 2016, Mw6.0 Hutubi earthquake. The results show that a compact pattern is the main feature of this event for only one main slip zone located at the hypocenter for both models, The slip distributions are dominated by a nearly pure-thrust fault, and there is no apparent surface rupture. The inversion revealed that the slip zone extends 10 km along strike and 12 km along dip. The released total seismic moment was about 9.0 -1017 Nm, corresponding to a magnitude of Mw6.0. It is difficult to solve for a best-fit rupture plane due to the sample slip pattern without obvious rupture directivity. This makes the far- field teleseismic data not sensitive enough to determine the fault geometric parameters. The source model of the reverse north-dipping plane fits well with the observed waveforms, and the results of the aftershock relocation outline a trend of north-dipping profiles, indicating the possibility of a reverse event. The inverted normal fault beneath the Qigu fold, interpreted by geological and seismic studies, may be the seismogenic fault for this reverse event.

Centrifuge experiments for shallow tunnels at active reverse fault intersection

Tunnels extend in large stretches with continuous lengths of up to hundreds of kilometers which are vulnerable to faulting in earthquake-prone areas.Assessing the interaction of soil and tunnel at an intersection with an active fault during an earthquake can be a beneficial guideline for tunnel design engineers.Here,a series of 4 centrifuge tests are planned and tested on continuous tunnels.Dip-slip suface faulting in reverse mechanism of 60°is modeled by a fault simulator box in a quasi-static manner.Failure mechanism,progression and locations of damages to the tunnels are assessed through a gradual increase in Permanent Ground Displacement(PGD).The ground surface deformations and strains,fault surface trace,fault scarp and the sinkhole caused by fault movement are observed here.These ground surface deformations are major threats to stability,safety and serviceability of the structures.According to the observations,the modeled tunnels are vulnerable to reverse fault rupture and but the functionality loss is not abrupt,and the tunnel will be able to tolerate some fault displacements.By monitoring the progress of damage states by increasing PGD,the fragility curves corresponding to each damage state were plotted and interpreted in related figures.