Stress Release Model Research Articles

Numerical Simulation and Experimental Study on Detecting Effective Prestress of 1860-Grade Strands Based on the Drilling Method

In this paper, we study the magnitude of the effective prestressing force of steel strands in prestressed reinforced concrete structures. Through the theory of micro-hole release, the functional relationship equation between tensile stress and strain-containing coefficients A and B is established. Then, Midas FEA NX 2022 (v1.1) finite element software is used to establish the stress-release model of strand drilling holes and analyze the influence of parameters such as drilling depth, drilling diameter, hole–edge distance, and tension stress on the amount of stress release. Finally, through a homemade tensioning platform, we verify the reasonableness of the finite element simulation calculation law and determine coefficients A and B. The results of the study show that based on Kirsch’s analytical formula and the theory of microvia release, the axial tension force and axial strain are linearly correlated; the Midas FEA NX finite element software can effectively simulate the force state of strand cross-section; and through the strand-drilled hole model simulation and analysis, it is found that the tension stress value and the stress-release amount are related to the tensile stress value and the tensile stress value. We found that the value of tensile stress and the amount of stress released are positively correlated; with the increase in the hole margin, the amount of stress released gradually decreases; with the increase in the diameter of the hole, the amount of strain released gradually increases; and the greater the depth of the hole, the greater the amount of strain release. Moreover, the use of a hole margin of 3–6 mm, a hole diameter of 1.5 mm and 1.8 mm, and a hole depth of 2.5 mm is more reasonable in the test conditions, as follows. Through the drilling test conditions of 1.5 mm drilling diameter, 2.5 mm drilling depth, and 4 mm hole side distance, we verified the measured strain value of the steel wire and the tensile force value of the linear correlation between the functional relationship and the use of this functional relationship to determine the theoretical derivation of the coefficient to be determined: A is 1.12 and B is 57.84.

Spatiotemporal Evolution of Microseismicity Seismic Source Properties at the Irpinia Near-Fault Observatory, Southern Italy

ABSTRACTWe estimate the source parameters of small-magnitude earthquakes that occurred during 2008–2020 in the Irpinia faults area (southern Italy). We apply a spectral decomposition approach to isolate the source contribution from propagation and site effects for ∼3000 earthquakes in the local magnitude range between ML 0 and 4.2. We develop our analyses in three steps. First, we fit the Brune (1970) model to the nonparametric source spectra to estimate corner frequency and seismic moment, and we map the spatial distribution of stress drop across the Irpinia area. We found stress drops in the range 0.4–8.1 MPa, with earthquakes deeper than 7 km characterized by higher average stress drop (i.e., 3.2 MPa). Second, assuming a simple stress-release model (Kanamori and Heaton, 2000), we derive fracture energy and critical slip-weakening distance. The spatial variability of stress drop and fracture energy allows us to image the present stress conditions of fault segments activated during the 23 November 1980 Ms 6.9 earthquake. The variability of the source parameters shows clear patterns of the fault mechanical properties, suggesting that the Irpinia fault system can be divided into three main sectors, with the northern and southern ones showing different properties from the central one. Our results agree with previous studies indicating the presence of fluids with different composition in the different sectors of the Irpinia fault system. In the third step, we compare the time evolution of source parameters with a time series of geodetic displacement recorded near the fault system. Temporal trends in the correlation between geodetic displacement and different source parameters indicate that the poroelastic deformation perturbation generated by the karst aquifer recharge is modulating not only the occurrence rate of microseismicity (D’Agostino et al., 2018) but may lead to rupture asperities with different sizes and characteristics.

A constrained-memory stress release model (CM-SRM) for the earthquake occurrence in the Corinth Gulf (Greece)

The complexity of seismogenesis requires the development of stochastic models, the application of which aims to improve our understanding on the seismic process and the associated underlying mechanisms. Seismogenesis in the Corinth Gulf (Greece) is modeled through a Constrained-Memory Stress Release Model (CM-SRM), which combines the gradual increase of the strain energy due to continuous slow tectonic strain loading and its sudden release during an earthquake occurrence. The data are treated as a point process, which is uniquely defined by the associated conditional intensity function. In the original form of the Simple Stress Release Model (SSRM), the conditional intensity function depends on the entire history of the process. In an attempt to identify the most appropriate parameterization that better fits the data and describes the earthquake generation process, we introduce a constrained “ $$m$$ -memory” point process, implying that only the $$m$$ most recent arrival times are taken into account in the conditional intensity function, for some suitable $$m \in N$$ . Modeling of this process is performed for moderate earthquakes (M ≥ 5.2) occurring in the Corinth Gulf since 1911, by considering in each investigation different number of steps backward in time. The derived model versions are compared with the SSRM in its original form and evaluated in terms of information criteria and residual analysis.

Simulating pulsar glitches: anN-body solver for superfluid vortex motion in two dimensions

ABSTRACTA rotating superfluid forms an array of quantized vortex lines that determine its angular velocity. The spasmodic evolution of the array under the influence of deceleration, dissipation, and pinning forces is thought to be responsible for the phenomenon of pulsar glitches, sudden jumps in the spin frequency of rotating neutron stars. We describe and implement an N-body method for simulating the motion of up to 5000 vortices in two dimensions and present the results of numerical experiments validating the method, including stability of a vortex ring and dissipative formation of an Abrikosov array. Vortex avalanches occur routinely in the simulations, when chains of unpinning events are triggered collectively by vortex–vortex repulsion, consistent with previous, smaller scale studies using the Gross–Pitaevskii equation. The probability density functions of the avalanche sizes and waiting times are consistent with both exponential and lognormal distributions. We find weak correlations between glitch sizes and waiting times, consistent with astronomical data and meta-models of pulsar glitch activity as a state-dependent Poisson process or a Brownian stress-accumulation process, and inconsistent with a threshold-triggered stress-release model with a single, global stress reservoir. The spatial distribution of the effective stress within the simulation volume is analysed before and after a glitch.

A Stress Release Model in Egypt

The complexity of seismogenesis calls for probabilistic rather than deterministic model. Towards that direction, the stress release models transpose the elastic rebound theory in a stochastic framework, where the stress level in a region increases gradually between earthquakes due to constant tectonic loading and is released suddenly when an event occurs. The data are modeled through point processes and particularly by means of the hazard function. The application is performed using moderate earthquakes (M ≥ 4.8) occurred in Egypt and the model is compared with the Poisson model by means of information criteria.

Linked stress release model and its application on earthquake data in java and sumatra

Elastic rebound theory explains stress release model in which stress will increase deterministically and decrease stochastically because of earthquake. Based on earthquakes occurrences, an area interacts with the other areas. Stress movement and interaction among areas have not been considered in stress release model. In this article, stress release model is developed into linked stress release model by considering interaction among areas. This model can be stated through conditional intensity function depending on accumulated stress release when earthquake occurs in a sub-region within a time period. The conditional intensity function is presented by exponential hazard function where each region has different hazard function stating that each region has specific characteristic. This research data consists of earthquake data occurring in Java Island and Sumatra Island during the period of January 2010 to December 2016. By using maximum likelihood estimate method, estimation of conditional intensity function of linked stress release model for earthquakes in each region is obtained. Probability of earthquake occurrence in southern Java is the same as probability in northern Sumatra. Most of proportion of accumulated stress in northern and southern Java is derived from their own regions while most of proportion of accumulated stress in northern and southern Sumatra is derived from other region.

Failure models driven by a self-correcting point process in earthquake occurrence modeling

The long-term recurrence of strong earthquakes is often modeled according to stationary Poisson processes for the sake of simplicity. However, renewal and self-correcting point processes (with nondecreasing hazard functions) are more appropriate. Short-term models mainly fit earthquake clusters due to the tendency of an earthquake to trigger other earthquakes. In this case, self-exciting point processes with nonincreasing hazard are especially suitable. To provide a unified framework for analysis of earthquake catalogs, Schoenberg and Bolt proposed the short-term exciting long-term correcting model in 2000, and in 2005, Varini used a state-space model to estimate the different phases of a seismic cycle. Both of these analyses are combinations of long-term and short-term models, and the results are not completely satisfactory, due to the different scales at which these models appear to operate. In this study, we propose alternative modeling. First, we split a seismic sequence into two groups: the leader events, non-secondary events the magnitudes of which exceed a fixed threshold; and the remaining events, which are considered as subordinate. The leader events are assumed to follow the well-known self-correcting point process known as the stress-release model. In the interval between two subsequent leader events, subordinate events are expected to cluster at the beginning (aftershocks) and at the end (foreshocks) of that interval; hence, they are modeled by a failure process that allows bathtub-shaped hazard functions. In particular, we examined generalized Weibull distributions, as a large family that contains distributions with different bathtub-shaped hazards, as well as the standard Weibull distribution. The model is fit to a dataset of Italian historical earthquakes, and the results of Bayesian inference based on the Metropolis–Hastings algorithm are shown.

A study on seismicity in the Yunnan region by using the multidimensional stress release model

The long-term seismic activity in the Yunnan region has attracted much attention due to frequent occurrences of disastrous earthquakes. We investigated the seismicity of the Yunnan region using the multidimensional stress release model (MSRM) to evaluate the long-term seismic hazard. MSRM combines three factors that affect earthquake occurrence, i.e., initial stress background, tectonic loading, and coseismic stress transfer, and can simulate and forecast the spatiotemporal seismicity. In this study, a complete catalog comprising 28 strong earthquakes (M ≥ 6.5) after 1900 in the Yunnan region was investigated using MSRM. We calculated the spatiotemporal variations of seismicity rates, and found that strong earthquakes occur at locations with higher seismic activity. Comparisons between the seismicity rates at the epicenter locations immediately before and after strong earthquakes show that the seismicity rates in the vicinity of the epicenters significantly decrease after strong earthquakes. The estimated seismicity rates at the ending time (January 1, 2025) suggest that strong earthquake potential in the section between Kunming and Huaning of the Xiaojiang fault and the northeastern section of the Lijiang-Xiaojinhe fault should receive more attention, while the seismicity in the southwestern part decreases and the seismicity in the middle segment of the Red River fault remains low.

Higher Strength and Ductility than Diamond: Nanotwinned Diamond/Cubic Boron Nitride Multilayer.

Recently, the nanotwinned structure has attracted considerable attention because of unprecedented improvement in its mechanical properties, thermal stability, and other properties. Here, we introduce the nanotwinned structure between two superhard materials [diamond and cubic boron nitride (cBN)] and obtain a nanotwinned diamond/cBN multilayered material with ultrahigh strength and unprecedented ductility. Under continuous shear deformation, the stress and total energy in the material develop in a zigzag way because of atomic reconfiguration. Further research shows that atomic reconfiguration occurs preferentially in the cBN region, followed by that in the diamond region by partial slip, and finally occurs at the interface through alternate "exchange" of the positions of C and B atoms. This multilevel stress release model can account for the significant increase in the strain range and peak stress of nanotwinned materials. These results could provide available information for the design of superhard materials with multilevel resistance to plastic deformation.

A restricted Linked Stress Release Model (LSRM) for the Corinth gulf (Greece)

The earthquake occurrence in the Corinth Gulf (Greece) is modeled by means of the Linked Stress Release Model, which combines the gradual increase of the strain energy due to continuous tectonic loading and its sudden release when an event occurs. The modeling is based on the theory of stochastic point processes and it is determined by the conditional intensity function. The modeled time–dependent seismicity incorporates stress transfer and interactions among the major fault segments that belong either to the western or to the eastern part of the study area. Static stress changes caused by the coseismic slip of eight characteristic events that occurred during the instrumental era were calculated. Their perturbations reveal that earthquakes occurring in the eastern part provoke excitation in the western part while the events that occurred in the western part do not affect the seismicity of the eastern part. This result was taken into account and the values of the model parameters were constrained accordingly. The analysis is also performed on synthetic earthquake catalogs developed by an earthquake simulator algorithm that can replicate the seismic activity in the study area and yields to comparable results.

SEISMIC HAZARD ASSESSMENT FOR THE CORINTH GULF AND CENTRAL IONIAN ISLANDS BY MEANS OF THE LINKED STRESS RELEASE MODEL

Εarthquake generation causes spatio-temporal stress changes on adjacent fault segments that can alter the occurrence probability of subsequent earthquakes onto them. The interaction is investigated with the Linked Stress Release Model, applied to fit historical data from two areas that accommodate high seismicity, the Corinth Gulf and the Central Ionian Islands. These two areas are divided in two subareas, based on seismotectonic features; Corinth Gulf is divided in the western and eastern part, whereas the area of Central Ionian Islands is divided in Kefalonia and Lefkada subareas. The results establish interactions between the subareas, especially in the Central Ionian Islands, and underline the differences in tectonic structures and earthquake mechanisms between these areas. Particularly, the seismicity in the Central Ionian Islands is proved to be more complex and active and yet more difficult to be examined, whereas the LSRM fits the Corinth Gulf data more easily.

Application of a linked stress release model in Corinth Gulf and Central Ionian Islands (Greece)

Spatio-temporal stress changes and interactions between adjacent fault segments consist of the most important component in seismic hazard assessment, as they can alter the occurrence probability of strong earthquake onto these segments. The investigation of the interactions between adjacent areas by means of the linked stress release model is attempted for moderate earthquakes (M ≥ 5.2) in the Corinth Gulf and the Central Ionian Islands (Greece). The study areas were divided in two subareas, based on seismotectonic criteria. The seismicity of each subarea is investigated by means of a stochastic point process and its behavior is determined by the conditional intensity function, which usually gets an exponential form. A conditional intensity function of Weibull form is used for identifying the most appropriate among the models (simple, independent and linked stress release model) for the interpretation of the earthquake generation process. The appropriateness of the models was decided after evaluation via the Akaike information criterion. Despite the fact that the curves of the conditional intensity functions exhibit similar behavior, the use of the exponential-type conditional intensity function seems to fit better the data.

Stress release model and proxy measures of earthquake size. Application to Italian seismogenic sources

This study presents a series of self-correcting models that are obtained by integrating information about seismicity and fault sources in Italy. Four versions of the stress release model are analyzed, in which the evolution of the system over time is represented by the level of strain, moment, seismic energy, or energy scaled by the moment. We carry out the analysis on a regional basis by subdividing the study area into eight tectonically coherent regions. In each region, we reconstruct the seismic history and statistically evaluate the completeness of the resulting seismic catalog. Following the Bayesian paradigm, we apply Markov chain Monte Carlo methods to obtain parameter estimates and a measure of their uncertainty expressed by the simulated posterior distribution. The comparison of the four models through the Bayes factor and an information criterion provides evidence (to different degrees depending on the region) in favor of the stress release model based on the energy and the scaled energy. Therefore, among the quantities considered, this turns out to be the measure of the size of an earthquake to use in stress release models. At any instant, the time to the next event turns out to follow a Gompertz distribution, with a shape parameter that depends on time through the value of the conditional intensity at that instant. In light of this result, the issue of forecasting is tackled through both retrospective and prospective approaches. Retrospectively, the forecasting procedure is carried out on the occurrence times of the events recorded in each region, to determine whether the stress release model reproduces the observations used in the estimation procedure. Prospectively, the estimates of the time to the next event are compared with the dates of the earthquakes that occurred after the end of the learning catalog, in the 2003–2012 decade.

Probability distribution of the waiting time in the stress release model: the Gompertz distribution

This communication aims to show some results on the distribution of the waiting time of a self-correcting point process that is known in seismology as the stress release model, and in actuarial sciences as the classical risk model. By assuming this model and conditional on the history of the process up to time $$t$$ , the waiting time of the next event from $$t$$ follows a Gompertz distribution, in which the shape parameter is history dependent. This reveals some new features of the model: (1) Just after a major event, a high probability can be attributed to very short waiting times, and not exclusively to long ones; (2) By updating the history while waiting for the next event, the expected waiting time is postponed in time and its variance decreases. We illustrate the application of a stress release model to a sequence of Italian earthquakes. A Bayesian approach is proposed to consider the uncertainty of the model parameters.

Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany

Time-dependent probabilistic seismic hazard assessment requires a stochastic description of earthquake occurrences. While short-term seismicity models are well-constrained by observations, the recurrences of characteristic on-fault earthquakes are only derived from theoretical considerations, uncertain palaeo-events or proxy data. Despite the involved uncertainties and complexity, simple statistical models for a quasi-period recurrence of on-fault events are implemented in seismic hazard assessments. To test the applicability of statistical models, such as the Brownian relaxation oscillator or the stress release model, we perform a systematic comparison with deterministic simulations based on rate- and state-dependent friction, high-resolution representations of fault systems and quasi-dynamic rupture propagation. For the specific fault network of the Lower Rhine Embayment, Germany, we run both stochastic and deterministic model simulations based on the same fault geometries and stress interactions. Our results indicate that the stochastic simulators are able to reproduce the first-order characteristics of the major earthquakes on isolated faults as well as for coupled faults with moderate stress interactions. However, we find that all tested statistical models fail to reproduce the characteristics of strongly coupled faults, because multisegment rupturing resulting from a spatiotemporally correlated stress field is underestimated in the stochastic simulators. Our results suggest that stochastic models have to be extended by multirupture probability distributions to provide more reliable results.

A new multidimensional stress release statistical model based on coseismic stress transfer

SUMMARY Following the stress release model (SRM) proposed by Vere-Jones (1978), we developed a new multidimensional SRM, which is a space–time–magnitude version based on multidimensional point processes. First, we interpreted the exponential hazard functional of the SRM as the mathematical expression of static fatigue failure caused by stress corrosion. Then, we reconstructed the SRM in multidimensions through incorporating four independent submodels: the magnitude distribution function, the space weighting function, the loading rate function and the coseismic stress transfer model. Finally, we applied the new model to analyse the historical earthquake catalogues in North China. An expanded catalogue, which contains the information of origin time, epicentre, magnitude, strike, dip angle, rupture length, rupture width and average dislocation, is composed for the new model. The estimated model can simulate the variations of seismicity with space, time and magnitude. Compared with the previous SRMs with the same data, the new model yields much smaller values of Akaike information criterion and corrected Akaike information criterion. We compared the predicted rates of earthquakes at the epicentres just before the related earthquakes with the mean spatial seismic rate. Among all 37 earthquakes in the expanded catalogue, the epicentres of 21 earthquakes are located in the regions of higher rates. The map of predicted earthquake rates at the ending time (1997 January 1) suggests that the next destructive earthquake in North China is likely to occur in the regions south of Datong, north of Beijing and east of Hejian.

Underground water stress release models

The accumulation of tectonic stress may cause earthquakes at some epochs. However, in most cases, it leads to crustal deformations. Underground water level is a sensitive indication of the crustal deformations. We incorporate the information of the underground water level into the stress release models (SRM), and obtain the underground water stress release model (USRM). We apply USRM to the earthquakes occurred at Tangshan region. The analysis shows that the underground water stress release model outperforms both Poisson model and stress release model. Monte Carlo simulation shows that the simulated seismicity by USRM is very close to the real seismicity.

Seismic hazard assessment in central Ionian Islands area (Greece) based on stress release models

The long-term probabilistic seismic hazard of central Ionian Islands (Greece) is studied through the application of stress release models. In order to identify statistically distinct regions, the study area is divided into two subareas, namely Kefalonia and Lefkada, on the basis of seismotectonic properties. Previous results evidenced the existence of stress transfer and interaction between the Kefalonia and Lefkada fault segments. For the consideration of stress transfer and interaction, the linked stress release model is applied. A new model is proposed, where the hazard rate function in terms of X(t) has the form of the Weibull distribution. The fitted models are evaluated through residual analysis and the best of them is selected through the Akaike information criterion. Based on AIC, the results demonstrate that the simple stress release model fits the Ionian data better than the non-homogeneous Poisson and the Weibull models. Finally, the thinning simulation method is applied in order to produce simulated data and proceed to forecasting.

Gambling scores for earthquake predictions and forecasts

SUMMARY This paper presents a new method, namely the gambling score, for scoring the performance earthquake forecasts or predictions. Unlike most other scoring procedures that require a regular scheme of forecast and treat each earthquake equally, regardless their magnitude, this new scoring method compensates the risk that the forecaster has taken. Starting with a certain number of reputation points, once a forecaster makes a prediction or forecast, he is assumed to have betted some points of his reputation. The reference model, which plays the role of the house, determines how many reputation points the forecaster can gain if he succeeds, according to a fair rule, and also takes away the reputation points betted by the forecaster if he loses. This method is also extended to the continuous case of point process models, where the reputation points betted by the forecaster become a continuous mass on the space–time–magnitude range of interest. We also calculate the upper bound of the gambling score when the true model is a renewal process, the stress release model or the ETAS model and when the reference model is the Poisson model.

Non-Poissonian earthquake occurrence in coupled stress release models and its effect on seismic hazard

SUMMARY Most seismic hazard estimations are based on the assumption of a Poisson process for earthquake occurrence, even though both observations and models indicate a departure of real seismic sequences from this simplistic assumption. Instrumental earthquake catalogues show earthquake clustering on regional scales while the elastic rebound theory predicts a periodic recurrence of characteristic earthquakes on longer timescales for individual events. Recent implementations of time-dependent hazard calculations in California and Japan are based on quasi-periodic recurrences of fault ruptures according to renewal models such as the Brownian Passage Time model. However, these renewal models neglect earthquake interactions and the dependence on the stressing history which might destroy any regularity of earthquake recurrences in reality. To explore this, we investigate the (coupled) stress release model, a stochastic version of the elastic rebound hypothesis. In particular, we are interested in the time-variability of the occurrence of large earthquakes and its sensitivity to the occurrence of Gutenberg‐Richter type earthquake activity and fault interactions. Our results show that in general large earthquakes occur quasi-periodically in the model: the occurrence probability of large earthquakes is strongly decreased shortly after a strong event and becomes constant on longer timescales. Although possible stress-interaction between adjacent fault zones does not affect the recurrence time distributions in each zone significantly, it leads to a temporal clustering of events on larger regional scales. The non-random characteristics, especially the quasi-periodic behaviour of large earthquakes, are even more pronounced if stress changes due to small earthquakes are less important. The recurrence-time distribution for the largest events is characterized by a coefficient of variation from 0.6 to 0.84 depending on the relative importance of small earthquakes.