Medium Earthquakes Research Articles

Conservativeness Study on the Seismic Analysis Method for Research Reactor Plant Structure Based on TMSR-LF1

The seismic performance analysis of research reactor plants is crucial for ensuring the safety of the entire reactor system. This paper analyzes the plant structure seismic performance of the 2WMt Thorium Molten Salt Reactor-Liquid Fuel 1 (TMSR-LF1) at the Shanghai Institute of Applied Physics, Chinese Academy of Sciences under the action of frequent earthquakes, fortification earthquakes, and rare earthquakes was analyzed by finite element software PKPM based on the seismic design method of civil code +1°. On this basis, a comparison was made between the seismic responses of structural pushover analysis and elastoplastic time history analysis under the action of rare earthquakes, and the conservatism of these two commonly used methods for elastoplastic analysis was systematically analyzed. The results indicate that the TMSR-LF1 plant structure exhibits well bearing and deformation capacity. It meets the seismic design goal of “no damage under small earthquakes,” “no unrepairable damage under medium earthquakes,” and “no collapse under large earthquakes (using static pushover analysis),” and the critical regions are entirely within the elastic range. Furthermore, the analysis reveals that the elastoplastic time history analysis method produced a significantly higher seismic response than the pushover analysis method, which indicates the conservativeness of the time history method. Therefore, it is recommended to use the elastoplastic time history analysis method to evaluate the seismic performance of research reactor plants under rare earthquake actions. The research in this paper provides important references for the seismic performance analysis of other Class II research reactor plants.

Seismic performance of self-centring connections with two energy dissipation stages for reusable modular steel buildings

This paper presented a feasibility study on a self-centring connection with two energy dissipation stages for use as a combined inter-module and intra-module connection in reusable modular steel buildings. The proposed connection was equipped with shape memory alloy (SMA) disc washers and friction dampers, the former for self-centring and the latter for energy-dissipation functions. The design concept of two energy dissipation stages was to achieve structural longevity and member reuse by 1) enabling rapid recovery after small and medium earthquakes, and 2) facilitating prompt repair if at all needed after large earthquakes. A spring analytical model was proposed, wherein each connection component was symbolised as a rotational spring. Based on the model, a design methodology to meet the two-stage performance goals was derived, where the critical story drift ratio between the two stages was expressed as a function of the properties of friction dampers and SMA disc washers. Detailed finite element simulations were used to validate the proposed design concept and the spring model and to assess the influence of the friction dampers and SMA disc washers on the hysteresis behaviour of the connection. The results demonstrated that the proposed connection would facilitate the design objectives when designed based on the proposed spring model to ensure structural longevity, member reuse, and efficient recovery and repair after seismic events.

Microseismicity of the Persian Gulf and the Zagros Mountain Massif According to Bottom Seismological Observations

Bottom seismological observations in the Persian Gulf over a short period made it possible to detect weak earthquakes with magnitudes (ML = –0.2–2.9), whose sources are located in the mantle under its water area and under the Zagros mountain range. On the section built across the coastline of the Persian Gulf, under the Zagros Mountains, the projections of the sources of the detected earthquakes form seismic focal layers, steeply dipping into the mantle to the northeast to depths of 120–180 km. The spatial distribution of strong and medium earthquakes, obtained from the updated earthquake catalog of the US Geological Survey and the ISC International Seismological Catalog, does not contradict the distribution of sources of micro- and weak earthquakes, but complements it, forming a separate seismic focal layer. According to the data obtained as a result of bottom seismological observations, the entire thickness of the earth’s crust of the region and the upper mantle, and not only the upper layers of the crust, as presented in a number of publications, are seismically active. It is possible that collision processes and accompanying phenomena (mantle seismicity and destruction of the granitic layer of the earth’s crust) are associated with the presumed presence and rotation of the earth’s surface with the center of rotation in the area of about. Cyprus.

Experimental Study on the New Type of Connecting Nodes of Prefabricated Stairs Using Flexible Grouting Material

In recent years, prefabricated buildings have been developing positively in China. Prefabricated concrete stairs are widely used in prefabricated concrete buildings because of their quick construction, convenient handling, reduced cost, and premium appearance. They also have promising application potential in cast-in-place concrete structures and steel buildings. The stairs are important escape routes during earthquakes and play the role of “safety islands.” Therefore, the study on the seismic performance of connecting nodes of prefabricated concrete stairs is significant. For a new flexible-hinge connecting node of the prefabricated stairs with flexible grouting material (FGM), the low-frequency cyclic loading test is carried out in this paper to study the stress performance of the end nodes of the stairs under in-plane and out-of-plane low-frequency cyclic loading. The results show that the new flexible-hinge connecting nodes of the prefabricated concrete stairs have moderate bearing capacity and stiffness, which can mitigate the effect of diagonal bracing under small and medium earthquakes and dissipate energy to a certain extent.

Study on seismic vulnerability analysis of the interaction system between saturated soft soil and subway station structures

The seismic vulnerability of interaction system of saturated soft soil and subway station structures was explored in this paper. The coupled nonlinear numerical models of interaction system were established using the u–p formulation of Biot′s theory to describe the saturated two-phase media. A refined finite element model of interaction system was developed to study its nonlinear seismic responses and seismic hazard mechanism. In this study, the multi-yield elastoplastic constitutive model was adopted for the soil, while a fiber section elastoplastic constitutive model was used for the structure. The seismic response of the structure was calculated by inputting the artificial seismic wave obtained from the power spectrum-triangular series method. The maximum inter-story drift angle was taken as a structural performance parameter for the subway station structure. The structural demand cloud was obtained under random ground motion sequences. Based on the probabilistic seismic demand model analysis method, the seismic vulnerability curve of the subway station structure was plotted, and the seismic vulnerability curve was analyzed as per the vulnerability of performance parameters. With the increase of soil strength, the vulnerability index of subway station structure under different peak acceleration ground motion decreased correspondingly. Based on the above vulnerability theory and analysis methods, it can be found from the above vulnerability theory and analysis methods that the subway station structure with established buried depth in saturated soft soil site exhibits a certain degree of safety and reliability, and can meet the seismic fortification goal of "no damage in small earthquakes, repairable in medium earthquakes and no collapse in large earthquakes". The results of vulnerability analysis are in line with the actual seismic survey, and the vulnerability analysis method proposed in this paper can be applied to the vulnerability analysis of underground structures on saturated soft soil foundation.

Effect of Numerous Small Deformations Due to Moderate Earthquakes on Seismic Response of Wooden Houses

In order to confirm the effect of multiple moderate earthquakes on the response deformation of wooden houses at the time of a major earthquake, an earthquake response analysis, considering performance deterioration due to repeated small deformations, was conducted. As a result, it was found that the effect of multiple moderate earthquakes on the mean response deformation during a major earthquake was small. On the other hand, in some cases, the response deformation was up to 1.2 times larger than that of the sound case. In the case of a house where the response deformation was near the criteria of continuous use and/or collapse, the influence of the response magnification was large. This shows the importance of giving higher seismic performance compared to the standard. The response deformation during repeated medium earthquakes may increase for houses with considerably low seismic performance. However, for the houses that meet current standards, little to no increase in response deformation was seen.

Seismic evaluation of a traditional Chinese palace-style timber structure

To assess the seismic performance of a traditional Chinese palace-style timber structure, an extended discrete element method (EDEM) model has been established. The model has been applied to analyze a single-story and five-bay timber-frame palace architecture, where sliding isolation of the column foot, semi-rigid connections of mortise and tenon joints, and damping characteristics of bracket sets (known as Dougong in Chinese) have been considered. The study investigates the dynamic characteristics, seismic responses, and structural vulnerabilities of the palace building. Results show that an error of the natural frequency between the EDEM model and results from code-recommended empirical formulas is only 6.88%, highlighting the rationality of the EDEM model. Furthermore, the relative displacement response of each position increases with the increment of inputting acceleration of seismic waves. The inter-structural layer drift of the column-beam frame is the largest and that of the roof truss is smaller, while Dougongs are the smallest. The likelihood of moderate damage is highest during a small earthquake, while the structure is prone to severe damage under a medium earthquake, The structure is susceptible to collapse under a large earthquake.

Quantitative Evaluation of Seismic Performance for Truss Structures Based on the Condition Number of Dynamic Matrix

The quantitative analysis of seismic performance under small and moderate earthquakes is of great significance. However, only using the stiffness distribution index is no longer applicable to seismic performance evaluation, and the influence of mass distribution must be introduced. In this study, under the action of small and medium earthquakes, the equation of motion can be simplified into the equilibrium equation of the dynamic matrix by the quasi-static method. Furthermore, a condition number index of dynamic matrix is proposed to evaluate the seismic performance of truss structures, which can consider both stiffness distribution and mass distribution. Then, the correctness of the proposed index is verified by comparing with the displacement and strain indexes. In addition, the performance of truss structure is studied by the condition number of stiffness matrix, mass matrix and dynamic matrix. It is found that since the condition number of stiffness matrix and the condition number of mass matrix cannot consider both stiffness and mass, it is not comprehensive to use these two indexes to evaluate the seismic performance of truss structures. The evaluation result based on the condition number of dynamic matrix is more reasonable under small and medium earthquakes.

Frequency-Dependent Velocity Changes of the 2018 Ms 4.5 Shimian Earthquake Revealed by Repeating Earthquakes

Abstract The wide application of seismic dense arrays has facilitated the monitoring of the coseismic velocity disturbance of small and medium earthquakes. In this study, a repeating earthquake cluster near the 2018 Ms 4.5 Shimian earthquake was relocated based on 10 groups of repeating earthquakes that occurred from 2013 to 2019, which were recorded by the Xichang seismic array. A repeating pair was obtained by estimating the overlap of the rupture region. Coda-wave interferometry was carried out in different frequency bands using the moving window cross spectrum and wavelet-domain trace stretching (WTS) methods. Our results show that velocity change at each frequency point can be obtained with the WTS method, and thus its frequency resolution is higher. In addition, the velocity changes of coda waves strongly depend on the frequency in the Shimian area, varying from +0.10% in the high-frequency band (5–10 Hz) to −0.23% in the low-frequency band (0.5–2 Hz). In particular, XC04, which is the station that closest to the epicenter, shows the largest velocity change in the low-frequency band, but the velocity change gradually decreases as the distance from the epicenter increases. It has been suggested that the low-frequency components of the coda waves of repeating earthquakes are more sensitive to medium variation. Combined with the earthquake relocation in the Shimian area, it was found that the normalized depth sensitivity calculated based on scattered waves can retain >10% sensitivity in the source area of the Shimian earthquake. Furthermore, the negative velocity changes calculated from low-frequency coda waves are likely attributed to the Shimian earthquake. It is recommended that the average interstation spacing of seismic dense array should be <30 km to facilitate the monitoring of the coseismic changes of small and medium earthquakes.

Characteristics of stress field and crustal kinematics of the southern region of Sichuan-Yunnan block, southern Tibet Plateau

The Red River fault is a massive tectonic shear zone of the Sichuan-Yunnan block, southern Tibet Plateau. The target area of this study is the Red River fault's middle-northern section and adjacent areas. Considering the spatial difference of tectonic structures and the inhomogeneity of focal mechanism solutions, we divided the target area into three structural units: the northern extension area, the middle strike-slip movement area, and the west complex rupture area. The study is carried out on the basis of zoning. Using the CAP method to invert the focal mechanism of moderate earthquakes and the principal compressive and tensile stress. Restoring the seismic source spectrum of small and medium earthquakes, then inversion the stress drops in three sub-units based on Brune model using digital waveform records. Our study suggests that: (1) Many high-stress drop earthquakes occurred in the transitional areas from the Weixi-Qiaohou fault to the Red River fault and from the Chuxiong fault to the Qujiang fault, also occurred in the Changning-Baoshan-Yongping area, revealing a large accumulation of local tectonic stress. (2) Some events with Δσ ≥ 20 MPa have occurred in the prominent low-speed anomaly area, indicating that a passive deformation crossed the Red River fault and extended to the west. Yangbi MS 6.4 earthquake (2021) occurred in a strongly locked area with high potential earthquake risk. (3) In the north of the study region, the movement of the Sichuan-Yunnan block to SE-SSE orientation was governed by the dextral strike-slip movement of the NW strike fault; in the middle region, the SE-orientated movement of the block relative to the South China block was governed by the sinistral slip movement of the SN-strike faults; and in the west region, the tectonic stress was governed by clockwise rotation of the block and the sinistral slip movement of the NE strike faults. We suggest that strike slip and rotation of the Red River fault's middle section may drive and aggravate passive movement in the north section, resulting in locally geophysical field responses. Therefore, the potential risk of a large earthquake in the middle-northern section of the Red River fault should be monitored.

Temporal variation in crustal shear wave splitting associated with a moderate earthquake around Nias Island, Indonesia

We investigate temporal variation in shear-wave splitting parameters of local earthquakes around Nias Island, the northern part of Sumatran forearc. We analyse a total of 79 high-quality splitting measurements recorded at a GEOFON seismic station (GSI) from 2009-2015. We observe that there is no clear time variation in the fast polarization of the splitting waves. On the other hand, an increase in the delay time of the splitting waves is found prior to a medium earthquake that occurred around the island in August 2010. Therefore, we suggest that this temporal change may be related to the change in crack geometry of rocks following the accumulation of the stress in the crust before the earthquake occurred.

Seismicity map to analyze the depth and magnitude earthquake zone in Kwandang Area of North Gorontalo Regency

Kwandang is a district located in the northern part of Gorontalo. The purpose of this research is to analyze the depth and magnitude earthquake zone that occurred in the district of Kwandang, Gorontalo Utara regency based on seismicity map. The astronomical research location is located at 0° 49' 39" S, 122° 55' 8" E. The method used in this research is seismicity map analysis. The earthquake that dominates in Kwandang, based on the value of its depth, namely shallow earthquake (0-70 km) and medium earthquake (70-300 km). This is caused by subduction activity in the direction of the subduction of the north arm of Sulawesi towards south of Tomini Bay. Whereas based on the strength of the earthquake in Kwandang sub-district is dominated by small earthquakes (-) with a light, mild earthquake. Based on the depth zonation, earthquakes mostly occurred in the west. Based on the magnitude, the earthquakes mostly occurred in the southwest.

Pengelolaan Wilayah Pesisir Berbasis Pengurangan Risiko Bencana Gempabumi dan Tsunami di Kabupaten Kulon Progo Daerah Istimewa Yogyakarta

This study discussed about management of coastal area in Kulon Progo Regency based on the risk of the earthquake and tsunami. The aim of this study was to identify potential hazard earthquake and tsunami, analyze the suitability of using land exists to spatial pattern planning, and describe direction of management area’s coastal based on reduction of earthquake and tsunami risk in Kulon Progo Regency. Data was used in this study was information about earthquake and tsunami occurrence obtained from the government institution and also United States Geological Survey (USGS), satelite imagary from digital globe. Data of spatial policy which was used in this study were document of Area Spatial Planing, Coastal Zoning Plan, and small islands at study site. Analyzer used in this study were spatial analyzis, peak ground acceleration analyzis, cross tabulation, and descriptive-qualitative. The result of this study showed that coastal’s area in Kulon Progo Regency categorized as having a medium earthquake with PGA value 134, 754 gal  and a high tsunami potential with an area of 7702, 614 Ha. The results of the assessment of the conformity of existing land use in 2016 to the spatial plan in the document of Coastal Zoning Plan of Kulon Progo Regency in 2014-2034 tends to show high deviation of space with the extent of using land mismatch of 10399,139 Ha of the total area of research. Based on that, the direction of coastal management of Kulon Progo Regency has five management scenarios, namely; (1) scenario a-1 in the form of early warning and direction of high population density; (2) b-I scenario in the form of early warning, mitigation, and direction of high population density; (3) b-II scenario in the form of warning, mitigation, and direction of medium population density; (4) b-III scenario in the form of early warning, mitigation, and low population density direction; and (5) scenario c-III in the form of early warning, mitigation, preparedness and low population density directive.

Shaking-table tests of a full-scale ten-story reinforced-concrete building (FY2015). Phase I: Free-standing system with base sliding and uplifting

In this paper, results are presented from shaking-table tests of a full-scale 10-story reinforced-concrete structure to confirm the behavior of a free-standing system with a base that permits both sliding and uplifting. The purpose of this system is to use the seismic resistance of the structure during a small or medium earthquake and a sliding and uplifting behavior of the free-standing system during a large earthquake. Cast-iron plates were installed on the grade beams of the lower part of the specimen building to generate a low friction coefficient. Thus, the specimen building should be able to move sideways during large earthquakes, although the specimen building should not move sideways during small earthquakes. In the tests, the specimen building was moved sideways during tests with JMA-Kobe 25%, 50%, and 100% amplitude excitations but not during that with JMA-Kobe 10% amplitude excitation, and the specimen building was uplifted at one of its corners for all amplitude excitations. The base sliding displacement was 84–189 mm, and the corner uplift was 5–40 mm. The sliding and uplift behavior led to small maximum inter-story drift ratios, and these behaviors did not increase the base overturning moments. Thus, allowing sliding and uplifting behavior can reduce building damage in an extremely large earthquake.

An Analysis of Rural Households' Earthquake-Resistant Construction Behavior: Evidence from Pingliang and Yuxi, China.

Due to the lack of earthquake-resistant rural houses, small and medium earthquakes caused massive casualties in rural China. In 2004, China began implementing the Earthquake Rural Housing Safety Project Policy (ERHSPP) to reduce earthquake losses, mainly promoting the adoption of earthquake-resistant structures in rural residents’ self-built houses through subsidies, training of construction craftsmen, and provision of earthquake-resistant housing drawings. We conducted a field survey, collecting 1169 rural households in Pingliang, Gansu Province, and 1501 rural households in Yuxi, Yunnan Province, China. We studied Earthquake-Resistant Construction Behaviors (E-RCB) by the logistic and the ordered logistic regression models. Results show that government housing subsidy promotes E-RCB of rural households; E-RCB was affected by ERHSPP, positively correlated with economic status and housing earthquake damage; E-RCB was negatively correlated with structure danger, house age, and earthquake experience; and housing earthquake damage, not earthquake experience, strikingly promoted E-RCB in rural China. The results could provide suggestions in communication risk strategies for the government. We suggest the local government should promote local acceptable disaster propaganda, provide hierarchical housing subsidies, pay attention to housing seismic supervision, publish earthquake-resistant housing design drawings, and conduct more earthquake-resistant technical training for rural craftsmen.

Crustal Density Inversion and Its Tectonic Structure in Badong-Zigui Area

Objectives The Badong-Zigui Basin is located in the west of the Three Gorges area, and it is surrounded by four different tectonic units: With the Xuefengshan thick-soil tectonic belt on the south, the Qinling orogenic belt on the north, the Huangling anticline on the east, and the eastern extension of the Sichuan Basin in the west. The Badong-Zigui basin is a north-south syncline structure, the sediments in the basin are dominated by Late Triassic-Late Turassic argillaceous rocks, and the special tectonic setting causes strong tectonic activities in the basin. Methods Using a three-dimensional gravity inversion algorithm based on Lagrangian multiplier constraints, the local Bouguer gravity anomaly in Badong-Zigui area is inverted, and the underground three-dimensional density structure of Badong-Zigui and adjacent areas is obtained. Results The inversion results show that the Zigui Basin is a low-density area compared with the surrounding area. The sedimentation thickness in the east is deeper than that in the west, and the sediment density is lower than that in the west. The small and medium earthquakes in the area are basically 4-12 km underground. Conclusions The north-south and north-east ancient water flows in the northern edge of the Zigui Basin successively provide sources for the sedimentation and filling of the basin, forming a structure with lower material density and deeper deposits in the eastern part of the basin; low-density materials in the east are transported and accumulated to the west in the basin. At the same time, it is squeezed by the eastward extension of the Sichuan Basin, and it is speculated that there is a tendency of east-west movement and compression in the basin.

Concept and Behavior of a Steel Ring Restrainer with Variable Stiffness and Buffer Capacity

In this paper, a novel restrainer called steel ring restrainer (SRR) is proposed to prevent the unseating of bridges. The restrainer is comprised of a steel ring, an upper guiding pulley, a downward guiding pulley, and two connections. The SRR can provide different stiffnesses under different seismic excitations. The SRR is not activated under daily load but provides smaller stiffness in small and medium earthquakes and even larger stiffness in strong earthquakes. The stiffness changes smoothly from small and medium earthquakes to strong earthquakes. This mechanism called buffer capacity reduces the impact on the connection between the SRR and structure. In order to study the effect of each design parameter on the mechanical properties of the SRR, 54 finite element (FE) models in four groups were established and analyzed. The results show that the diameter of the cross-section of the steel ring has an important influence on the initial stiffness, secondary stiffness, buffering capacity, and ultimate bearing capacity of the SRR, the radius of the curved part of the steel ring significantly affected the initial stiffness and ultimate displacement, the nonworking length of the SRR was decided by the length of the straight part of the steel ring, and the diameter of the guide pulley governed the ultimate bearing capacity and ultimate displacement. Additionally, the predicted formulas of the design parameters were derived and eight models were employed to investigate the effectiveness of the formulas, in order to be applied in the seismic design.

Monitoring the Processes of Interseismic Accumulation and Coseismic Release of Stresses in the Medium Nearby Earthquake Sources Based on the Analysis of Tidal Response of the Earth’s Surface

Abstract—The Global Seismographic Network (GSN) incorporating more than 150 seismic stations all over the world allows recording not only high-frequency seismic signals but also the response of the medium to semidiurnal and diurnal tidal impact. The correlation method for the analysis of GSN data developed by us makes it possible to detect variations in the amplitudes of tidal response associated with elastic moduli of the medium with an accuracy of 0.5%. The processes of stress accumulation and fracturing in the zone of a tectonic fault can significantly affect elastic properties of the medium which, in turn, may cause changes in tidal response of the medium in the vicinity of the earthquake’s source. In this work, a linear dependence is detected between the change in the amplitude of tidal response at GSN stations and the magnitude of the coseismic stress change in the medium in the vicinity of the station estimated from GPS data. The developed method for the analysis of tidal tilts can be used for studying the processes of accumulation and redistribution of tectonic stresses before the strong earthquakes in seismically active regions.

Seismic Analysis and Evaluation of Y-shaped EBF with an Innovative SSL-SSBC

During severe earthquakes, the ductility and energy dissipation capacity of shear links in Y-shaped eccentrically braced frames (EBFs) are crucial to achieve desirable seismic performance and structural safety. In this study, an innovative SSL-SSBC combining the advantages of a shear slotted bolted connection (SSBC) and a very short shear link is developed to improve the seismic performance of Y-shaped EBFs. Finite element (FE) analysis methods are first validated through comparison with existing experimental results for slotted bolted connection and very short shear links. Further, FE simulations of the SSBC, very short shear link with shear slotted bolted connection (SSL-SSBC), and Y-shaped EBF are conducted to determine their mechanical behavior systematically. The FE results demonstrate that a reasonable SSBC can effectively increase the ductility and energy dissipation capacity through friction slipping, allowing the SSBC to maintain elastic behavior throughout the entire range of seismic loading, while the very short shear link in the SSL-SSBC could undergo severe damage to dissipate seismic energy. As expected, the SSL-SSBC is capable of working as both a shear dissipation damper and a metallic ductile damper in the Y-shaped EBF. This study also clearly identifies that no yielding or damage of the very short shear links occurs during small and medium earthquakes, and the deformation and damage of the very short shear link can be minimized during severe earthquakes, allowing the seismic resilience capacity of the Y-shaped EBF to be dramatically enhanced.

A Distributed Multi-Sensor Machine Learning Approach to Earthquake Early Warning

Our research aims to improve the accuracy of Earthquake Early Warning (EEW) systems by means of machine learning. EEW systems are designed to detect and characterize medium and large earthquakes before their damaging effects reach a certain location. Traditional EEW methods based on seismometers fail to accurately identify large earthquakes due to their sensitivity to the ground motion velocity. The recently introduced high-precision GPS stations, on the other hand, are ineffective to identify medium earthquakes due to its propensity to produce noisy data. In addition, GPS stations and seismometers may be deployed in large numbers across different locations and may produce a significant volume of data consequently, affecting the response time and the robustness of EEW systems.In practice, EEW can be seen as a typical classification problem in the machine learning field: multi-sensor data are given in input, and earthquake severity is the classification result. In this paper, we introduce the Distributed Multi-Sensor Earthquake Early Warning (DMSEEW) system, a novel machine learning-based approach that combines data from both types of sensors (GPS stations and seismometers) to detect medium and large earthquakes. DMSEEW is based on a new stacking ensemble method which has been evaluated on a real-world dataset validated with geoscientists. The system builds on a geographically distributed infrastructure, ensuring an efficient computation in terms of response time and robustness to partial infrastructure failures. Our experiments show that DMSEEW is more accurate than the traditional seismometer-only approach and the combined-sensors (GPS and seismometers) approach that adopts the rule of relative strength.