Displacement field reconstruction in landslide physical modeling by using a terrain laser scanner e Part 2:Application and large strain/displacement and water effect analysis

Deformation analysis is fundamental in geotechnical modeling.Nevertheless,there is still a lack of an effective method to obtain the deformation field under various experimental conditions.In this study,we introduce a processebased physical modeling of a pileereinforced reservoir landslide and present an improved deformation analysis involving large strains and water effects.We collect multieperiod point clouds using a terrain laser scanner and reconstruct its deformation field through a point cloud processing workflow.The results show that this method can accurately describe the landslide surface deformation at any time and area by both scalar and vector fields.The deformation fields in different profiles of the physical model and different stages of the evolutionary process provide adequate and detailed landslide information.We analyze the large strain upstream of the pile caused by the pile installation and the consequent violent deformation during the evolutionary process.Furthermore,our method effectively overcomes the challenges of identifying targets commonly encountered in geotechnical modeling where water effects are considered and targets are polluted,which facilitates the deformation analysis at the wading area in a reservoir landslide.Eventually,combining subsurface deformation as well as numerical modeling,we comprehensively analyze the kinematics and failure mechanisms of this complicated object involving landslides and pile foundations as well as water effects.This method is of great significance for any geotechnical modeling concerning large-strain analysis and water effects.

Displacement field reconstruction in landslide physical modeling by using a terrain laser scanner e Part 1:Methodology,error analysis and validation

Laser scanning technology has been widely used in landslide aspects.However,the existing deformation analysis based on terrain laser scanners can only provide limited information,which is insufficient for understanding landslide kinematics and failure mechanisms.To overcome this limitation,this paper proposes an automated method for processing point clouds collected in landslide physical modeling.This method allows the acquisition of quantitative three-dimensional(3D)deformation field information.The results show the organized and spatially related point cloud segmentation in terms of spherical targets.The segmented point clouds can be fitted to determine the locations of all preset targets and their corresponding location changes.The proposed method has been validated based on theoretical analysis and numerical and physical tests,which indicates that it can batch-process massive data sets with high computational efficiency and good noise resistance.Compared to existing methods,this method shows a significant potential for understanding landslide kinematics and failure mechanisms and advancing the application of 3D laser scanning in geotechnical modeling.

A data and physical model dual-driven based trajectory estimator for long-term navigation

Long-term navigation ability based on consumer-level wearable inertial sensors plays an essential role towards various emerging fields, for instance, smart healthcare, emergency rescue, soldier positioning et al. The performance of existing long-term navigation algorithm is limited by the cumulative error of inertial sensors, disturbed local magnetic field, and complex motion modes of the pedestrian. This paper develops a robust data and physical model dual-driven based trajectory estimation(DPDD-TE) framework, which can be applied for long-term navigation tasks. A Bi-directional Long Short-Term Memory(Bi-LSTM) based quasi-static magnetic field(QSMF) detection algorithm is developed for extracting useful magnetic observation for heading calibration, and another Bi-LSTM is adopted for walking speed estimation by considering hybrid human motion information under a specific time period. In addition, a data and physical model dual-driven based multi-source fusion model is proposed to integrate basic INS mechanization and multi-level constraint and observations for maintaining accuracy under long-term navigation tasks, and enhanced by the magnetic and trajectory features assisted loop detection algorithm. Real-world experiments indicate that the proposed DPDD-TE outperforms than existing algorithms, and final estimated heading and positioning accuracy indexes reaches 5° and less than 2 m under the time period of 30 min, respectively.

Rainfall-triggered waste dump instability analysis based on surface 3D deformation in physical model test

Landslide is the second largest natural disaster after earthquake. It is of significance to study the evolution laws and failure mechanism of landslides based on its surface 3D deformation information. Based on the rainfall-triggered waste dump instability model test, we studied the failure mechanisms of the waste dump by integrating surface deformation and internal slope stress and proposed novel parameters for identifying landslide stability. We developed a noncontact measurement device, which can obtain millimeter-level 3D deformation data for surface scene in physical model test;Then we developed the similar materials and established a test model for a waste dump. Based on the failure characteristics of slope surface, internal stress of slope body and displacement contours during the whole process, we divided the slope instability process in model test into four stages: rainfall infiltration and surface erosion, shallow sliding, deep sliding, and overall instability. Based on the obtained surface deformation data, we calculated the volume change during slope instability process and compared it with the point displacement on slope surface. The results showed that the volume change can not only reflect the slow-ultra acceleration process of slope failure, but also fully reflect the above four stages and reduce the fluctuations caused by random factors. Finally, this paper proposed two stability identification parameters: the volume change rate above the slip surface and the relative velocity of volume change rate. According to the calculation of these two parameters in model test, they can be used for study the deformation and failure mechanism of slope stability.

Mechanical behaviors of backfill-rock composites: Physical shear test and back-analysis

The shear behavior of backfill-rock composites is crucial for mine safety and the management of surface subsidence.For exposing the shear failure mechanism of backfill-rock composites,we conducted shear tests on backfill-rock composites under three constant normal loads,compared with the unfilled rock.To investigate the macro-and meso-failure characteristics of the samples in the shear tests,the cracking behavior of samples was recorded by a high-speed camera and acoustic emission monitoring.In parallel with the experimental test,the numerical models of backfill-rock composites and unfilled rock were established using the discrete element method to analyze the continuous-discontinuous shearing process.Based on the damage mechanics and statistics,a novel shear constitutive model was proposed to describe mechanical behavior.The results show that backfill-rock composites had a special bimodal phenomenon of shearing load-deformation curve,i.e.the first shearing peak corresponded to rock break and the second shearing peak induced by the broken of aeolian sand-cement/fly ash paste backfill.Moreover,the shearing characteristic curves of the backfill-rock composites could be roughly divided into four stages,i.e.the shear failure of the specimens experienced:stage I:stress concentration;stage II:crack propagation;stage III:crack coalescence;stage IV:shearing friction.The numerical simulation shows that the existence of aeolian sand-cement/fly ash paste backfill inevitably altered the coalescence type and failure mode of the specimens and had a strengthening effect on the shear strength of backfillrock composites.Based on damage mechanics and statistics,a shear constitutive model was proposed to describe the shear fracture characteristics of specimens,especially the bimodal phenomenon.Finally,the micro-and meso-mechanisms of shear failure were discussed by combining the micro-test and numerical results.The research can advance the better understanding of the shear behavior of backfill-rock composites and contribute to the safety of mining engineering.

Associations of daily sedentary behavior,physical activity,and sleep with irritable bowel syndrome:A prospective analysis of 362,193 participants

Background:Irritable bowel syndrome(IBS)substantially affects quality of life and requires early prevention.This study aimed to elucidate the relationships between IBS and daily behaviors,including sedentary behavior(SB),physical activity(PA),and sleep.In particular,it seeks to identify healthy behaviors to reduce IBS risk,which previous studies have rarely addressed.Methods:Daily behaviors were retrieved from self-reported data of 362,193 eligible UK Biobank participants.Incident cases were determined by self-report or health care data according to RomeⅣcriteria.Results:A total of 345,388 participants were IBS-free at baseline,during a median follow-up of 8.45 years,19,885 incident IBS cases were recorded.When examined individually,SB and shorter(≤7 h/day)or longer(>7 h/day)sleep duration were each positively associated with increased IBS risk,and PA was associated with lower IBS risk.The isotemporal substitution model suggested that replacing SB with other activities could provide further protective effects against IBS risk.Among people sleeping≤7 h/day,replacing 1 h of SB with equivalent light PA,vigorous PA,or sleep was associated with 8.1%(95%confidence interval(95%CI):0.901-0.937),5.8%(95%CI:0.896-0.991),and 9.2%(95%CI:0.885-0.932)reduced IBS risk,respectively.For people sleeping>7 h/day,light and vigorous PA were associated with a 4.8%(95%CI:0.926-0.978)and a 12.0%(95%CI:0.815-0.949)lower IBS risk,respectively.These benefits were mostly independent of genetic risk for IBS.Conclusion:SB and unhealthy sleep duration are risk factors for IBS.A promising way to mitigate IBS risk for individuals sleeping≤7 h/day and for those sleeping>7 h/day appears to be by replacing SB with adequate sleep or vigorous PA,respectively,regardless of the genetic predisposition of IBS.

Physical model investigation on effects of drainage condition and cement addition on consolidation behavior of tailings slurry within backfilled stopes

Estimation of stressses within the tailings slurry during self-weight consolidation is a critical issue for cost-effective barricade design and efficient backfill planning in underground mine stopes.This process requires a good understanding of self-weight consolidation behaviors of the tailings slurry within practical stopes,where many factors can have significant effects on the consolidation,including drainage condition and cement addition.In this paper,the prepared tailings slurry with different cement contents(0,4.76wt%,and 6.25wt%)was poured into1.2 m-high columns,which allowed three drainage scenarios(undrained,partial lateral drainage near the bottom part,and full lateral drainage boundaries)to investigate the effects of drainage condition and cement addition on the consolidation behavior of the tailings slurry.The consolidation behavior was analyzed in terms of pore water pressure(PWP),settlement,volume of drainage water,and residual water content.The results indicate that increasing the length of the drainage boundary or cement content aids in PWP dissipation.In addition,constructing an efficient drainage boundary was more favorable to PWP dissipation than increasing cement addition.The final stable PWP on the column floor was not sensitive to cement addition.The final settlement of uncemented tailings slurry was independent of drainage conditions,and that of cemented tailings slurry decreased with the increase in cement addition.Notably,more pore water can drain out from the cemented tailings slurry than the uncemented tailings slurry during consolidation.

Unleashing the Power of Information Theory: Enhancing Accuracy in Modeling Physical Phenomena

When building a model of a physical phenomenon or process, scientists face an inevitable compromise between the simplicity of the model (qualitative-quantitative set of variables) and its accuracy. For hundreds of years, the visual simplicity of a law testified to the genius and depth of the physical thinking of the scientist who proposed it. Currently, the desire for a deeper physical understanding of the surrounding world and newly discovered physical phenomena motivates researchers to increase the number of variables considered in a model. This direction leads to an increased probability of choosing an inaccurate or even erroneous model. This study describes a method for estimating the limit of measurement accuracy, taking into account the stage of model building in terms of storage, transmission, processing and use of information by the observer. This limit, due to the finite amount of information stored in the model, allows you to select the optimal number of variables for the best reproduction of the observed object and calculate the exact values of the threshold discrepancy between the model and the phenomenon under study in measurement theory. We consider two examples: measurement of the speed of sound and measurement of physical constants.

Physical Space Was Not Expanding

Plurality of characteristic peaks observed in number density distribution of galaxy redshift reveals that extent of physical space has been finite. Significant portion of observed celestial objects is found pair-wise associated, i.e., the observed lights were emitted from one and same luminescent source but seen at different sky directions of observer, which is a unique phenomenon that can occur but only in finite space. Cosmic microwave radiation has always been interpreted as afterglow of Big Bang event. However, such radiation is shown unobservable to current observer if Hubble-Lemaître Correlation is interpreted as caused by receding motion of celestial objects. On the other hand, cosmic radiation can be understood as a common and ordinary phenomenon due to space lens, a unique property only of finite space. From Sloan Digital Sky Survey data, internal diameter of physical space is measured as 2.0 billion light years. If celestial objects were receding, hence physical space was expanding, then characteristic peaks of finite physical space should not appear evenly in number density distribution of redshift of the objects but more sparsely with respect to redshift increase. However, as revealed by the data, locations of the characteristic peaks in the distributions are rather even that do not match the locations as required by receding motion of object. Therefore, as evidenced by the data, physical space was not expanding, at least during the recent 18 billion years. In addition, considerable portion of observed quasars is found sharing a common factor of ~1/2 for their respective gravitation redshifts.

Reliability modeling of mutual DCFP considering failure physical dependency

Degradation and overstress failures occur in many electronic systems in which the operation load and environmental conditions are complex.The dependency of them called dependent competing failure process(DCFP),has been widely studied.Electronic system may experience mutual effects of degradation and shocks,they are considered to be interdependent.Both the degradation and the shock processes will decrease the limit of system and cause cumulative effect.Finally,the competition of hard and soft failure will cause the system failure.Based on the failure mechanism accumulation theory,this paper constructs the shock-degradation acceleration and the threshold descent model,and a system reliability model established by using these two models.The mutually DCFP effect of electronic system interaction has been decomposed into physical correlation of failure,including acceleration,accumulation and competition.As a case,a reliability of electronic system in aeronautical system has been analyzed with the proposed method.The method proposed is based on failure physical evaluation,and could provide important reference for quantitative evaluation and design improvement of the newly designed system in case of data deficiency.

Hydrodynamic Performance of a Newly-Designed Pelagic and Demersal Trawls Using Physical Modeling and Analytical Methods for Cameroonian Industrial Fisheries

This study proposed the newly-designed Pelagic and demersal trawls for the fishing vessels operating in Cameroonian waters in pelagic and demersal fishing grounds. The engineering performances of both trawls were investigated using physical modelling method and analytical method based on the predicted equations. In a flume tank, a series of physical model tests based on Tauti’s law were performed to investigate the hydrodynamic and geometrical performances of both trawls and to assess the applicability of the analytical methods based on predicted equations. The results showed that in model scale, the working towing speed and door spread for the pelagic trawl were 3.5 knots and 1.85 m, respectively, and for the bottom trawl net they were 4.0 knots and 1.8 m. At that speed and door spread, the drag force, net opening height, and wing-end spread of the pelagic model trawl were 36.73 N, 0.89 m, and 0.86 m, respectively, and the swept area was 0.76 m2. Bottom trawl speed and door spread were 30.43 N, 0.38 m, and 0.45 m, respectively, and the swept area was 0.25 m2. The maximum difference between the experimental and analytical results of hydrodynamic performances was less than 56.22% and 41.45%, respectively, for pelagic and bottom trawls, the results of the geometrical performances obtained using predicted equations were close to the experimental results in the flume tank with a maximum relative error less than 12.85%. The newly developed pelagic and bottom trawls had advanced engineering performance for high catch efficiency and selectivity and could be used in commercial fishing operations in Cameroonian waters.

Discussion on the Impact of“Shift System”Teaching Model of Physical Education on Students’Mental Health

The“shift system”teaching model of physical education is an emerging education model that aims to improve students’independent choice and personalized development.However,there are also some challenges in the practical application of this model.For example,there are mental health issues for some students including difficulty in adaptation,social interaction,high psychological pressure,etc.Based on this,this article analyzes the impact of the“shift system”teaching model of physical education on students’mental health and explores the optimization path of the physical education“shift system”teaching model in order to promote students’mental health and all-round development.

Large-scale complex physical modeling and precisionanalysis

Large-scale 3D physical models of complex structures can be used to simulate hydrocarbon exploration areas. The high-fidelity simulation of actual structures poses challenges to model building and quality control. Such models can be used to collect wideazimuth, multi-azimuth, and full-azimuth seismic data that can be used to verify various 3D processing and interpretation methods. Faced with nonideal imaging problems owing to the extensive complex surface conditions and subsurface structures in the oil-rich foreland basins of western China, we designed and built the KS physical model based on the complex subsurface structure. This is the largest and most complex 3D physical model built to date. The physical modeling technology advancements mainly involve 1） the model design method, 2） the model casting flow, and 3） data acquisition. A 3D velocity model of the physical model was obtained for the first time, and the model building precision was quantitatively analyzed. The absolute error was less than 3 mm, which satisfies the experimental requirements. The 3D velocity model obtained from 3D measurements of the model layers is the basis for testing various imaging methods. Furthermore, the model is considered a standard in seismic physical modeling technology.

The analysis of frequency-dependent characteristics for fluid detection: a physical model experiment

According to the Chapman multi-scale rock physical model, the seismic response characteristics vary for different fluid-saturated reservoirs. For class I AVO reservoirs and gas-saturation, the seismic response is a high-frequency bright spot as the amplitude energy shifts. However, it is a low-frequency shadow for the Class III AVO reservoirs saturated with hydrocarbons. In this paper, we verified the high-frequency bright spot results of Chapman for the Class I AVO response using the frequency-dependent analysis of a physical model dataset. The physical model is designed as inter-bedded thin sand and shale based on real field geology parameters. We observed two datasets using fixed offset and 2D geometry with different fluid- saturated conditions. Spectral and time-frequency analyses methods are applied to the seismic datasets to describe the response characteristics for gas-, water-, and oil-saturation. The results of physical model dataset processing and analysis indicate that reflection wave tuning and fluid-related dispersion are the main seismic response characteristic mechanisms. Additionally, the gas saturation model can be distinguished from water and oil saturation for Class I AVO utilizing the frequency-dependent abnormal characteristic. The frequency-dependent characteristic analysis of the physical model dataset verified the different spectral response characteristics corresponding to the different fluid-saturated models. Therefore, by careful analysis of real field seismic data, we can obtain the abnormal spectral characteristics induced by the fluid variation and implement fluid detection using seismic data directly.

Wide angle reflections in OBC seismic physical model experiment

Wide angle acquisition has been taken as a significant measure to obtain high quality seismic data and is getting greater attention, In this paper, we discuss ocean bottom cable （OBC） seismic wide angle reflections on the basis of a layered model experiment. Some experiment results don＇t support theoretical conclusions. The main experimental conclusions are： 1. Wide angle reflection energies are stronger than non-wide-angle reflections （up to twice as strong） but there is a big difference between observations and theoretical calculations that suggest the wide angle reflection energies are 15 times the non- wide-angle reflection energy. The reflection energy increases gradually rather than sharply as the theoretical calculations suggest. 2. The reflection events remain hyperbolic when the offset increases. 3. Wide angle reflection dominant frequency is about 20-30% less than non- wide-angle reflections and decreases as the offset increases. The non-wide-angle reflection dominant frequency shows no obvious variation for small offsets. 4. There is no wave shape mutation or polarity reversal near the critical angle. 5. The reflection event group features are the same for both cases of incidence angle greater and less than the critical angle. 6. Direct arrivals, multiples, and water bottom refractions influence the wide angle reflections of the sea floor.

Replacement of leisure-time sedentary behavior with various physical activities and the risk of dementia incidence and mortality:A prospective cohort study

Background:Whether or not there is targeted pharmacotherapy for dementia,an active and healthy lifestyle that includes physical activity(PA)may be a better option than medication for preventing dementia.We examined the association between leisure-time sedentary behavior(SB)and the risk of dementia incidence and mortality.We further quantified the effect on dementia risk of replacing sedentary time with an equal amount of time spent on different physical activities.Methods:In the UK Biobank,484,169 participants(mean age=56.5 years;45.2%men)free of dementia were followed from baseline(2006-2010)through July 30,2021.A standard questionnaire measured individual leisure-time SB(watching TV,computer use,and driving)and PA(walking for pleasure,light and heavy do-it-yourself activity,strenuous sports,and other exercise)frequency and duration in the 4 weeks prior to evaluation.Apolipoprotein E(APOE)genotype data were available for a subset of 397,519(82.1%)individuals.A Cox proportional hazard model and an isotemporal substitution model were used in this study.Results:During a median 12.4 years of follow-up,6904 all-cause dementia cases and 2115 deaths from dementia were recorded.In comparison to participants with leisure-time SB<5 h/day,the hazard ratio((HR),95%confidence interval(95%CI))of dementia incidence was 1.07(1.02-1.13)for 5-8 h/day and 1.25(1.13-1.38)for>8 h/day,and the HR of dementia mortality was 1.35(1.12-1.61)for>8 h/day.A 1 standard deviation increment of sedentary time(2.33 h/day)was strongly associated with a higher incidence of dementia and mortality(HR=1.06,95%CI:1.03-1.08 and HR=1.07,95%CI:1.03-1.12,respectively).The association between sedentary time and the risk of developing dementia was more profound in subjects<60 years than in those>60 years(HR=1.26,95%CI:1.00-1.58 vs.HR=1.21,95%CI:1.08-1.35 in>8 h/day,p for interaction=0.013).Replacing 30 min/day of leisure sedentary time with an equal time spent in total PA was associated with a6%decreased risk and 9%decreased mortality from dementia,with exercise(e.g.,swimming,cycling,aerobics,bowling)showing the strongest benefit(HR=0.82,95%CI:0.78-0.86 and HR=0.79,95%CI:0.72-0.86).Compared with APOEε4 noncarriers,APOEε4 carriers are more likely to see a decrease in Alzheimer’s disease incidence and mortality when PA is substituted for SB.Conclusion:Leisure-time SB was positively associated with the risk of dementia incidence and mortality.Replacing sedentary time with equal time spent doing PA may be associated with a significant reduction in dementia incidence and mortality risk.

Relationships between Features of EmergingAdulthood, Situated Decisions toward PhysicalActivity, and Physical Activity among CollegeStudents: The Moderating Role of ExerciseIntensity Tolerance

A significant portion of emerging adults do not achieve recommended levels of physical activity (PA). Previous studies observedassociations between features of emerging adulthood and PA levels, while the potential psychological mechanisms that mightexplain this phenomenon are not fully understood. In this context, there is some evidence that situated decisions towardphysical activity (SDPA) and exercise-intensity tolerance might influence PA level. To provide empirical support for thisassumption, the current study investigated whether (i) features of emerging adulthood are linked to SDPA, which, in turn,might affect PA engagement;(ii) exercise-intensity tolerance moderate the relationship between SDPA and PA level;and (iii)SDPA is a mediator of the relationship between features of emerging adulthood and PA levels under the prerequisite thatexercise-intensity tolerance moderates the link between SDPA and PA engagement. In this study a group of 1,706 Chinesecollege students was recruited and asked to complete a set of questionnaires assessing their SDPA, PA levels, exercise-intensitytolerance, and features associated with emerging adulthood, namely Self-exploration, Instability, and Possibility. Our resultsindicated that SDPA positively predicted PA levels and this relationship became stronger when exercise-intensity tolerance wasused as a moderator. Furthermore, it was observed that individuals with a higher level of Instability and a lower level ofPossibility during emerging adulthood exhibited a lower level of SDPA. Taken together, the results of our study providefurther insights on a potential psychological mechanism linking features of emerging adulthood and physical activity.

LAGFD-WAM numerical wave model-Ⅰ. Basic physical model

The LAGFD-WAM wave model is a third generation wave model. In the present paper the physical aspect of the model was shown in great detail including energy spectrum balance equation, complicated characteristics equations and source functions.

Quantitative Damage Detection for Planetary Gear Sets Based on Physical Models

Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to resolve this problem, an approach based on physical models is presented to detect damage quantitatively in planetary gear set. A particular emphasis is put on a feature generation and selection method, which is used for sun gear tooth breakage damage detection quantitatively in planetary gear box of helicopter transmission system. In this feature generation procedure, the pure torsional dynamical models of 2K-H planetary gear set is established for healthy case and sun gear tooth-breakage case. Then, a feature based on the spectrum of simulation signals of the dynamical models is generated. Aiming at selecting the best feature suitable for quantitative damage detection, a two-sample Z-test procedure is used to analyze the performance of features on damage evolution tracing. A feature named SR, which had better performance in tracking damage, is proposed to detect damage in planetary gear set. Meanwhile, the sun gear tooth-chipped seeded experiments with different severity are designed to validate the method above, and then the test vibration signal is picked up and used for damage detection. With the results of several experiments for quantitative damage detection, the feasibility and the effect of this approach are verified. The proposed method can supply an effective tool for degradation state identification in condition monitoring and health management of helicopter transmission system.

Physical Modeling of Fold-and-Thrust Belt Evolution and Triangle Zone Development:Dabashan Foreland Belt(Northeast Sichuan basin,China) as an Example

Triangle zones, generally found in foreland fold-and-thrust belts, serve as favorable objects of petroleum exploration. Taking the Dabashan foreland belt as an example, we studied the formation and development of triangle zones, and investigated the effect of d^collements and the mechanical contrast of lithology by employing the method of physical modeling. Four experimental models were conducted in the work. The results showed that ＇sand wedges＇ grew episodically, recorded by deformational length, height and slope angle. The height versus shortening rate presented an S-shape curve, and uplifting occurred successively in the direction of the foreland belt. During the formation of the triangle zone, layer-parallel shortening took place at the outset; deformation decoupling then occurred between the upper and lower brittle layers, divided by a middle-embedded silicone polymers layer. The upper brittle layers deformed mainly by folding, while the lower sand layers by thrusting. As shortening continued, the geometry of a triangle zone was altered. We consider that the triangle zone in the Dabashan foreland belt was modified from an early one based on available seismic profiles and the experimental results. In addition, dccollements and mechanical contrast impose significant influence on structural development, which can directly give rise to structural discrepancies. More d^collements and obvious mechanical contrast between brittle layers can promote the coupling between the upper and lower brittle layers. Basal d^collement controls the whole deformation and decreases the slope angle of the wedge, while roof d^collement determines whether a triangle zone can be formed.