Component Fragility Research Articles

Quantitative evaluation method for post-earthquake functionality loss of pedestrian flow pathways within a complex building using evacuation and rescue simulation

The complex building is a single building, characterized by its large size and complicated structural systems, such as high-rise-buildings, long-span-podium, and large underground space, as well as diverse functions. The pedestrian flow pathways within a complex building play a crucial role in urgent evacuation and rescue following seismic events. This study proposed a quantitative method for evaluating the functionality loss of pedestrian flow pathways within the complex building following seismic events. The method performed the component fragility analysis and constructed the speed reduction models that considered the variations of occupants' motions under different damage states of various nonstructural components. To evaluate the functionality loss of pedestrian flow pathways, the evacuation and rescue scenarios were established by analyzing the maximum speeds and behavioral delays of occupants at different spatial locations within the post-earthquake complex building. Based on the simulation, a quantitative index was constructed. Finally, a process accounting for uncertainties such as component damage was presented by generating the engineering demand parameters. A case study was employed to demonstrate the functionality loss of pedestrian flow pathways on each floor and in different areas within the post-earthquake complex building, which has reference significance for improving the post-earthquake complex building 's evacuation capacity as soon as possible to deal with secondary risk.

Impact of choice of fragility approaches on seismic risk quantification of nuclear power plants

Development and evaluation of seismic fragility of structures and components is crucial in seismic probabilistic risk assessment of nuclear power plants. Simulation-based fragility approaches are a prevailing trend in the literature, while industry-recommended methodologies rely heavily on engineering judgment and deterministic analysis. In this paper, four critical components are selected, modeled and analyzed as a case study. Their fragilities are evaluated using both state-of-the-art fragility methods and code-recommended methods with approximate models. The impact of the choice of fragility approaches on the fragilities of the components and conditional core damage probability of the plant are assessed. The findings reveal that the recommended approaches employed with approximate models have limitations in estimating the median capacity of complex equipment. While there is a notable variance in the treatment of uncertainty among fragility approaches, its influence on core damage probability remains limited unless the component is the primary contributor to core damage.

A response-based internal pressure risk assessment method for PCCV with steel fiber reinforcement

The probabilistic risk assessment (PRA) is a hot topic for highlighting the reliability and safety of infrastructures, especially for nuclear power plants (NPPs). The current internal pressure risk assessment method for prestressed concrete containment vessel (PCCV) generally adopts the internal pressure to characterize its fragility (namely internal-pressure-based fragility), even though the failure of PCCV is factually more tightly associated with PCCV’s realistic responses. This study proposes a novel response-based probabilistic risk assessment method for PCCV under internal pressure. The method adopts the response of the containment to characterize the fragility of components. Additionally, the steel fiber is introduced to form steel fiber reinforced concrete (SFRC) PCCV and the fragility and risk of the SFRC PCCV are quantitatively studied. The results indicate that a real and larger dispersion for the internal pressure risk of the PCCV would be induced by adopting the proposed internal pressure risk assessment method. The strategy of the addition of steel fiber to the conventional PCCV can decrease the internal pressure risk by about 72.1 % on average.

Effect of uncertainties in cable corrosion and material strength on seismic fragility of long-span cable-stayed bridges in marine environments

This paper presents an investigation into the seismic fragility of cable-stayed bridges and considers the complex uncertainties in cable corrosion and material strength. Under certain assumptions and using the limited measured data available for steel corrosion, a cable corrosion model is established. The probability distribution of several parameters, including the corrosion rate, corrosion initiation time, chloride concentration, and cable replacement in the corrosion model, is considered. In addition, the influence of the stress level of cables is also considered in the model by the amplification coefficient of the corrosion rate. To consider the effect of the uncertainties in cable corrosion and material strength on the seismic fragility of this bridge, the uniform design (UD) method is used to generate reasonable bridge samples and to build probabilistic seismic demand models. The results indicate that cable corrosion has a significant impact on the seismic fragility of cable-stayed bridges. The seismic fragility of girders and piers are the smallest and the highest among all bridge components, respectively. The material strength uncertainties have a significant influence on the seismic fragility of bridge components. The coupling between the uncertainties in cable corrosion and material strength does not increase the seismic fragility of the bridge components in most cases because of the cancellation effect of the two uncertainties to some extent. In addition, cable replacement has a significant influence on the seismic fragility of bridge components. In order to correctly evaluate the performance of cable-stayed bridges in service, it is necessary to consider the uncertainties in cable corrosion and material strength in a seismic fragility analysis of long-span cable-stayed bridges with different service periods.

Fragility assessment of sea-crossing cable-stayed bridge subjected to multi-hazard action via TKC and R-vine copula

Seismic fragility analysis methods commonly used for assessing structural components and systems have certain limitations. This paper introduces a new semi-parametric approach for structural component fragility analysis, the TKC method. This method is based on log-transformed kernel density estimation (log-TKDE) and copula functions, which establish the joint probability distribution (JPD) of a structural response value (d) and a disaster-inducing factor strength parameter (α) using log-TKDE and match the marginal cumulative distributions (MCDs) of d and a via bivariate copula functions. A novel method for evaluating structural system fragility is also proposed based on the R-vine copula function. This approach accounts for the intricate correlations among different components, providing a precise estimation of the multidimensional JPD. The reliability and accuracy of the proposed methods are demonstrated through a seismic fragility analysis of a sea-crossing cable-stayed bridge under earthquake load. Furthermore, a multi-hazard fragility analysis of bridge components and systems is conducted considering hazards such as earthquake, wind, and wave loads. A comparison is made with the seismic fragility of bridges subjected to earthquake loads alone. The results show that the median and 95% confidence of the damage probability of structural components calculated by the TKC method and Monte Carlo simulation (MCS) closely match, which validates the proposed method. The TKC method is also more accurate and computationally efficient than the MCS method with the same Bootstrap sample size and confidence level (95%). The proposed structural system fragility assessment method based on the R-vine copula accounts for complex correlations between components and yields more accurate results than the first-order boundary method. Load spectrum characteristics, structural component characteristics, and other factors cause the multi-hazard fragility of bridge components and systems to differ substantially from their seismic fragility. The difference rate of system damage probability can reach 28.82%. In evaluating the anti-disaster performance of sea-crossing bridges, it is necessary to incorporate the marine environmental load and consider the dynamic response coupling effect of the bridge excited by seafloor ground motions with extreme wind and wave loads. This approach can guide the optimization of bridge designs and facilitate multi-hazard fragility analysis in accordance with real damage probabilities.

Effect of Ground Motion Time–Frequency Non-Stationarity on Seismic Response of High-Speed Railway Simply Supported Bridge Based on Wavelet Packet Transform

Time–frequency non-stationarity is a ground motion characteristic which is frequently neglected in current seismic design and research. This paper studies its impact on the seismic response of high-speed railway simply supported bridge (HSRSSB). A method for generating time–frequency stationary earthquakes (TFSEs) and time–frequency non-stationary earthquakes (TFNSEs) using wavelet packet transform is proposed. A finite element model of a three-span HSRSSB is established using OpenSees. The seismic response is obtained through non-linear dynamic time history analysis, and the fragility curves of bridge components and system are calculated through incremental dynamic analysis. Finally, the reasons for the differences are analyzed by comparing the differences in seismic response of bridge, component fragility and system fragility under two groups of ground motion. The results show that the time–frequency non-stationarity of ground motion has an effect on the bridge response and fragility under strong earthquakes. TFNSE will lead to larger ground motion response, and the damage probability of bridge components and systems is higher. The reason is related to the damage and period extension of bridges under ground motion. Structures with prolonged period anti-seismic measures need to pay attention to this effect.

Exploring the Effect of Near-Field Ground Motions on the Fragility Curves of Multi-Span Simply Supported Concrete Girder Bridges

Investigating the impact of near-field ground motions on the fragility curves of multi-span simply supported concrete girder bridges is the main goal of this paper. Fragility curves are valuable tools for evaluating seismic risks and vulnerabilities of bridges. Numerous studies have investigated the impact of ground motions on the fragility curves of bridges. Ground motions are commonly categorized into two sets, based on the distance of the recorded station from the seismic source: far-field and near-field. Studies examining the influence of near-field records on bridge fragility curves vary depending on the specific bridge type and type of fragility curve being analyzed. Due to the widespread use of multi-span simply supported concrete girder bridges in the Central and Southeastern United States, this study makes use of this bridge type. This research investigates the component fragility curves for column curvatures, bearing deformations, and abutment displacements by employing 3-D analytical models and conducting nonlinear time history analysis. These curves illustrate the impact of near-field ground motions on different components. The component fragility curves for two sets of records, 91 near-field ground motions and 78 far-field ground motions, were obtained and compared. These findings demonstrate that near-field ground motions have a greater damaging effect on columns and abutments than far-field earthquakes. When it comes to bearing deformations, the far-field earthquake impact is more severe at lower intensities, whereas the impact of the near-field ground motion is stronger at higher intensities.

Effects of Deck-Abutment Pounding on the Seismic Fragility Curves of Box-Girder Highway Bridges

ABSTRACT Earthquake-induced pounding in bridges is a complex contact phenomenon in which the dynamic responses of structures, including collisions between deck and abutments, are strongly related to structural properties and earthquake excitation. The goal of this study is to develop and compare the seismic fragility curves of overall system and individual components of regular and irregular box-girder highway bridges in two cases: with pounding and without pounding. For this purpose, four levels of altitudinal irregularity, ranging from regular to highly irregular, are considered. To extend the results for all bridges in the same class, different sources of uncertainties related to earthquakes, structural geometries, and material properties are taken into account. The analytical fragility curves have been developed based on nonlinear time history analyses in OpenSees finite element software for the cases with and without pounding effects. The process has been repeated for each two-, three-, and four-span classes at four irregularity levels. The fragility function parameters for the two cases with and without pounding have been compared for all classes considered in this study. Using fragility functions, this paper clarifies the interactive roles of irregularity and pounding between deck and abutments for seismic vulnerability of multi-span box-birder highway bridges. The results indicate that collisions often show an adverse effect on all structural components. It has also been observed that the detrimental effect of pounding on seismic fragility is more apparent in irregular bridges when compared with regular ones. In addition, the study introduces a conversion coefficient to clarify the effects of pounding on the fragility of bridge components and the overall system. This coefficient can be applied in both conventional analytical methods like static or simplified analysis and technical earthquake models like HAZUS, adjusting fragility values for pounding and irregularity effects.

System fragility evaluation of a curved highway bridge structure considering multi-direction seismic excitations

This paper presents the impact of varying the input seismic excitation directions on the system fragility of a geometrically complex highway bridge structure. The traditional approach of fragility derivation in the principal loading directions (longitudinal and transverse) results in an under/overestimation of the system fragility. To reduce such errors, the contribution of all major vulnerable components to the system fragility in the critical loading direction must be considered. For this purpose, a series of nonlinear time-history analyses were conducted for a testbed configured geometrically curved highway bridge structure in Japan. Shear strain, ductility, and distortion strain were considered as engineering demand parameters for bearings, concrete pier, and steel piers, respectively. The demand dependency among the components was considered using the correlation coefficient matrix for fragility estimation. Subsequently, fragility functions with respect to the input loading directions were generated for the bridge components and system to quantify their sensitivity to seismic input excitation directions. The results show that the component fragility is significantly influenced by the input excitation direction. A relative comparison of the system fragility for different loading directions indicated that a 150° loading direction yielded a higher fragility demand. The findings suggest that the critical fragility assessment should not always be decided only along the principal loading directions.

A Quantitative Evaluation Model for the Seismic Resilience of Water Supply Systems Based on Fragility Analysis

A quantitative evaluation model is proposed to assess the seismic resilience of water supply systems. The water supply system is divided into three parts: water sources, aboveground infrastructures, and underground pipeline network, and importance factors for the different parts are quantified. Resilience demand is expressed as the desirable functionality loss and the recovery time of the water supply system after an earthquake. First, seismic fragility models are established for the different components of the water supply system. A water quality index is utilized to represent the impact of earthquakes on the water sources, the seismic performances of aboveground infrastructures are represented by fragility curves, and the repair rate in terms of number of repairs per kilometer is adopted for the pipeline network. Then, the post-earthquake functionality of the water supply system is quantified based on seismic fragility analysis. Changes in the water quality index are used to indicate the functionality losses related to water sources, the functionality losses of aboveground infrastructures are represented by the economic losses derived from component fragility curves, and post-earthquake functionality losses in the underground pipeline network are quantified by hydraulic simulations. The functionalities of the three parts are calculated separately, and then the overall system functionalities are obtained as the sum of the weighted functionalities of the three parts. Finally, a repair strategy is developed and the recovery time is calculated considering the system damage scenarios, system functionality analyses, and resource reserves. The proposed resilience assessment model considers all components of the water supply system, and the results are reliable when the basic information is complete and accurate.

Global maximum flow based time-domain simulation method for evaluating power system resilience

With climate change, extreme weather is occurring frequently, which can cause serious damage to energy supply systems. It is of great significance to study the performance of power transmission system under extreme weather for prevention and reinforcement before and after disasters. This paper proposes a time-domain simulation model for quantifying power system resilience under extreme typhoon scenario. Firstly, the power system resilience assessment method based on global maximum flow (GMF) is presented, which is applied to map the overall system operation performance via creating a network indicator while considering component fragility, system topology, and power flow. A specific resilience expression (RES) is proposed to describe percentage improvement of each component in the resilience metrics by considering the overall system performance. Secondly, power system vulnerability model and time-domain simulation methodology are established. The proposed method is demonstrated by four case studies using the IEEE-30 node test system under specific typhoon scenarios. From the GMF based RES index, the component repair strategy is formulated accordingly. The proposed restoration strategy, compared with the traditional expert strategy can effectively measure the resilience contribution of each component to the whole power system, and minimizes the power system performance losses due to extreme typhoon. The proposed approach quantitatively evaluates real-time system resilience to extreme typhoons, and it can also identify the system critical areas and assess the benefits of different resilience enhancement strategies. The resilience assessment framework can also be applied to other extreme scenarios and contribute to planning and construction of strong smart grid in the future.

Optimal design of cable-stayed bridge and its approach spans under spatially varying ground motions

The out-of-phase vibration between neighboring structures owing to their different vibration characteristics and spatially varying seismic excitations may result in strong impact between the adjacent structural components, which might result in detrimental damage to the structures. To preclude such damage, the gap size of the expansion joint and the vibration period ratio between the adjacent structures should be carefully selected. Herein, the framework of performance-based seismic design (PBSD) is extended to optimize the gap size and period ratio between the cable-stayed bridge and its approach spans under the spatially varying ground motions. Considering the computational burden, an equivalent cable-stayed bridge model is proposed and verified, and then adopted in the optimization process. Based on the multi-stripe analysis (MSA) method, the component fragility curves (pylons, bearings, and local damage) for the typical cable-stayed bridge are derived, and then the corresponding structural fragility functions, namely, repair cost ratios (RCRs) are derived. The optimal gap size and period ratio between main bridge and approach spans could be identified by the proposed optimization framework under both uniform and spatially varying excitations. The analytical results demonstrated that the optimal gap size and period ratio depend on the earthquake characteristics and the excitation methods. The optimized RCR values of the bridge subjected to the spatial varying ground motions are much larger than those of bridge under the uniform excitation.

Seismic fragility and loss estimation of self-centering steel braced frames under mainshock-aftershock sequences

This paper highlights the importance of considering local component failure of self-centering braces (SCBs) when examining the seismic fragility and economic performance of emerging self-centering steel braced frames, with a particular focus on the influence of mainshock-aftershock (MS-AS) sequences. The design and modelling of the prototype buildings are first presented, where the failure mechanism and simulation technique for single-core and dual-core SCBs are explained. Seismic fragility analysis and economic loss evaluation are subsequently conducted, where the damage state, component fragility, and repair cost of the considered braces are comprehensively discussed. The study confirms that MS-AS sequences have a pronounced influence on various performances of the structures. Under the maximum considered earthquake (MCE), the probabilities of collapse for structures with single-core and dual-core SCBs (structures S-SCF and D-SCF) increase from 18% to 28% and from 10% to 16%, respectively, when aftershock is additionally considered. MS-AS sequences have a small influence on the peak absolute floor acceleration of both structures. When aftershock is additionally considered, the probabilities of exceedance of the 0.5% residual inter-story drift threshold increase from 25% to 31% and from 16% to 19%, respectively, for structures S-SCF and D-SCF; the 50% percentile loss ratio of the two structures increases from 0.09 to 0.16 and from 0.08 to 0.11, respectively; and the expected losses over a 50-year period of the two structures are increased by 25.7% and 22.9%, respectively. Apart from the non-negligible influence of MS-AS sequences, the importance of appropriate modelling of tendon fracture is also highlighted.

Fragility Study of Buried Pipeline Networks Based on Copula Function

The seismic fragility of water supply networks is an important research component for lifeline engineering in earthquake-prone regions. An accurate computational model was established to rapidly and efficiently assess pipeline damage under seismic excitation. In this study, the fragility of the pipeline network is deduced based on Copula function technology and the series-parallel model. This solves the low accuracy problem caused by simplifying elbow, tee, and other nodes and ignores the correlation between connected components in the fragility calculation of the buried pipeline network. Then, the shaking table tests of the elbow pipe, tee pipe, and scale pipeline network are performed, and the prototype pipeline network’s finite element comparative calculation model is also established. Then, the optimal Copula function for the pipeline network, the Gumbel Copula function, is obtained by calculating the correlation between each component’s seismic demand. It was found that the seismic demand of pipe and elbow components in the sand is higher than that in the clay, while the opposite is valid for the tee component. After that, a two-parameter log-normal distribution is employed to obtain the seismic fragility of three types of components in different soil properties. It was also found that the maximum failure probability can be obtained from the elbow leakage. The fragility of the elbow pipe is greater than that of the tee pipe. The fragility of components is then applied to the fragility calculation of the scale pipeline network by a series-parallel model, and the obtained results are compared with numerical simulations. It is demonstrated that the series-parallel combination calculation-based results have a high safety reserve for the pipeline design.

Resilience assessment and enhancement evaluation of power distribution systems subjected to ice storms

• A probabilistic framework for assessing and evaluating the enhancements of the ice storm resilience of power distribution systems is developed; • Fragility models of power distribution components subjected to ice storms are developed; • Three failure modes of power distribution components induced by trees, ice, and wind, are investigated for the first time; • The impact of tree failures on the resilience of power distribution systems is thoroughly investigated. Overhead power distribution systems are very susceptible to ice storms. Each year power outages due to ice storms result in extensive economical loss and restoration costs all around the world. Climate change and aging further highlight the need for resilient power distribution systems against ice storms. This paper proposes a probabilistic framework for assessing and evaluating the enhancements of the ice storm resilience of power distribution systems, with a focus on fragility modeling of power distribution components (i.e., power poles and wires). The framework is able to assess the impact of ice storms on the resilience of power distribution systems and evaluate the cost-effectiveness of resilience enhancement strategies such as upgrading poles and vegetation management. Specifically, the limitations of tree-induced risk assessment in previous studies are overcome by developing fragility models of tree-induced component failures and using an empirical tree damage fragility function. The fragility of distribution components subjected to ice storms is thoroughly investigated by considering four different failure modes and the effect of wind attack angle. The proposed framework is demonstrated with a power distribution network in Oklahoma.

Experimental damage observations and component fragilities for wood-framed houses with cripple walls

Assessment of damage to homes following a significant earthquake has found that the primary reason for major structural damage and failure is due to inadequate lateral bracing of cripple walls and inadequate sill bolting of the cripple wall to the foundation. Since the 1970s, methods to retrofit weak cripple walls and improve sill anchorage have been developed and implemented on many dwellings to improve their seismic performance, most notably available are the Federal Emergency Management Agency (FEMA) P-1100 guidelines. To assess the seismic vulnerability of existing and retrofitted cripple walls, experimental programs were performed and documentation of the evolution of damage during these experiments were produced and correlated to the structural capacity and residual drift of the specimens. Using the documented damage evolution, existing damage fragility functions were revised for wood light-frame sub-assemblies. In this article, an overview of the cripple wall experimental program is provided, including the variables investigated. Documentation of the damage evolution during these experiments is presented. Damage states based on repair triggers associated with imposed displacements of the experiments are defined. Finally, a discussion of how the damage observations were used to develop probabilistic component-level damage fragility functions for cripple-wall dwellings is provided.

Probabilistic seismic fragility assessment of vertical storage tank with a floating roof

Vertical storage tank is an important facility of oil depot, which may cause catastrophic accidents during strong earthquake, resulting in serious economic and environment consequences. The manuscript studies the seismic fragility of tank with a floating roof. A refined finite element model of the tank with three height-to-diameter ratios is developed. Time-history responses of sloshing wave height, base shear force and base bending moment of tank with and without a floating roof are analyzed. Then, time-history analysis of 55 ground motions is performed to establish seismic demand models for various responses and the most proper intensity measure is determined based on the dispersion and determination coefficient. Appropriate component-level and system-level damage states are defined by identifying possible failure modes during strong earthquake. Seismic fragility curves for different responses are derived for four damage states by cloud analysis. The results indicate that combined spectral acceleration is the most effective and sufficient IM and using only one component fragility to evaluate seismic performance may underestimate the tank system fragility. The results can provide practical advice for seismic risk assessment of individual tank or entire tank farm.

Effect of near-fault vertical ground motions on failure mode of long-span sea-crossing cable-stayed bridges

Existing investigations have proved that the near-fault vertical ground motion (VGM) would have a significant effect on the seismic performance of bridge structures. This study mainly investigates the combined effect of VGM and horizontal ground motion (HGM) on failure mode and component damage sequence of long-span sea-crossing cable-stayed bridges. For this purpose, a long-span sea-crossing cable-stayed bridge considering the pile-soil effect and hydrodynamic effects is selected in this paper. The seismic demand models and limit state models are developed under the combination of VGM and HGM to perform the component fragility analysis, which aims to evaluate the damage state and sequence of key components. The results indicate that VGM has little effect on the damage probability of the bearings, but an adverse effect on the damage probability of the pylons and piers. The vulnerable component would be changed from the bearing to the pier and pylon with strong VGM. Meanwhile, the three-dimensional fragility surface of each component based on the horizontal peak ground velocity (Vx) and the ratio of vertical to horizontal component (αV/H) is obtained by convolution. Thus, the effects of Vx and αV/H on the damage mechanism of the cable-stayed bridge in different damage states are quantified.

Time-Dependent Risk Assessment of a Containment Building Subjected to Mainshock-Aftershock Seismic Sequences

The additional hazard from aftershocks and the progressive degradation of structural capacity induced by aftershock sequences can increase the seismic risk of structures. This paper aims to assess the time-dependent risk of a containment building subjected to mainshock-aftershock sequences. To quantify the seismic risk at the system level, a new Markov-based framework for the system analysis is proposed in this study. In this proposed framework, the seismic performance of internal equipment is characterized by the fragility of nonstructural components, and the contributions of various failure events and accident sequences are identified using the event tree and fault tree. To consider the seismic performance of damaged structures, state-dependent fragility curves are generated through a proposed fragility method, which can incorporate the effect of initial damage states on the residual capacity. Further, in order to measure the seismic performance of a system, the system-level fragility is derived using fragilities of all basic components and accident sequences. Finally, the Markov chain is introduced to account for the stochastic process describing the damage progression and uncertainty in the aftershock occurrence, and then the time-dependent risk of a containment building at a system level is obtained in both post- and pre-mainshock scenarios. To gain insight and familiarity with the risk of a system under seismic sequences, a series of parametric studies are also conducted in this study. The results provide quantitative information about the effect of aftershocks on the seismic risk of a system, and it is suggested that the contribution of aftershocks should be considered in the seismic risk management to ensure the seismic safety of containment buildings during the service life.

Life‐cycle seismic fragility of a cable‐stayed bridge considering chloride‐induced corrosion

AbstractThe coastal or sea‐crossing bridges located in seismic regions are experiencing long‐term chloride‐induced corrosion in their life cycles and have a high risk of suffering from strong earthquakes. Thus, the fragilities of these bridges must be properly evaluated under the multiple hazards of corrosion and earthquake. Conventional fragility assessment requires expensive computational efforts despite extensive applications in previous research. To this end, this paper proposes a life‐cycle fragility analysis framework based on the endurance time method to investigate the deterioration impact on the seismic fragility of bridges. An example sea‐crossing cable‐stayed bridge is utilized as a case study and modeled by OpenSees considering different service years. The life‐cycle fragility curves of the example bridge are generated using the artificial endurance time series. Fragility analysis results show that the proposed method is capable of assessing the life‐cycle seismic fragility of the bridge with high efficiency. The bearing shows a higher damage probability than the pylon and pier. As the service time increases, the structural deterioration has a marginal impact on the system fragility of the bridge, while the component fragility varies across different components. The structural deterioration results in beneficial effects on the pylon and the bearing at the pylon but exerts adverse effects on the pier and the bearing at the pier.