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Homotopy perturbation method spread to express a good solution of one of most important equation in various areas in science which is the Bateman-Burgers’ Equation. Homotopy perturbation method (HPM) investigate a particular success in solving linear and nonlinear Betman differential equations in both one and two dimension cases.

This paper examines the seismic response of two full-scale pile-to-deck connections of marginal wharves built in the 1980s at the Port of Los Angeles. The first test represented a precast pretensioned concrete pile-deck connection at Berth 145. This berth required extending the deck for a new crane rail and a new line of piles. The proposed wharf upgrade considered leaving the existing piles if their lateral displacement capacity exceeded the expected seismic demands. A representative connection was tested to assess the rotation capacity under reversed cyclic loading. The second test represented a typical steel pile-deck connection used in Berth 226. In this structure, the piles support a crane rail. A reversed cyclic loading test was also conducted to assess the connection deformation capacity. Both connections were able to carry the imposed axial load throughout, even when the flexural strength had degraded. The precast pile-deck connection maintained the flexural strength up to a rotation of 0.04 rad, and the steel pile-deck connection maintained its flexural strength up to a rotation of 0.015 rad.

In this paper we will study the existence and uniqueness of mild solution for the semilinear initial value problem of non-integer order: u ( α ) ( t ) = A u ( t ) + f ( t , u ( t ) , G u ( t ) , S u ( t ) ) , where, α ∈ ( 0 , 1 ] and f ( t , u ( t ) , G u ( t ) , S u ( t ) ) is a given function.

Pile-supported marginal wharves have geometrical characteristics that make them prone to torsional response when subjected to earthquake induced inertial forces. Because of expected early system non-linear response due to the soil-structure interaction, lateral displacement demands on the piles cannot readily be estimated from conventional elastic modal response spectrum analyses and modal combination techniques. These displacement demands may be obtained using non-linear time-history analysis. Nevertheless, modeling the non-linear response of the wharf is still impractical in many design offices. For this reason, simple approximate methods that can estimate the critical pile displacement demand as the spectral displacement corresponding to a predominant translational (transverse) mode natural period of the wharf multiplied by a Displacement Magnification Factor (DMF) is adequate for design purposes. This paper revisits the earlier work of Benzoni and Priestley (2003) and computes, through non-linear timehistory analysis, DMFs of short, long and linked segment wharves. Furthermore, the paper also reports shear key forces observed in the non-linear analyses of linked segment wharves. Finally, equations are proposed for calculating the DMFs and to estimate the forces for the design of shear keys.

Over the past several years, the Ports of Los Angeles (POLA) and Long Beach (POLB) have undertaken numerous engineering studies to improve the seismic design of pile-supported wharf structures. It was concluded that the displacement-based seismic design methodology results in more robust and economical wharf structures. The displacement-based design allows plastic hinges to form at predetermined locations, which can be readily identified and repaired after an earthquake. Both Ports sponsored and funded specialized studies and an experimental program at the University of California at San Diego (UCSD) to confirm seismic design assumptions. Also, port-wide ground motion studies were completed to develop acceleration and displacement response spectra and time-histories for the different levels of earthquakes specific to each Port. Displacement-based seismic design procedures for pile-supported container wharves are included in two separate documents: "The Port of Los Angeles Code for Seismic Design, Upgrade and Repair of Container Wharves" and the "POLB Wharf Design Criteria." This paper addresses the seismic, structural, geotechnical, and soil-structure interaction aspects of these documents and discusses various studies that were undertaken to support the development of the displacement-based seismic design.

The strength and degradation behavior of reinforced concrete bridge columns under seismic loading were investigated. Experimental tests were conducted on four reduced-scale column specimens that incorporated deficiencies selected to be representative of those present in existing bridges designed before 1971. The columns were fixed against rotation at both the top and bottom, resulting in a transfer of shear forces through the column even after the lower hinging region lost its flexural capacity. The specimens were subjected to increasing levels of cycled inelastic displacements under constant axial load. The focus of the study was to characterize the load and displacement capacities present in older columns for purposes of seismic assessment and retrofit design. Flexure-dominated failures occurred in three of the specimens. A rapid degradation in flexural strength was observed at the bottom hinging regions of the tested columns because of the presence of lap splices and poor confinement. Top hinging regions that did not have lap splices exhibited degradation in flexural capacities at higher displacement ductilities because of eventual longitudinal bar buckling. In the fourth specimen, flexural yielding was initially observed at both the top and bottom of the column, but this was followed by an eventual brittle shear failure. Various procedures for assessing flexural and shear behaviors were compared with the observed experimental results.

The Berths 136-147 Container Terminal is located in the north and eastern portions of the West Basin of the Port of Los Angeles (POLA) and was built in the 1980's. The proposed project is to expand and modernize the container terminal at Berths 145-147 and upgrade the existing wharf facilities in order to increase capacity from the current (2003) level of approximately 0.9 million 20-foot (6.1 meter) equivalent units (TEUs) of containerized cargo. Major construction elements include dredging, wharf upgrades, installation of an underwater bulkhead, and development of a landside buffer with the surrounding community. A significant feature of design was testing of a representative pile to deck connection simulating existing conditions, in order to evaluate performance under the design seismic event. Upon completion of construction, new 100-foot (30.5 meter) gauge container cranes will be installed at the terminal. At full operation, expected by 2025, the upgraded terminal will handle approximately 2.4 million TEUs per year. This paper addresses the design and construction challenges of the Berths 145-147 wharf upgrade project. Copyright 2010 ASCE.

The Port of Los Angeles (POLA) is a major seaport serving as a "Gateway to the Pacific" both to the Southern California region and nation. The Port has eight liquid bulk facilities comprising a total of 114 acres to handle various types of commodities for both import and export. Handling facilities include tankers, barges, bulk carriers and storage tanks with convenient rail access. The Marine Oil Terminal Engineering and Maintenance Standards (MOTEMS) were approved by the California Building Standards Commission on January 19, 2005, and are codified as Chapter 31F (Marine Oil Terminals), Title 24, California Code of Regulations, Part 2, California Building Code. These standards apply to all existing and new marine oil terminals in California, and include criteria for inspection, structural analysis and design, mooring and berthing, geotechnical considerations, fire, piping, mechanical and electrical systems. Chapter 31F was published by the Building Standards Commission on August 10, 2005 and became effective on February 6, 2006. The POLA developed MOTEMS Program to audit the eight liquid bulk facilities located within the Port of Los Angeles including: 1) Berths 70-71 terminal operated by Westway, 2) Berths 118-120 terminal operated by Kinder Morgan, 3) Berths 148- 151 terminal operated by Conoco-Phillips, 4) Berth 163 terminal operated by Shore Terminals LLC, 5) Berths 164 terminal operated by Ultramar, Inc., 6) Berths 167-169 terminal operated by Shell Oil, 7) Berths 187-191 terminal operated by Vopak, and 8) Berths 239-240C terminal operated by Exxon-Mobil. This paper addresses the audit and design challenges of the POLA MOTEMS program including the preparation of the Initial Audit Report for each facility, and the preparation of Plans, Specifications, and Estimates (PS&E's) to bring the identified facilities into compliance with MOTEMS standards. Copyright 2010 ASCE.

The Pier E Redevelopment Project targets reconfiguring and combining two irregularly shaped adjacent container terminals to establish a more efficient and environmentally friendly facility. This project aims at replacing the existing wharf structures with modern structures over wharf slope areas stabilized by rock dike revetment or ground improvement. Also, the existing Pier E wharf will be rehabilitated and widened to accommodate a 137'-9" gauge crane, and eventually extended to the south to connect with the wharf at the Pier F terminal. The wharf layout consists of a 4,250-foot long berth composed of 6 wharf segments separated by transverse expansion joints. The design of the wharf considers variation in soil properties and proposed wharf slope stabilization solutions at the different wharf segments. This paper addresses the wharf structural design considerations. A performance based approach was used for the seismic design of the wharf structure for inertia and kinematic loading. The design philosophy objective is to provide a ductile structure with plastic hinges forming in the piles to dissipate the earthquake energy. A series of non-linear static pushover analyses that consider the nonlinear soil behavior were performed to evaluate the structure's displacement capacity and shear demand. The substitute structure method was used to calculate the seismic displacement demands for three levels of ground motions. A non-Linear Time History Analysis was performed for the linked wharf units to verify the displacement demands and determine shear key forces. Pier E utilizes a wider gauge crane with a higher vertical load and translational elastic period of the mode with the maximum participating mass being about 1.3 to 1.5 seconds. The wharf seismic design considered the crane mass impact on the wharf displacement demand. Copyright 2010 ASCE.

The Port of Long Beach (POLB) acknowledged in the late 1990's that the continuous increase in container throughput volume would require establishing a consistent system of standards and guidelines for the design of container wharves to successfully execute the necessary capital improvement. The understanding of seismic requirements for design of pile-supported wharves has considerably increased during recent years. New and larger ships provided new challenges; new details and practices for the design and construction of wharves were developed and followed by new codes and guidelines for port structures. This work, however, was driven by different authorities, often not closely coordinated: Code Writing Authorities, Owners (Ports), and Consultants. As a result of the rapid development in this field, the resulting documents for the seismic design of wharves made their interpretation sometimes difficult. POLB recognized the need for uniform and port-specific guidelines and developed port specific Wharf Design Criteria. This paper specifically addresses the Seismic Design Criteria. They include Ground Motions and Performance Criteria, Geotechnical Considerations with particular attention to soil-structure interaction, Structural Design and Analysis Methods, and Seismic Detailing. These subjects are specifically adjusted for site-specific conditions in POLB, such as seismicity, foundation soils, construction practices and the requirements of the Port's Engineering Bureau, which had an important function in the development of the criteria. All seismic design and analysis procedures are based on displacement-based procedures. The development of the criteria was reviewed at various stages by experts in structural, geotechnical, and earthquake engineering disciplines. An experimental program verified the analytical assumptions. POLB's recent wharf construction experience confirmed the practicality of the construction details. It is anticipated that these Criteria will provide more uniformity, focus on design, quality assurance, and minimize construction costs, while providing better coordination between POLB's engineering staff and consultants.

ASCE 7-05 sets the minimum life-safety standards for designing buildings and other structures. However, it does not directly address all of the issues designers typically face in the seismic design of piers and wharves, especially with respect to dealing with kinematic loading from permanent ground deformation. In 2005, ASCE's Codes and Standards Committee and Coastal, Oceans, Ports, and Rivers Institute formed a formal Standards Committee to develop a national consensus standard for seismic design of pile supported piers and wharves. Within this Standards Committee, several Task Committees were formed to address various aspects of seismic design of piers and wharves. Task Committee 7 was charged with developing standards for the geotechnical and soil-structure interaction aspects pertaining to piers and wharves. In addition to recommending different levels of ground motions for different performance levels and importance categories of the structure, the ground motions per ASCE 7-05 are being adopted to maintain consistency with the minimum standards of this document. This paper discusses the efforts to develop the standards and commentaries for the ground motion, geotechnical, and soil-structure interaction aspects of the proposed standard, especially those that are unique to piers and wharves.

Many ports in the Pacific are experiencing significant growth as a result of increased business trade. In these areas of the world, container wharves need to be designed for a combination of gravity loads and seismic loading. The connection between the pile and the wharf is critical as large ductility requirements may be relied upon these connections. This paper discusses the results of an experimental program funded by the Port of Los Angeles (POLA) to improve and enhance the performance of pile-deck connections that will satisfy the requirements of the new "Performance Based Seismic Design Code for Container Wharves" issued by the port. Two full-scale units, representing typical seismic and non-seismic pile-deck connections were tested under reversed cyclic loading. The test units showed lateral displacement reserves significantly greater than those that corresponded to the structural strain-limits in the new Seismic Design Code for the Port of Los Angeles.

The design of wharf systems in areas of high seismicity is quite challenging. The seismic code for the Port of Los Angeles (POLA) specifies the performance for two levels of earthquake intensity, the Operating Level Earthquake (OLE) and the Contingency Level Earthquake (CLE). According to this design procedure, structural behaviors should be controlled well even in large earthquake events, but available information is quite scant and additional experiments are required to obtain better understanding. A current testing program underway at the University of California, San Diego (UCSD) for POLA is aimed at validating the performance of pile foundation behavior in light of the new code. This paper presents detailed information of the testing plan, such as test piles, test set up plan, instrumentation, and so forth. The test has not been carried out yet (November 1, 2006), but it will be conducted soon and test results will be published.

This paper discusses the Seismic Engineering Program that has been developed at the Port of Los Angeles (POLA). Over the years, experts have collaborated with POLA staff in a continuous effort to develop a modern seismic code for container wharves. Since 1990, several workshops have been conducted and many documents and technical papers have been published. The current code, “The POLA Code for Seismic Design, Upgrade and Repair of Container Wharves” (POLA, 2004), emphasizes performance-based design and soil-structure interaction to reflect the challenges of designing container wharf structures in an active fault region of Southern California. A Technical Advisory Board consisting of experts in structural and geotechnical earthquake engineering disciplines has reviewed the development of the code at all stages. Recent wharf construction at the Port confirmed the practicality of the design procedure and construction details. In addition, the Port sponsored and funded an experimental program at the University of California at San Diego to confirm code assumptions. A Port-wide ground-motion and fault study program was undertaken to develop uniform seismic ground motion hazards for the entire Port to augment the Port’s future projects and develop more consistent designs. At the time of writing this paper, POLA is in the process of preparing a book to present its efforts on seismic code development of container wharves. It is hoped that this comprehensive seismic engineering program will provide useful information to other port agencies and the marine design industry both nationally and internationally.

This paper addresses the seismic design of some structural components of the Pier 400 Crude Oil Marine Terminal at the Port of Los Angeles (POLA). With 81 feet (24.64m) water depth at the pier headline, this project will be the largest tanker-handling berth on the West Coast. It is located in a region of high seismic activity and challenging geological sub-surface conditions. These factors combine to present unique design issues. The paper is limited to the seismic analysis and design of the Unloading Platform and the North Trestle providing access to the platform. It describes the geotechnical conditions and areas of special interest, mainly problems encountered in connection with the large horizontal displacements of these structures. Of particular interest is the issue of determining the minimum necessary gap between the trestle and the platform to accommodate the relative displacement of both structures to avoid damaging closure.

This study was conducted to investigate the flexural and shear performance of older columns for purposes of seismic assessment and retrofit design, particularly with regard to assessing the residual strengths present in degraded hinge regions. In this first of a two-part paper, experimental observations and results of tests on eight reduced-scale specimens that incorporated deficiencies present in older bridge columns are presented. The columns were fixed against rotation at both the top and bottom to enable shear transfer, even after a flexural hinging region degrades. Test variables included columns aspect ratio, longitudinal reinforcing ratio, lap splice length, and retrofitting detail. Shear failures were observed both outside and within the plastic hinge regions.