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International Journal of Offshore and Polar Engineering Vol. 13, No. 3, September 2003 (ISSN 1053-5381) Copyright by The International Society of Offshore and Polar Engineers Nonlinear Behaviour of Laterally Loaded Long Piles Penetrating Soft Clay Below Water Table Subjected to Cyclic Loading—Sensitivity Analysis Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada This paper presents the theoretical formulation of sensitivity analysis of laterally loaded piles embedded in soft clay located below the water table. The pile structure is considered to be a 1-dimensional beam. The supporting soft clay isdefined by means of a p-y model. The pile stiffness and material characteristics of a soil’s p-y relationship are taken as thedesign variables. They are considered distributed parameters of a continuous type. The pile-soil system subjected to lateralloading is analyzed in the framework of sensitivity theory by means of an adjoint method for a nonlinear system. The firstvariation of functional of maximum deformations due to the changes of the design variables is formulated based on a virtualwork principle with the aid of variational calculus. The unknown variations of generalized deformations imposed on thepile-soil system are determined by reference to physical relationships that are extended in the scope of sensitivity theoryon the dependence on the design variables. The sensitivities of maximum generalized lateral deflections are determined interms of sensitivity integrands associated with suitable variations of the design variables.
important to identify key factors, in addition to usages that affect the performance of the structure in-service and its evaluation. The The response of a pile to lateral forces and bending moments deterioration of the structure during in-service operations can be is a typical example of the soil-structure interaction system. The lateral loading can result from many sources, for instance, when manifested by excessive deformations or various kinds of distress the high-rise building is subjected to wind load, or when an of strength types. The key factors that cause deterioration of the earthquake induces waves that propagate in a lateral direction.
structure are load, material degradation, environment, construc- Bridge abutments and supports are other examples of structures tion quality and other mechanisms. The primary factor (Hudson supported by piles that have to resist breaking forces exerted by et al., 1997) in most deteriorations of the deformation type is moving vehicles. Offshore structures are the systems that support load and material aging. It is thus essential to develop a method lateral load caused by ocean waves, water currents and various that provides a theoretical basis for an assessment of maximum forces connected with operational processes (Reese and Van Impe, deformations expressed in terms of possible changes of material 2001). The laterally loaded long piles are considered a part of the properties. It is particularly useful to refer such an analysis to the infrastructure that contains assets in transportation, energy pro- structural model that is employed in the design process, which duction, buildings and recreational facilities (Hudson et al., 1997).
defines an initial condition. The discussed criteria can be suit- The development of infrastructure systems integrates the design ably introduced through the distributed parameter sensitivity the- process with maintenance services, future rehabilitation, renova- ory. The application of sensitivity theory to the class of laterally tion and replacement activities in the overall planning and costing.
Traditionally, infrastructure design practices have considered ini- • it is developed in the vicinity of the initial solution considered tial condition, load and material properties as the primary input variables for structural design without taking into account the • the material characteristics are considered spatial functions; effect of environmental and material degradation over time. Such • it is able to indicate the locations of the changes of the sys- an approach does not adequately assess the actual service life tem’s material properties that are critical for an increase of max- of the structure. The performance of an infrastructure element or facility is considered good if it performs as designed and provides • the performance functional of maximum generalized defor- an acceptable level of service over its intended life. The develop- mations that is formulated in the scope of variational calculus ment of good performance models depends on the condition and makes the analysis transparent with respect to spatial variables; assessment methods, load, material behaviour prediction and the • it is possible to assess quantitatively the impact of each taking into account of climatic and environmental conditions. It is change of the material property on the change of maximum defor- The method of sensitivity analysis presented here is in refer- ence to laterally loaded piles embedded in nonlinear soil and is Received April 7, 2003; revised manuscript received by the editors based on the virtual work principle. Thus it contains intrinsically July 25, 2003. The original version was submitted directly to the all the characteristic features this principle requires. It demands knowledge of the physical behavior of the entire system through KEY WORDS: Laterally loaded piles, nonlinear soil-structure interac- tion systems, infrastructure systems, distributed parameter sensitivity the fact of involvement of the work of all internal forces of the analysis of nonlinear systems, adjoint method, sensitivity operators/ entire system. This is mathematically expressed by means of a spatial integral. In the sensitivity formulation presented here, the

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