**Peer Reviewed**

**Source**

**Conference**

**Publisher**

**Theme**

**Author**

**Concept Tag**

- 15-point difference (1)
- 15-point difference format (1)
- 15-point scheme (1)
- 25-point scheme (1)
- analytic solution (1)
- bandwidth (1)
- cc cc cc cc (1)
- critical angle (1)
- deep water (1)
- deflection (2)
- deformation (1)
- difference operator (1)
- Difference Scheme (1)
- dispersion (1)
- edge wave (1)
- energy spectra (1)
- equation (1)
- finite difference (1)
- flexible pile (1)
- frequency (1)
- frequency-space domain (1)
- GBT (1)
- generalized beam theory (1)
- ij ij (3)
- ij ij ij (2)
**ij ij ij ij (4)**- impedance matrix (1)
- interaction (1)
- kinematic-dynamic element (1)
- Laterally (1)
- longitudinal (1)
- LU decomposition (1)
- membrane (1)
- modeling (1)
- nonlinear (1)
- nonlinear interaction (1)
- Offshore (1)
- offshore projects planning and execution (1)
- order term (1)
- pile head (1)
- plastic (1)
- platform design (1)
- Reservoir Characterization (3)
- shear strain (1)
- soil-pile interaction model (1)
- spectra (1)
- spectral (1)
- stiffness (1)
- subsea system (1)
- surface elevation (1)
- transfer matrix (1)
- transfer matrix coefficient (1)
- University (1)
- Upstream Oil & Gas (3)
- uu uu uu uu (1)
- variance (1)
- velocity field (1)
- virtual work (1)

**File Type**

Zhu, Ming-xing (Jiangsu Electric Power Design Institute (JSPDI) Co., Ltd. of China Energy Engineering Group) | Lu, Hong-qian (Jiangsu Electric Power Design Institute (JSPDI) Co., Ltd. of China Energy Engineering Group) | Wang, Lei (Jiangsu Electric Power Design Institute (JSPDI) Co., Ltd. of China Energy Engineering Group) | Gong, Wei-ming (Southeast University)

**ABSTRACT**

Determining the response of the laterally loaded piles analytically is one of the challenging problems due to the complexity of soil-pile interaction models and the difficulty to solve governing difference equations. In this paper, a general solution for laterally loaded piles is proposed for multilayered soil systems with any forms of *p-y* curves. The generalized solution of laterally loaded pile was formulated based on the transfer matrix approach. The elastic and plastic transfer matrix coefficients for pile segment at any depth were analytically obtained through Laplace transformation. Validations of the proposed method are performed through comparison between our predictions with the results from existing methods. Good agreements are reached which implies that the proposed method can be employed as an alternative method to effectively evaluate the response of laterally loaded piles. Moreover, a parametric study on pile bending stiffness is performed to investigate its influence on the ultimate capacity of laterally loaded piles in the same soil profile. We found that these three piles with different bending stiffness would have the same limit state distribution of soil resistance along the pile with the same rotation center below soil surface, which will yield identical ultimate lateral bearing capacity and corresponding maximum bending moment *(M*max) for the piles. Under the concept of the maximum bending moment *(M*max), it would be more rigorous to define a rigid pile when plastic moment *M*p along the pile exceeds *M*max and to define a flexible pile when *M*p is less than *M*max, especially for piles in multilayered soil deposits.

**INTRODUCTION**

Piles are extensively used as foundations not only to transfer vertical loads from upper structures to surrounding soils, but also to bear horizontal forces and moments simultaneously. In offshore engineering (e.g., offshore wind turbine and oil production platforms), the piles are mainly designed to resist the lateral loads mainly from the wind to the upper structure, water pressure and seismic activity to the foundation (Basu et al., 2008). The subgrade reaction concept of laterally loaded piles was introduced since the piles behave as Winkler model against lateral loads. To determine the pile responses rigorously is one of the challenging problems due to the complexity of soil-pile interaction and difficulty of solving the governing fourth order differential equation on the basis of subgrade reaction approach.

Zhang, Y. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China) | Hong, G.W. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China) | Feng, W.B. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China)

By using perturbation method, second-order analytical solutions of short edge-wave interactions were introduced. In this paper, the analytic expressions and numerical calculations of the main kinematicdynamic elements such as free surface elevation, velocity and energy of regular edge waves, spectrum and its characteristics of irregular edge waves were given. The calculation results had shown that significant distinctions on these kinematic-dynamic elements could appear due to different values of slope angle, the mode number and nonlinear interactions of edge waves. **INTRODUCTION**

Edge waves are the trapped-waves propagating alongshore, which may occur near coastal region. They play an important role in the deformation of beach morphology, long-shore currents and wave runup etc. Linear analytic solutions of edge waves of 0-mode on a constant sloping beach were derived by Stokes (1846), which exponentially decay offshore and their energy is concentrated near shore region. Using the linear shallow water equations, Eckart (1951) obtained an approximation solutions of edge waves of infinite number modes to the same problem. Based on full water wave equations, Ursell (1952) presented the full linear solutions of finite mode edge waves. According to Ursell’s solutions, as the full mode number N becomes larger, the edge wave surface elevation, which has nodes N, become more complicated. The comparisons of the above mentioned Eckart’s and Ursell’s solutions were made by Yeh (1986) etc. It is shown that the error of the shallow water approximation is larger as the beach slope gets steeper and the distance is farther from the shoreline. Recently, several excitation mechanisms of edge waves were proposed by Gallagher (1971),Guza & Davis(1974),Bowen & Guza (1978), Foda & Mei (1981), Lippman& Holman (1997), Lin (2005) etc. based on nonlinear resonant interactions of three waves, four waves, wavebreaking in the surf zone. Most of them were based on nonlinear shallow water equation of long waves on gentle slope.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.31)

In this paper, aiming at suppressing dispersion effectively with a smaller impedance matrix bandwidth in frequency-space domain, we propose an optimal 15-point difference scheme using weighted averaging operator, averaging the mass acceleration term and coefficient optimization. Meanwhile, we respectively apply compressed storage method and perfectly matched layer (PML) boundary condition to store the huge impedance matrix and eliminate the reflection from the boundary. Finally, through the comparison with 9-point scheme (Jo et al, 1996), 25-point scheme (Shin et al, 1998) and time-domain method, it is proved that this difference scheme can effectively suppress dispersion in frequency domain without adding too much calculation amount.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.98)

First-order Generalized Beam Theory (GBT) describes the behaviour of prismatic structures by ordinary uncoupled differential equations, using deformation functions for bending, torsion and distortion. In secondorder theory, the differential equations are coupled by the effect of deviating forces. By introduced the virtual works of longitudinal membrane bending moment and membrane shear strain into the GBT system, the complete expansions of the third order GBT equation, were obtained in the form of a series of large discretized iterated functions and converted to sets of tangent stiffness matrices for numerical analyses. By deriving out the membrane stresses as the third order terms

Generalized Beam Theory (GBT) unifies the conventional theories for the analysis of prismatic thin-walled structural members with a consistent notation. Besides the four rigid body modes with which the conventional beam theory deals with, namely extension, bending about the two principal axes and torsion, the higher order modes of deformation which involve cross section distortion are included in the theory. It provides elegant and economical solutions to a wide range of complex problems and a natural transition from beam theory to folded plate theory. As a unique advantage, especially for the cold formed cassette analysis, GBT is capable to consider a single buckling mode and the combination of any selected buckling modes as specified by the user. This is not possible with any other method. The development of GBT was pioneered by Schardt (1966, 1982, 1984, 1994) and his colleagues at the University of Darmstadt in Germany, work that has extended over more than 20 years.

SPE Disciplines:

Thank you!