Bending Moment Profiles Research Articles

Application of PISA method for monopile design in layered soil

The foundation design for offshore wind turbines (OWTs) is critical to ensuring their structural integrity and long-term stability. Large-diameter monopiles are widely used for OWTs owing to their proven effectiveness. The conventional design approach, derived from the oil and gas industry’s p-y model, has limitations when applied to monopiles for OWTs. Consequently, a novel design method based on the PISA joint industry research project was developed, which extends beyond the traditional lateral soil resistance (p-y curves) and incorporates additional soil reaction components from shaft friction, pile base shear, and base moment. Unlike the simplistic rule-based conventional approaches, the proposed method necessitates site-specific 3D finite element (FE) simulations for precise calibration of soil reaction curves. Although successfully applied in European offshore wind farms, the PISA method’s performance in regions with distinct seabed compositions, such as China, remains to be verified. Therefore, this paper presents a comprehensive case study conducted at the Xiangshan wind farm, a representative site characterized by layered soil. The study employed in-situ investigations (cone penetration test, borehole) and laboratory tests (direct simple shear, bender element) to delineate the seabed soil profile and derive essential soil parameters for accurate foundation design. To facilitate the design, an Abaqus-based design tool was developed, which automated the extraction of soil reaction curves from the 3D FE simulations, calibration of PISA springs, and execution of one-dimensional beam-spring analyses employing Timoshenko beam theory. Comparative analyses were performed on the computed responses of piles, encompassing load-deflection curves, pile deflections, and bending moment profiles. The outcomes from the 3D FE simulations, uncalibrated rule-based PISA model, and calibrated PISA model were compared to validate the PISA method for monopile design in layered soil conditions.

Soil–Structure Interactions in a Capped CBP Wall System Triggered by Localized Hydrogeological Drawdown in a Complex Geological Setting

Retaining walls are often used to construct basements and underground station boxes. This unique case study compares the field-measured contiguous bored pile (CBP) wall, surrounding geology, and hydrogeology or groundwater responses against the results using 2D and 3D numerical back analyses of a deep excavation project that experienced localized groundwater drawdown through the leaking ground anchor points. Site observations indicated that the ground anchor installation works had caused larger than expected through-the-wall leakages that subsequently triggered nearby ground and building settlements. In order to study the complex soil–structure interaction behavior, back analyses using a hybrid modeling technique of through-the-wall transient hydrogeological seepage and geomaterial stress-strain analyses was implemented. Through these soil-structure interaction back analyses, it was evidently revealed that the presence of the continuous capping beam was key in providing pile head restraints against the active earth pressures when the groundwater was depressed, as well as efficiently distributing the beneficial wall corner effects towards the middle CBP wall, leading to smaller bending moment magnitudes, characterized by their ‘S-shaped’ profiles. This behavior had been correctly diagnosed, as opposed to the ‘D-shaped’ bending moment profile usually only seen in a typical free-head cantilever wall in similar geology. The eventual results show that the wall and ground responses, i.e., deflection, bending moment, and settlement, were reasonably well predicted when compared against the instrumented field data, thus validating the reliability of the geotechnical modeling technique, key geological parameters, and hydrogeological fluctuations adopted in the 2D and 3D numerical models, as well as the beneficial contributions of the continuous capping beam, which tend to be overlooked during routine retaining wall design.

A methodology to calibrate the PICSI cyclic p-y model using experimental results and optimisation

Fatigue life estimation of the components of a drilling conductor system is often a critical design consideration. The analysis is usually performed using a coupled system, with the soil-conductor interaction modelled using p-y springs that remain constant throughout the analysis. This means that shifts in bending moment profile that occur due to degradation and recovery of the soil during or after cycling are not accurately modelled. While the PICSI framework (White et al., 2022) can model changes in stiffness and strength of p-y curves due to cycling and pore-pressure dissipation, guidance has not yet been provided on how to calibrate its parameters. This paper presents an experimental methodology for this calibration process based on centrifuge and p-y model testing in reconstituted carbonate silt and kaolin clay. The procedure uses numerical optimisation, and the calibrated parameters are validated against results from an independent set of centrifuge tests on carbonate silt using a flexible pile of similar dimensions to a conductor. It is found that the calibrated model is able to match the changes in cyclic bending moment through a sequence of different packets of cyclic loading. This calibration procedure provides an objective approach for more accurate modelling of conductor fatigue.

Dynamic analysis of tripod pile foundation in clays for offshore wind turbines

Tripod pile foundation is pursued as an efficient foundation system for offshore wind turbines (OWTs) installed in deeper waters (20–50m). In this application, the foundations would be subjected to dynamic loads including due to wind, waves, and earthquakes. This paper presents a numerical method for analyzing the dynamic responses of tripod pile foundation installed in clay based on a simplified bounding surface model to capture the clay stiffness degradation. Their behaviors under lateral monotonic, cyclic and seismic loads were investigated, and their bearing mechanism was analyzed. The results revealed that the loading direction significantly affects the ultimate bearing capacity of tripod pile foundation as the foundation capacity results from either a Pile A in tension and a Pile B in compression or vice versa. The evolution of axial force, bending moment and lateral displacement profiles of the Pile A and Pile B with the number of cycles exhibit different characteristics under lateral one-way and two-way cyclic loading. The foundation experiences cumulative rotation angles toward the Pile A side under seismic load due to the lower vertical bearing capacity of the Pile A compared to the Pile B. The tower top experiences the maximum lateral displacement and rotation angle, and the top of tripod support experiences the maximum bending moment. These findings should be considered in the design of OWT tripod pile foundations.

Numerical seismic analysis of high-piled wharf strengthened with CFRP

High-piled wharves are widely employed in coastal areas, but their vulnerability to earthquake damage necessitates effective strengthening measures. This research focuses on investigating the effectiveness of carbon fiber reinforced polymer (CFRP) laminates in enhancing the seismic resistance of high-piled wharves. Full-scale 3D numerical high-piled wharves, divided into As-built groups and Retrofit groups, were established herein. During modeling, the concrete damage plasticity model (CDP) and the finite-infinite coupling element were contemplated. Two representative ground motions, i.e., the EI Centro wave and the Northridge wave, with peak accelerations of 0.2g and 0.4g, respectively, were utilized to simulate different earthquake scenarios. The responses of the resulting earthquake-induced deck displacement, pile distortion, and pile bending moment profile were explored. The computational analysis revealed significant improvements in the seismic performance of the retrofitted wharves compared to the as-built structures, proving that the externally bonded CFRP method was of great significance in improving overall structural seismic performance. Notably, the retrofitted wharf exhibited reduced deck displacement and remarkable decreases in pile deformation and bending moment. The modeling and analysis techniques can be applied to general wharves or other buildings strengthened with CFRP.

Evaluation of Soil–Foundation–Structure Interaction for Large Diameter Monopile Foundation Focusing on Lateral Cyclic Loading

In this study, the monotonic and cyclic behavior of an offshore wind turbine with a monopile foundation installed in a sand layer were evaluated in the centrifuge. A simplified offshore wind turbine was modeled, and the lateral load was applied to the tower under displacement control. The monotonic loading test evaluated ultimate lateral load capacity and bending moment profiles under different loading levels. During cyclic loading, variations of moment-rotation responses, cyclic stiffness, and bending moments along the pile were observed. The initial rotational stiffness of the monopile decreased as the loading level increased. In the fatigue limit state (FLS) and service limit state (SLS) loading conditions, no noticeable variation in stiffness was observed with the number of cycles. However, in the ultimate limit state (ULS), the stiffness of the monopile increased during the first few cycles, followed by a decreasing rate of increase, and reached a certain value. The loading rate had a weakening effect on the monopile–soil interaction, which was supported by the bending moments induced in the monopile.

Field and laboratory experiments on performance of double-pile substructure of bridge along slope strike

This study aims to investigate the performance of the double-pile substructure of the bridge along the slope strike utilizing field and laboratory experiments. In the field experiments, the bending moment profiles of piles increase from negative to positive and then decrease to zero as the depth increases, significantly differing from those of portal anti-slide piles in slope engineering and monopiles in bridge engineering. Furthermore, the profiles of front and rear piles differ in magnitude and the locations of maximums, and it is mainly caused by the load redistribution at the tie beam and different extra earth pressures. After the field experiments, the laboratory model experiments were conducted to investigate the effects of slope angles, pier heights, and loading patterns (i.e. vertical load, lateral load, and surcharge) on the performance of the double-pile substructure. These experimental results were employed to present some fitting formulas for predicting the bending moment profiles and validate two simplified theoretical methods, however, these formulas and methods have their limitations and thus preferable methods are required in the subsequent work.

Evaluation of Liquefaction-induced Lateral Force on Pile in Slope by Centrifuge Tests

Pile foundations in liquefied ground may be subjected to a substantial force induced by lateral soil movement, which is crucial in the seismic design of pile-supported structures. Thus, this study aims to investigate the liquefaction-induced lateral force to piles by conducting centrifuge tests. Pile–deck systems installed in liquefiable finite slope with an angle of 27° were constructed and tested with different base motions. Results show that the liquefied slope pushes the piles toward the downslope, causing a large bending moment. The linear and uniform distributions of lateral soil pressure, which have been previously suggested for pile analysis in liquefied ground, were examined and compared with the measured maximum bending moment. The linear soil pressure profile reasonably predicted the bending moment compared to the results of the uniform profile. The empirical gradient factor of the linear profile was calibrated for the single piles and then implemented in the pile group analysis. The calibrated factor improved conventional methods for predicting the bending moment profile of group piles.

A numerical methodology to predict the lateral load response of monopiles installed in SAND considering soil stiffness degradation

Most of the routine work concerning the design of laterally loaded monopile foundations is conducted using simplified one-dimensional (1D) models based on p-y curves. However, many of these curves have been derived from slender piles typically used in the oil and gas industry, which behave differently than rigid monopiles used as offshore wind turbine foundations. Moreover, these curves usually represent the soil response without considering its degradation, which may significantly modify the monopile lateral response. Hence, this work proposes a numerical methodology based on the finite element method to derive suitable curves for 1D models of monopiles installed in sand. First, a three-dimensional (3D) finite element model (FEM) of the monopile and the surrounding soil was constructed. In this model, the monopile had an elastic and linear material behavior. The soil response was addressed using the Mohr-Coulomb criterion combined with three different soil stiffness degradation models. For extracting the p-y curves from the 3D FEM, a 10th-order polynomial was used to fit the bending moment profiles; consequently, an 8th-order polynomial described the soil reaction profiles. Results obtained using the proposed 3D FEM and a 1D model based on the derived p-y curves were then verified against experimental results obtained through centrifuge modeling. Furthermore, the proposed 1D model adequately matched the experimental results, especially for small displacement conditions.

Effect of Relative Stiffness of Pile and Soil on Pile Group Effect

Pile groups are designed to sustain complex loads in various engineering. During the design of a pile group, the obvious pile group effect should be considered for closely spaced pile groups. However, the group effect considered by different scholars varies, which makes it hard for engineers to consider the pile group effect for the design of a pile group. In this study, the finite element (FE) method is proposed to advance our understanding of the variations of pile group effects developed by different researchers, based on the concept of soil–pile relative stiffness. The relationship between soil–pile relative stiffness and normalized lateral load–displacement curves and bending moment profile response of the pile group is investigated. The results show that the pile group effect increases with the increase in soil–pile relative stiffness; the pile group effect increases with the decrease in pile spacing, increases with the increase in of number of piles in the group, and is significantly affected by pile group arrangement as well.

Effect of embedding depth on the monotonic lateral response of monopiles in sand: centrifuge and numerical modelling

An experimental campaign is conducted on a 100g centrifuged monopile model, impact driven, into saturated dense sand, down to three embedding depths, corresponding to three slenderness ratios of 5, 4 and 3. These models are instrumented with optical fibres to measure the bending moment profile along the monopile. A new method is developed to determine the experimental soil reaction curves by considering the distributed moment part from the measured bending moment. This distributed moment is assessed by the one-dimensional finite-element (1D FE) model of the PISA (pile soil analysis) method. The key features of this study are: (a) the monopile behaves from pure rotation to combined rotation–flexure as the slenderness ratio is enhanced from 3 to 5, inducing a less pronounced linear rotation–deflection response at ground level; (b) although the distributed moment assessed in the PISA project is very low, the developed method is useful to explore the experimental local behaviour of laterally loaded monopiles; (c) the 1D FE PISA model captures reasonably well the overall behaviour of laterally loaded centrifuged driven monopiles, even if it is less accurate for the local behaviour.

A New p–y Curve for Laterally Loaded Large-Diameter Monopiles in Soft Clays

In harsh offshore environmental conditions, the monopile foundations supporting offshore wind turbines must be designed for lateral loads such as winds, waves, and currents. The Beam on Nonlinear Winkler Foundation (BNWF) method has been widely used because of its clear concept and lower calculation cost. The selection of a reasonable p–y curve is critical to the calculation accuracy of this method. This paper clarified the defects of widely used API p–y curves for soft clays and then proposed a new p–y curve with better versatility and applicability. The suitability of the proposed p–y curve was validated by comparing it with the calculation results from the three-dimensional finite element method (3D FEM). Compared with the API p–y curve, the proposed p–y curve can better predict the lateral behavior of large-diameter piles in soft clays, such as the load–displacement curve of the pile head, lateral deflection profile, and bending moment profile. The research findings can provide guidance for the design of monopile foundations supporting offshore wind turbines in soft clays.

Dynamic and monotonic response of Monopile Foundations for Offshore wind turbines using centrifuge testing

The seismic response of monopile foundations is a growing area of research as the offshore wind industry expands worldwide, including in earthquake prone regions of the world. This paper presents dynamic centrifuge tests aimed at investigating the dynamic response of monopiles in both dry and saturated sandy soils. The latter case includes soil liquefaction under strong input motions, with measured excess pore pressures indicating liquefaction. The natural frequency of the monopile-soil system is experimentally determined by measuring the response to a sine sweep motion. Strong earthquakes are then applied at this frequency and its harmonics. This paper discusses the response of the monopile in terms of the peak accelerations observed in the dry and saturated tests, as well as using response spectra and amplification ratios. The dynamic bending moments along the pile are also measured to infer the bending moment profile with depth. Finally, two identical monopiles are pushed-over in each of the centrifuge tests to establish the pre and post-earthquake monotonic response, including the lateral stiffness and capacity, which are compared for the dry model tests and the saturated case.

Direct displacement-based design of coupled walls with steel shear link coupling beams

Coupled walls with replaceable steel shear link coupling beams are used to minimize the repair cost and downtime of buildings after major earthquakes. In this study, the direct displacement-based design (DDBD) method for coupled walls with steel shear link coupling beams using inelastic displacement spectra is developed. For capacity design, a continuum model of the coupled walls that accounts for the stiffness degradation due to expected damage in the first mode is adopted, to obtain equations to estimate the shear forces and bending moments generated due to higher modes. The effectiveness of the DDBD design method for coupled walls with steel shear link coupling beams is assessed by comparing the drift demands with nonlinear response history analysis (NLRHA) results and for capacity design purposes the shear force and bending moment profiles obtained from NLRHA are compared with the results obtained from the equations derived in this study and the weighted capacity design (WCD) method. The results obtained for 5-, 10-, and 15-story coupled walls with steel shear link coupling beams, show that the proposed design methodology is suitable to achieve the design objectives.

Spudcan-pile interaction in thick soft clay and soft clay overlying sand: A simplified numerical solution

A drilling jack-up is often deployed to perform drilling activities or well intervention at an existing fixed jacket platform. Depending on the clearance distance between the aft spudcan and the nearest pile, the installation of the spudcan may have an adverse effect on the platform pile which in turn could compromise the integrity of the jacket structure. This paper presents a simplified method for assessing the effect of spudcan installation on the pile foundation of a jacket platform in thick soft clay and soft clay overlying sand layers. Adopting a two-stage uncoupled approach, in which predetermined free-field lateral soil displacements are applied to a beam-column model with soil modelled using p-y curves, the soil displacements around a penetrating spudcan is estimated by an analytical solution derived from spherical cavity expansion theory. With appropriate consideration for the volume of soil displaced by the penetrating spudcan for the cases of thick soft clay and consideration for soil squeezing for soft clay overlying sand, the computed free-field lateral soil displacements are in fair agreement with the measured profiles in centrifuge tests and can be used in a beam-column model to estimate the induced bending moment in the pile in practice.The pile response to the free-field lateral soil displacements is assessed using a beam-column model incorporating p–y curves, considering the effect of soil remoulding caused by the installation of the spudcan where appropriate. A numerical model which considers the evolving lateral soil displacements due to the progressive advancement of the penetrating spudcan is also studied. The computed pile bending moment profiles are consistent with the measured profiles in the centrifuge tests and those computed by 3D large deformation finite element (LDFE) model. The proposed practical method is simple but yet effective to assess the influence of the installation of a spudcan foundation on an adjacent pile of a jacket platform in thick soft clay and soft clay overlying sand.

Numerical Study of Laterally Loaded Piles in Soft Clay Overlying Dense Sand

This paper presents the results of three dimensional finite element analysis of laterally loaded pile groups of configuration 1×1, 2×1 and 3×1, embedded in two-layered soil consisting of soft clay at liquid limit overlying dense sand using Plaxis 3D. Effects of variation in pile length (L) and clay layer thickness (h) on lateral capacity and bending moment profile of pile foundations were evaluated by employing different values of pile length to diameter ratio (L/D) and ratio of clay layer thickness to pile length (h/L) in the analysis. Obtained results indicated that the lateral capacity reduces non-linearly with increase in clay layer thickness. Larger decrease was observed in group piles. A non-dimensional parameter Fx ratio was defined to compare lateral capacity in layered soil to that in dense sand, for which a generalized expression was derived in terms of h/L ratio and number of piles in a group. Group effect on lateral resistance and maximum bending moment was observed to become insignificant for clay layer thickness exceeding 40% of pile length. For a fixed value of clay layer thickness, lateral capacity and bending moment in a single pile increased significantly with increase in pile length only up to an optimum embedment depth in sand layer which was found to be equal to three times pile diameter and 0.21 times pile length for pile with L/D 15. Scale effect on lateral capacity has also been studied and discussed. Doi: 10.28991/cej-2021-03091686 Full Text: PDF

Finite element analysis of cyclic lateral responses for large diameter monopiles in clays under different loading patterns

It is very important to analyze the lateral cyclic response of monopiles for the design of offshore wind turbines (OWTs). A three-dimensional finite element method for lateral cyclic responses of large-diameter monopiles is developed based on a simplified constitutive model of clays that has been successfully encoded into the ABAQUS software package. The applicability of this method is validated by simulating the existing centrifugal model test. The method can predict the nonlinear hysteresis responses of monopiles in clays during cyclic loading, and the evolution of bending moment and lateral deflection profile of monopile with loading cycles. Various lateral cyclic loads with different loading patterns including one-way and two-way loading, symmetric and asymmetric loading, variable-amplitude and constant-amplitude loading are applied to monopiles. The impact of different cyclic loading patterns on lateral responses of large-diameter monopiles is systematically investigated. The research results can provide some reference for the engineering design of large-diameter monopiles under lateral cyclic loads.

Influence of lateral cyclic loading on the piled-raft foundation embedded in layered soil

The work includes an experimental analysis was performed to determine the impact of several variables on the behavior of laterally loaded piled raft model (2×2) having a ratio of length to diameter (L/D=40) and a diameter spacing (S / D) ratio of 3, 5 and 7 at frequency (0.2) Hz embedded in layered soil. The results are submitted as load-deflection curves and bending moment profiles. The effects of degree of saturation, number of cycles, level of cyclic loads, and the location of piles in a row are studied in this work. The results illustrated that increasing degree of saturation for clay soil (mid-layer) decreasing the lateral resistance of this model by about (25%, 31%, and 39%) for S/D=3, 5, and 7 respectively and bending moment by about (7%, 15%, and 17%) for S/D=3, 5, and 7 respectively. The piles in the front rows resist the soil with its full capacity, while in the trailing rows (i.e back) the shadowing effect tends to cause a reduction in soil resistance. The results clarified that maximum bending moment for trailing row less than the leading row by about 7%. The presence of vertical loads lead to an improvement in the lateral resistance of the model with dry clay soil about (28%, 26% and 12%) for S/D=3, 5, and7 respectively, whereas the increase in the horizontal resistance of the model with partially saturated clay soil about (40%, 45%, and 44%) for S/D=3, 5, and 7 respectively, compared with the absence of vertical loads.

A Numerical Analysis on the Behavior of Single Battered Pile under Pullout Loading

Batter or raker piles are piles driven at an inclination with a vertical to resist large inclined or lateral forces. Many structures like offshore structures and towers are subjected to overturning moments due to wave pressure, wind load, and ship impacts. Therefore in such structures, a combination of the vertical and batter piles is used to transfer overturning moments in compression and tension forces to the foundation. This paper presents a three-dimensional finite element analysis using PLAXIS 3D software to study the battered pile's behavior under the effect of pullout load. Several variables that influence the pile tension capacity embedded in sandy soil are investigated. The pile models are steel piles embedded in the dense sand at different batter angles (0, 10, 20, and 30) degrees with two embedment ratios, L/d (15 and 20). To clarify the pile shape's influence on a pullout capacity, two shapes are used, a circular pile with a diameter equal to 20 mm and a square pile with a section of 15.7×15.7 mm. These dimensions are chosen to achieve an equal perimeter for both shapes. The numerical results pointed that the pile pullout capacity increases with the increasing of the batter angle and embedment ratio, and the maximum values are marked at a batter angle of 20o. The shape of the bending moment profile is a single curvature, and the peak values are located approximately at the midpoint of the battered pile, while a zero value is located at the pile tip and pile head.

Quantification of the Effect of Train Type on Concrete Sleeper Ballast Pressure Using a Support Condition Back-Calculator

Monitoring ballast support condition and improving current sub-structure and ballast maintenance strategies is critical to ensuring safe and efficient railroad operations. Researchers at the University of Illinois at Urbana-Champaign (Illinois) have developed a ballast support condition back-calculator, a non-destructive instrumentation method and corresponding analysis tool that quantifies ballast pressure distributions under concrete sleepers without interrupting revenue service train operations. This laboratory-validated non-intrusive method uses concrete sleeper bending moment profile and rail seat loads as inputs to back-calculate the reaction distribution using a Simulated Annealing optimization algorithm that incorporates Pareto Distribution as the random variable generator. In order to further understand in-service ballast support conditions, concrete surface strain gauges were installed on concrete sleepers at a revenue service field site to measure strains that could subsequently be converted into bending moments. This site is on a shared use rail corridor with traffic ranging from high speed passenger to heavy axle load (HAL) freight trains. Rail-mounted strain gauges were used to measure strains that were used to calculate the vertical wheel-rail loads to approximate rail seat loads. This paper quantifies the ballast pressure distributions beneath concrete sleepers under different types of rolling stock and evaluates how ballast support condition changes as a function of accumulated tonnage. A wide range of loads were observed at the field site, ranging from 4 to 35 kips (18–156 kN). Corresponding ballast pressures ranged from 14 to 175 psi (97–1,207 kPa), with sleeper-ballast contact area corresponding to 60% of the bottom of the sleeper area. The accumulation of 12.24 million gross tons (MGT) (12.44 million tons) did not generate a quantifiable change in ballast pressure values nor did it generate a change in the ballast support condition. The research results presented in this paper demonstrate the potential of the back-calculator to provide a stand-alone non-invasive method to quantify ballast support conditions, sleeper health, and sleeper bearing stress. Back calculator data will aid the rail industry in optimizing tamping cycles, enhancing safety, and developing more representative concrete sleeper flexural designs based on actual support conditions.