Dynamic Axial Pile Stiffness and Damping in Soil with Double Inhomogeneity

The vertical response of a fixed-head floating single pile embedded in sand is obtained experimentally under 1g conditions. Specifically, pile head stiffnesses and axial strains generated along the pile length for a range of static and dynamic pile head loadings are measured. To account for the effects of soil non-linearity on the static response of the pile, a range of low- to high-magnitude static displacements is considered. Likewise, for the dynamic response, varying amplitudes of vertical harmonic accelerations for a wide range of frequencies are considered. Results obtained from the experiments under both the static and dynamic loading conditions indicate that the pile head stiffness is dependent on the direction of pile head loading – that is, whether the pile is pushed or pulled. To gain further insight into such direction-dependent pile head stiffness, three-dimensional non-linear finite-element analyses are carried out. Numerical results show very good agreement with the experimentally measured pile head stiffnesses. Axial strains generated along the pile length due to head loadings, on the other hand, depend on the amplitude of both the static and the dynamic loadings.

SummaryAn approximate static solution is derived for the elastic settlement and load‐transfer mechanism in axially loaded end‐bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed‐form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth‐dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth‐independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.

In this study, an analytical model is developed to obtain the static response of the vertically loaded pile in the inhomogeneous soil with arbitrary properties varying along the depth. The soil displacement is expressed by the product of the axial displacement function and the shape function attenuating with the distance from the pile periphery. Through the minimum potential energy principle, the governing equations are established for the axial displacement function and the shape function. The governing equation for the shape function is independent of soil properties and it can be explicitly solved. The governing equation for the axial displacement function contains variable coefficients due to the inhomogeneity of soil and it is solved using the weighted residual method. An iterative procedure is introduced to implement the solution. The proposed model is validated by comparing the present solutions with those obtained by the available methods. The parametric study shows that the pile head stiffness is affected by the distribution of soil shear modulus heavily, in which the average shear moduli are the same for these distributions. Moreover, the relationship between the pile head stiffness and the pile slenderness ratio for a floating pile is different from that for an end-bearing pile.

Identification of effective 1D soil models for large-diameter offshore wind turbine foundations based on in-situ seismic measurements and 3D modelling

A procedure for the time domain analysis of axial single pile response is developed. A time domain soil‐pile interaction force is formulated through a simple mechanical idealization of the soil medium, developed from the dynamic behavior of a plane strain continuous elastic medium. A transfer matrix is formulated in the time domain treating the pile shaft as a continuous beam. The response of single piles subjected to harmonic excitation is calculated using both the current time domain analysis procedure and a previously published frequency domain analysis procedure. The comparison between the two results verify the current procedure developed for time domain analysis. Numerical examples are provided for single piles subjected to transient loading.

In this chapter, simplified methods for static and dynamic analysis of pile foundations under axial loads are discussed. Firstly, a number of analytical solutions for Winkler springs and dashpots are briefly reviewed. Secondly, exact and approximate solutions for stiffness of single piles are derived for both homogeneous and inhomogeneous soil profiles using the Winkler model. The approximate solutions are based on energy principles obtained my means of shape functions analogous to those used in finite-element formulations. Thirdly, solutions for grouped piles are derived using the superposition approach of Poulos and Davis. To this end, a family of interaction factors accounting for pile-soil-pile interaction is reviewed. It is shown that soil inhomogeneity and pile-to-pile interaction may have a profound impact on pile head stiffness and ensuing settlement. Results are presented in the form of dimensionless graphs and charts that elucidate critical aspects of the problem, and detailed comparisons with more rigorous numerical continuum solutions are provided. Application examples are presented and discussed.

Numerical investigation on gas production from Shenhu (China): Influence of layer inclination and horizontal inhomogeneities

It is necessary to understand the response of monopile foundations for large offshore wind turbines (OWTs) with rated powers of under cyclic loading. For this purpose, a monopile model test study was conducted in saturated medium dense sand under long-term unidirectional lateral sinusoidal cyclic loading for cycles. The model pile was constructed with displacement transducers on the pile head and strain gauges along the pile length. The experimentally obtained bending moment, displacement, soil reaction evaluation along the pile length, pile head displacement accumulation, and lateral soil-pile stiffness were substantially different from the results of the American Petroleum Institute (API)-recommended method of determination and were significantly affected by the number of loading cycles. The experimentally based soil reaction -pile displacement curves obtained considering the maximum soil reactions for particular cycles were compared with the - curves recommended by the API. The maximum soil reaction during the increase in pile displacement obtained experimentally was significantly higher than the soil reaction obtained with the API method. The p–y curves obtained experimentally show similarities with those determined with the API method at only small pile displacements in the initial stage of the curves.

Piles are often used in groups, and the behavior of pile groups under the applied loads is generally different from that of single pile due to the interaction of neighboring piles, therefore, one of the main objectives of this paper is to investigate the influence of pile group (bearing capacity, load transfer sharing for pile shaft and tip) in comparison to that of single piles. Determination of the influence of load transfer from the pile group to the surrounding soil and the mechanism of this transfer with increasing the load increment on the tip and pile shaft for the soil in saturated and unsaturated state (when there is a negative pore water pressure). Different basic properties are used that is (S = 90%, γ d = 15 kN / m 3 , S = 90%, γ d = 17 kN / m 3 and S = 60%, γ d =15 kN / m 3 ). Seven model piles were tested, these was: single pile (compression and pull out test), 2×1, 3×1, 2×2, 3×2 and 3×3 group. The stress was measured with 5 cm diameter soil pressure transducer positioned at a depth of 5 cm below the pile tip for all pile groups. The measured stresses below the pile tip using a soil pressure transducer positioned at a depth of 0.25L (where L is the pile length) below the pile tip are compared with those calculated using theoretical and conventional approaches. These methods are: the conventional 2V:1H method and the method used the theory of elasticity. The results showed that the method of measuring the soil stresses with soil pressure transducer adopted in this study, gives in general, good results of stress transfer compared with the results obtained from the theoretical and conventional approaches.

Multichannel radiometer measurements of a newly formed contrail taken from a NASA ER‐2 aircraft over northern Oklahoma during the FIRE Cirrus‐II experiment are used in a split‐window retrieval of the contrail's particle size and optical depth. The effect of horizontal inhomogeneity in an underlying cirrus layer on the contrail retrieval is studied through the use of multi‐dimensional radiative transfer model simulations. Estimates of the contrail's effective radius are significantly smaller (5–7 µm) than those in the underlying cirrus (21 µm). The effect of horizontal inhomogeneity in the underlying cirrus on contrail particle size and optical depth retrievals is generally smaller than the corresponding effects of particle shape or spectral variations in surface emissivity on the retrievals. The differences in particle size retrievals are 10 percent or less as a result of the inhomogeneity, while they are from 10 to 40 percent for ice cylinders, and range from 1 to 40 percent for ice spheroids. Horizontal inhomogeneity affected the optical depth retrievals by only one or two percent, while surface emissivity variations affected the retrievals by 12 to 24 percent, and particle shape produced differences as large as 9 percent.

On the response of the ocean upper layer to synoptic variability of the atmosphere

Reliably representing both horizontal cloud inhomogeneity and vertical cloud overlap is fundamentally important for the radiation budget of a general circulation model. Here, we build on the work of Part I of this two‐part paper by applying a pair of parametrizations that account for horizontal inhomogeneity and vertical overlap to global re‐analysis data. These are applied both together and separately in an attempt to quantify the effects of poor representation of the two components on radiation budget.Horizontal inhomogeneity is accounted for using the ‘Tripleclouds’ scheme, which uses two regions of cloud in each layer of a gridbox as opposed to one; vertical overlap is accounted for using ‘exponential‐random’ overlap, which aligns vertically continuous cloud according to a decorrelation height. These are applied to a sample of scenes from a year of ERA‐40 data. The largest radiative effect of horizontal inhomogeneity is found to be in areas of marine stratocumulus; the effect of vertical overlap is found to be fairly uniform, but with larger individual short‐wave and long‐wave effects in areas of deep, tropical convection. The combined effect of the two parametrizations is found to reduce the magnitude of the net top‐of‐atmosphere (TOA) cloud radiative forcing by 2.25 W m−2, with shifts of up to 10 W m−2in areas of marine stratocumulus.The effects on radiation budget of the uncertainty in our parametrizations is also investigated. It is found that the uncertainty in the impact of horizontal inhomogeneity is of order±60%, while the uncertainty in the impact of vertical overlap is much smaller. This suggests an insensitivity of the radiation budget to the exact nature of the global decorrelation height distribution derived in Part I. Copyright © 2010 Royal Meteorological Society

The profile distributions of soil organic carbon (SOC), soil organic nitrogen (SON), soil pH and soil texture were rarely investigated in the Lancangjiang River Basin. This study aims to present the vertical distributions of these soil properties and provide some insights about how they interact with each other in the two typical soil profiles. A total of 56 soil samples were collected from two soil profiles (LCJ S-1, LCJ S-2) in the Lancangjiang River Basin to analyze the profile distributions of SOC and SON and to determine the effects of soil pH and soil texture. Generally, the contents of SOC and SON decreased with increasing soil depth and SOC contents were higher than SON contents (average SOC vs. SON content: 3.87 g kg−1 vs. 1.92 g kg−1 in LCJ S-1 and 5.19 g kg−1 vs. 0.96 g kg−1 in LCJ S-2). Soil pH ranged from 4.50 to 5.74 in the two soil profiles and generally increased with increasing soil depth. According to the percentages of clay, silt, and sand, most soil samples can be categorized as silty loam. Soil pH values were negatively correlated with C/N ratios (r = −0.66, p < 0.01) and SOC contents (r = −0.52, p < 0.01). Clay contents were positively correlated with C/N ratios (r = 0.43, p < 0.05) and SOC contents (r = 0.42, p < 0.01). The results indicate that soil pH and clay are essential factors influencing the SOC spatial distributions in the two soil profiles.

BackgroundSoil microbes exist throughout the soil profile and those inhabiting topsoil (0–20 cm) are believed to play a key role in nutrients cycling. However, the majority of the soil microbiology studies have exclusively focused on the distribution of soil microbial communities in the topsoil, and it remains poorly understood through the subsurface soil profile (i.e., 20–40 and 40–60 cm). Here, we examined how the bacterial community composition and functional diversity changes under intensive fertilization across vertical soil profiles [(0–20 cm (RS1), 20–40 cm (RS2), and 40–60 cm (RS3)] in the red soil of pomelo orchard, Pinghe County, Fujian, China.ResultsBacterial community composition was determined by 16S rRNA gene sequencing and interlinked with edaphic factors, including soil pH, available phosphorous (AP), available nitrogen (AN), and available potassium (AK) to investigate the key edaphic factors that shape the soil bacterial community along with different soil profiles. The most dominant bacterial taxa were Proteobacteria, Acidobacteria, Actinobacteria, Chloroflexi, Crenarchaeota, and Bacteriodetes. Bacterial richness and diversity was highest in RS1 and declined with increasing soil depth. The distinct distribution patterns of the bacterial community were found across the different soil profiles. Besides, soil pH exhibited a strong influence (pH ˃AP ˃AN) on the bacterial communities under all soil depths. The relative abundance of Proteobacteria, Actinobacteria, Crenarchaeota, and Firmicutes was negatively correlated with soil pH, while Acidobacteria, Chloroflexi, Bacteriodetes, Planctomycetes, and Gemmatimonadetes were positively correlated with soil pH. Co-occurrence network analysis revealed that network topological features were weakened with increasing soil depth, indicating a more stable bacterial community in the RS1. Bacterial functions were estimated using FAPROTAX and the relative abundance of functional bacterial community related to metabolic processes, including C-cycle, N-cycle, and energy production was significantly higher in RS1 compared to RS2 and RS3, and soil pH had a significant effect on these functional microbes.ConclusionsThis study provided the valuable findings regarding the structure and functions of bacterial communities in red soil of pomelo orchards, and highlighted the importance of soil depth and pH in shaping the soil bacterial population, their spatial distribution and ecological functioning. These results suggest the alleviation of soil acidification by adopting integrated management practices to preserve the soil microbial communities for better ecological functioning.

Until recently very few successful attempts, have been made to analyze the behavior of piles and pile systems. This is partly associated with the historical development of piling in that a strong tradition of empiricism has become part of the folklore of piling. When one attempt to take into account aspects such as the effect of pile installation major difficulties apparently arise, but the fact that a complete solution cannot be derived does not preclude the use of analytical approaches based on simple models of soil behavior.In this paper a simple numerical technique based on load transfer approach is developed to capture the response of the soil to displacement, as experimental technique of instrumenting the pile along the length of pile would have been very costly. This technique uses the available load settlement data from pile load test not instrumented along pile during load testing and back figures the response of soil along pile length.Once the load settlement response of soil along pile length is known, the curves can be used for the same site to study the effect of different length and/or diameter of the pile on the load settlement curve of pile. In addition, the load settlement curve for other sites can be generated if the soil profile does not vary remarkably from that soil profile from which the load settlement response of soil is developed. This technique is then applied to load settlement data of three pile load tests conducted in various localities of NWFP.