Axial Force Distribution Research Articles

Vertical Bearing Capacity Properties Study of Punched Cast-in-Place Pile Based on Field Test in Driving Analysis Test on Piles of a Thermal Power Plant

Through the vertical static load test of pile, studied and demonstrated the applicability of cast-in-place piles in the construction of a thermal power plant’s in Guangxi Zhuang Autonomous Region, china. By testing the internal force of pile shaft, obtained the distribution of axial force, side friction and tip resistance, and ascertained the vertical bearing capacity of punched cast-in-place piles in the engineering geological conditions of this project. This research provides the important quality control standards and design basis for the follow-up pile foundation construction of large area of this project, and also provides reference for other projects in this area.

Finite Element Analysis of Composite Soil-Nail Retaining Structure in Foundation Pit Engineering

Base on general three dimension nonlinear numerical simulation software, mechanism of composite soil-nail retaining structures in foundation-pit engineering are analyzed in this paper. Research contents include construction process simulation of excavation by steps, soil nailing installation and panel manufacture etc. Tension distribution range of soil layer, bottom heaving in the pit and axial force distribution along nail etc. are analyzed through the comparison of mechanical characteristics between computational results and field test data in the case of micro pile composite soil-nail support engineering. The action mechanism and working performance of composite soil-nail retaining support are also systematically studied and theoretical basis can be provided in optimal design, popularization and application.

Open face 터널시공으로 인한 단독말뚝의 거동

본 연구에서는 3차원 유한요소해석을 실시하여 견고한 점토에 기시공되어 있는 단독말뚝의 하부에서 실시된 open face 터널굴착에 의한 말뚝의 거동을 분석하였다. 수치해석에서는 터널굴착으로 인한 말뚝의 거동을 규명하기 위하여 지반, 말뚝의 침하 및 전단응력전이 메커니즘을 심도 있게 분석하였다. 터널굴착으로 인해 Greenfield 조건의 지표면의 침하를 크게 초과하는 말뚝침하가 발생하였으며, 말뚝과 인접지반 사이 경계면에서의 전단응력전이현상으로 인해 말뚝에 작용하는 축력의 분포가 매우 크게 변화하였다. 말뚝침하의 증가로 인하여 말뚝의 겉보기지지력(apparent pile capacity)이 약 30% 감소하는 것으로 분석되었다. 터널굴착에 따른 지중응력 및 변형에 의해 말뚝의 마찰력이 증가하는 현상이 발생하고 이에 따라 말뚝의 축력이 터널의 굴착에 따라 지속적으로 감소하였다. 순수하게 터널굴착에 의하여 단독말뚝에는 설계하중의 최대 21%에 상응하는 인장력이 유발되는 것으로 분석되었다. 말뚝은 터널의 시공이 말뚝의 중심에서 종방향으로 <TEX>${\pm}1$</TEX>-2D (D: 터널직경)에서 실시될 때 가장 큰 영향을 받는 것으로 나타났다. 말뚝선단 인근에서는 (-)의 과잉간극수압이 발생하였으며, 말뚝상부 부근에서는 (+)의 과잉간극수압이 발현하였다. 터널굴착에 의한 말뚝의 사용성은 축력변화에 비해서는 말뚝의 침하에 의해 큰 영향을 받는 것으로 분석되었다. Three-dimensional (3D) finite element analyses have been performed to study the behaviour of a single pile to open face tunnelling in stiff clay. Several key factors such as tunnelling-induced ground and pile settlement, and shear transfer mechanism have been studied in detail. Tunnelling resulted in the development of pile settlement larger than the Greenfield soil surface settlement. In addition, due to changes in the shear transfer between the pile and the soil next to the pile with tunnel advancement, axial force distributions along the pile change drastically. The apparent allowable pile capacity was reduced up to about 30% due to the development of tunnelling-induced pile head settlement. The skin friction on the pile was increased with tunnel advancement associated with the changes of soil stresses and ground deformation and hence axial pile force distribution was reduced. Maximum tunnelling-induced tensile force on the pile was about 21% of the designed pile capacity. The zone of influence on the pile behaviour in the longitudinal direction may be identified as <TEX>${\pm}1$</TEX>-2D (D: tunnel diameter) from the pile centre (behind and ahead of the pile axis in the longitudinal direction) based on the analysis conditions assumed in the current study. Negative excess pore pressure was mobilised near the pile tip, while positive excess pore pressure was computed at the upper part of the pile. It has been found that the serviceability of a pile experiencing adjacent tunnelling is more affected by pile settlement than axial pile force changes.

풍화암에서 실시된 터널굴착으로 인한 단독말뚝 및 군말뚝의 거동

본 연구에서는 3차원 탄-소성 유한차분해석을 통해 기존재하는 단독말뚝, <TEX>$3{\times}3$</TEX>및 <TEX>$5{\times}5$</TEX> 군말뚝의 바로 아래 풍화암 지반에서 실시된 터널시공으로 인한 말뚝의 거동을 분석하였다. 수치해석에서는 터널굴착으로 인한 말뚝의 거동을 규명하기 위하여 지반/말뚝의 침하 및 전단응력전이(shear stress transfer) 메커니즘을 심도있게 분석하였다. 터널굴착으로 유발된 지반의 침하와 말뚝-지반 사이 경계면에서의 상대변위 발생으로 인해 말뚝에 작용하는 전단응력 및 축력의 분포가 매우 크게 변화하였다. 계산된 결과에 의하면 터널굴착으로 인해 말뚝의 두부로부터 말뚝길이의 약 80%에 해당되는 위치까지는 상향의 전단응력이 발생하였고, 그 하부에서는 하향의 전단응력이 발생하였다. 이로 인해 말뚝의 축력이 터널의 굴착에 따라 지속적으로 감소하고, 순수한 터널의 시공으로 인하여 말뚝에는 인장력이 발생하였는데 이로 인해 말뚝에는 최대 <TEX>$0.36P_a$</TEX>의 인장력이 발생하였다, 여기서 <TEX>$P_a$</TEX>는 터널굴착이전에 말뚝두부에 작용하는 설계하중이다. 말뚝의 거동은 경계면에서의 전단강도 발현 정도에 가장 큰 영향을 받는 것으로 나타났다. 군말뚝의 경우 일반적으로 말뚝의 숫자가 증가할수록 터널의 시공에 의해 말뚝의 침하가 증가하는 것으로 나타났으며, 이와는 반대로 말뚝의 축력변화는 군효과(shielding effect)로 인해 단독말뚝의 경우에 비해 작은 것으로 분석되었다. 터널굴착으로 인한 말뚝침하의 증가로 인한 겉보기지지력(apparent pile capacity) 감소는 단독말뚝에 비해 군말뚝에서 두드러지는 것으로 분석되었다. The effects of tunnelling in weak weathered rock on the behaviour of a pre-existing single pile and pile groups (<TEX>$3{\times}3$</TEX> and <TEX>$5{\times}5$</TEX> pile groups) above a tunnel have been studied by carrying out three-dimensional (3D) elasto-plastic numerical analyses. Numerical modelling of such effects considers the response of the single pile and pile groups in terms of tunnelling-induced ground and pile settlement as well as changes of the shear transfer mechanism at the pile-soil interface due to tunnelling. Due to changes in the relative shear displacement between the pile and the soil at the pile-soil interface with tunnel advancement, the shear stresses and axial pile force distributions along the pile change drastically. Based on the computed results, upward shear stresses are induced up to about Z/L=0.775 from the pile top, while downward shear stresses are mobilised below Z/L=0.775, resulting in a reduction in the axial pile force distribution with depth equivalent to a net increase in the tensile force on the pile. A maximum tensile force of about <TEX>$0.36P_a$</TEX> developed on the single pile solely due to tunnelling, where <TEX>$P_a$</TEX> is the service axial pile loading prior to tunnelling. The degree of interface shear strength mobilisation at the pile-soil interface was found to be a key factor governing pile-soil-tunnelling interaction. Overall it has been found that the larger the number of piles, the greater is the effect of tunnelling on the piles in terms of pile settlement, while changes of the axial pile forces for the piles in the groups are smaller than for a single pile due to the shielding effect. The reduction of apparent allowable pile capacity due to tunnelling-induced pile head settlement was significant, in particular for piles inside the groups.

사용 중인 단독 및 군말뚝의 측면에서 실시된 터널굴착으로 인한 말뚝의 거동

본 연구에서는 3차원 유한요소해석을 실시하여 사용 중인 단독말뚝 및 군말뚝의 측면에서 실시된 터널굴착에 의한 말뚝의 거동을 분석하였다. 수치해석에서는 터널굴착으로 유발된 말뚝-지반 경계면에서의 전단응력전이를 미끄러짐(slip)을 고려할 수 있는 접촉요소(interface element)를 이용하여 분석하였다. 본 연구는 말뚝-지반경계면에서의 전단응력, 말뚝의 축력 및 지반 및 말뚝의 변형에 대한 분석을 포함한다. 탄성이론에 근거한 기존의 연구는 말뚝의 거동에 영향을 미치는 주요인자들을 적절히 고려하지 못하여 말뚝의 거동을 명확하게 분석할 수 없는 것으로 나타났다. 터널굴착으로 유발된 말뚝-지반 사이에서의 전단응력전이로 인하여 말뚝인접 지반의 전단응력 및 말뚝의 축력분포가 크게 변하는 것으로 나타났는데, 터널 springline 상부에서는 하향의 마찰력이 발생하였으며, 그 하부에서는 상향의 저항력이 발현되어 말뚝에는 압축력이 발생하였다. 경계면에서의 전단응력 발현정도는 말뚝-지반의 상호거동에 가장 큰 영향을 미치는 것으로 분석되었다. 군말뚝의 축력분포에 대한 분석결과 단독말뚝에 비해 터널굴착의 영향을 덜 받는 것으로 나타났다. 터널굴착으로 유발된 말뚝의 침하와 관련된 말뚝의 겉보기 지지력 감소는 크지 않은 것으로 분석되었다. Three-dimensional (3D) numerical analyses have been performed to study the behaviour of single piles and grouped piles to adjacent tunnelling in the lateral direction of the pile. In the numerical analyses, the interaction between the tunnel, the pile and the soil next to the piles and shear transfer mechanism have been analysed allowing soil slip at the pile-soil interface by using interface elements. The study includes the shear stresses at the soil next to the pile, the axial force distributions on the pile and the pile settlement. It has been found that existing elastic solutions may not accurately estimate the pile behaviour since several key issues are excluded. Due to changes in the shear transfer between the pile and the soil next to the pile with tunnel advancement, the shear stresses and axial force distributions along the pile change drastically. Downward shear stress develops above the tunnel springline while upward shear stress is mobilised below the tunnel springline, resulting in a compressive force on the pile. In addition, mobilisation of shear strength at the pile-soil interface was found to be a key factor governing pile-soil-tunnelling interaction. It has been found that grouped piles are less influenced by the tunnelling than the single pile in terms of the axial pile forces. The reduction of apparent allowable pile capacity due to pile settlement resulted from the tunnelling seemed to be insignificant.

Three-dimensional numerical analyses of the response of a single pile and pile groups to tunnelling in weak weathered rock

The effects of tunnelling in weak weathered rock on the behaviour of a pre-existing single pile and pile groups (3×3 and 5×5 pile groups) in weathered residual soil above a tunnel were studied by performing three-dimensional (3D) elasto-plastic numerical analyses. Due to changes in the relative shear displacement between the pile and the soil at the pile–soil interface resulting from the ground deformation occurring with tunnel advancement, the shear stresses and axial pile force distributions change drastically. Upward shear stresses are induced throughout most of the length of the pile except near the tip of the pile, where downward shear stresses are mobilised, resulting in a reduction in the axial pile force distribution with pile depth equivalent to a net increase in the tensile force on the pile. In doing so, the shear transfer mechanism at the pile–soil interface associated with the tunnelling has been fully investigated. A maximum tensile force of approximately 0.20Pa developed on the single pile solely due to tunnelling based on the concrete analysis conditions where Pa is the service axial pile loading prior to tunnelling. Overall, a larger number of piles causes a greater effect of tunnelling on the piles in terms of pile settlement, whereas changes in the axial pile forces for piles in groups causes a smaller effect than for a single pile due to the shielding effect. Empirical methods that estimate pile settlements need to be modified. More deformations and stresses are induced on the tunnelling lining when there is a pile group above a tunnel than when there is a single pile. The reduction of the apparent allowable pile capacity due to tunnelling-induced pile head settlement was significant, in particular for grouped piles. Several insights into the pile response to tunnelling obtained from numerical analyses are reported and discussed.

Load transfer behaviour of a tapered rigid pile

Based on Mohr–Coulomb theory and the load transfer method, a new method of analysing the load–settlement relation and the axial force distribution model in a tapered pile is suggested. The method proposed in the paper considers the influence of the pile–soil radial interaction on the bearing capacity and settlement behaviour. The calculation results show that the pile–soil radial interaction is strengthened and the bearing capacity of a single pile is increased when the taper angle of a rigid pile is increased. The reliability was verified by two model tests. Calculated results obtained by the proposed method were compared with the test data. The close agreement between the calculated and measured values confirmed that the method is reasonably accurate for analysing the behaviour of tapered rigid piles.

Optimization Simulations of Support System by Composite Soil-Nail Retaining Structure

Mechanism of composite pre-reinforced micro pile soil-nail and pure soil-nail retaining structure in foundation-pit engineering are analyzed in this paper through general three dimension nonlinear numerical simulation software. Research contents include whole construction process simulation of construction such as excavation by steps, piles and soil-nail installation and panel manufacture etc. By the comparison of mechanical characteristics between the pure soil-nail and composite soil-nail retaining structures in the same slope engineering example, differences of tension distribution range of soil layer, deformation features, mechanical characteristics of support and axial force distribution along nails etc. are analyzed. Research results are verified by in-site projects and measured data. The action mechanism and working performance of composite soil-nail retaining support are also systematically studied and theoretical basis can be provided in the similar application.

NONLINEAR ANALYSIS OF OFFSHORE STRUCTURES UNDER WAVE LOADINGS

The structural design requirements of an offshore platform subjected wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. A nonlinear response analysis of a fixed offshore platform under wave loading is presented, the structure is discretized using the finite element method, wave force is determined according to linearized Morison equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the one year return period wave and must be able to survive the 100 year return period storm conditions. The result of the study shows that the nonlinear response investigation is quite crucial for safe design and operation of offshore platform.

Performance of Transportation Infrastructure

Performance of Transportation Infrastructure

Numerical analysis of the interface shear transfer mechanism of a single pile to tunnelling in weathered residual soil

Three-dimensional (3D) numerical analyses have been carried out to study the behaviour of a single pile to adjacent tunnelling in the lateral direction of the pile. The numerical analyses have included comparisons between the current study, previous elastic solutions and advanced 3D elasto-plastic analyses. In the numerical analyses, the interaction between the tunnel, the pile and the soil next to the pile has been analysed. The study includes the axial force distributions on the pile, the relative shear displacement between the pile and the soil, the shear stresses at the soil next to the pile and the pile settlement. In particular, the shear stress transfer mechanism along the pile related to tunnel advancement has been analysed by using interface elements allowing soil slip. It has been found that existing solutions may not accurately estimate the pile behaviour since several key issues are not included. Due to changes in the relative shear displacement between the pile and the soil next to the pile with tunnel advancement, the shear stresses and axial force distributions along the pile change drastically. Downward shear stress develops at the upper part of the pile, while upward shear stress is mobilised at the lower part of the pile, resulting in a compressive force on the pile. A maximum compressive force of about 0.25–0.52Pa was developed on the pile, solely due to tunnelling, depending on the pile tip locations relative to the tunnel position, where Pa is the service pile loading prior to tunnelling. The majority of the axial force on the pile developed within ±2D in the transverse direction (behind and ahead of piles) relative to the pile position, where D is the tunnel diameter. In addition, mobilisation of shear strength at the pile–soil interface was found to be a key factor governing pile–soil–tunnelling interaction. The reduction of apparent allowable pile capacity due to tunnelling was dependent on the pile location relative to the tunnel position. Some insights into the pile behaviour in tunnelling obtained from the numerical analyses will be reported and discussed.

Seismic Performance Analysis of Transmission Tower System Based on MATLAB Numerical Calculation

Transmission tower line system dynamic response and failure mechanism are very complex under seismic load, the dynamic response and cooperation mechanism of the upper structure, pile and soil of transmission tower line system under seismic load based on the MATLAB numerical calculation method in this paper, and the displacement, acceleration velocity and displacement of axial force distribution of different positions of transmission tower line system are calculated by building transmission tower line of the stiffness matrix, equivalent load node, system quality matrix, motion equation and the upper structure of whole pile of model and with the help of the solution of the MATLAB function. The numerical calculation results show that the soil-consider the upper structure of pile-coordination effects for displacement and acceleration amplification effect are obvious, but the truss of axial force amplification effect is relatively small. Meanwhile, the earthquake action soil pile-between the upper structure are strong dynamic interaction, which provides certain theoretical guidance for recognizing transmission tower line system dynamic response mechanism under earthquake and adopting efficient anti-seismic measures.

Seismic Performance Analysis of Transmission Tower System Based on MATLAB Numerical Calculation

Transmission tower line system dynamic response and failure mechanism are very complex under seismic load, the dynamic response and cooperation mechanism of the upper structure, pile and soil of transmission tower line system under seismic load based on the MATLAB numerical calculation method in this paper, and the displacement, acceleration velocity and displacement of axial force distribution of different positions of transmission tower line system are calculated by building transmission tower line of the stiffness matrix, equivalent load node, system quality matrix, motion equation and the upper structure of whole pile of model and with the help of the solution of the MATLAB function. The numerical calculation results show that the soil-consider the upper structure of pile-coordination effects for displacement and acceleration amplification effect are obvious, but the truss of axial force amplification effect is relatively small. Meanwhile, the earthquake action soil pile-between the upper structure are strong dynamic interaction, which provides certain theoretical guidance for recognizing transmission tower line system dynamic response mechanism under earthquake and adopting efficient anti-seismic measures.

The Finite Element Analysis on Mechanical Properties of the Meridians Stair Skeleton of Medical Exhibition Center in Taizhou City

The alien space meridians stair steel structure is first adopted in Taizhou medical city exhibition center project. Based on the finite element calculation method for curved beam element stiffness matrix, convergence standard controls and iteration method of solving the modification and optimization in this paper, the complex alien space meridians framed calculation model is built, and the distribution of axial force and bending moment distribution of the stairs meridians skeleton structure are calculated, and the position and numbers are determined. Numerical results show that the maximum space alien meridians stair axial force is 34.5 KN and maximum bending moment is 5.9 KN•m, which satisfy the standard requirement, then the size curvature big, mechanical transmission line complex and local internal force big technology problem skeleton structure have been solved .Therefore, a strong engineering application value achieves in this paper.

Numerical Simulation on Framed Anti-Sliding Piles

As a new bracing structure, the framed anti-sliding piless based on spatial framework structure, which have the advantages of less displacement in the top of the piles and large anti-force, are developed as a new retaining structure, and can be used to reduce the piles deformation. However, the previous calculation models of double-row piles ignored the deformation coordination action between linking beams and ring beams, the interaction between piles and beams. Further more the calculation results based on the models are not accurate enough. In this paper, a spatial force model of the framed anti-sliding piles is presented. Taking framed anti-sliding piles as a single-layer multi-span frame affected by piles, beams and soils, the spatial synergic interaction between top ring beam and linking beam, as well as the affection of soil-arch on the frame are analyzed. The horizontal displacement in front of the framed anti-sliding piles and distribution of axial force and moment of piles are studied by Finite element method. The results reflect commendably the stress and distortion character of the framed anti-sliding piles. Finally, some rules about the pile-beam-soil interaction in the pile structure are summarized.

Analysis of Single Pile Settlement in Layered Soils Based on Shear Displacement Method

Based on the theory of shear displacement method, the transfer matrix of pile in layered soils was deduced, so the analytical theory of settlement of single pile in layered soils is established, which can take into account the nonlinear influence of soils, and with which settlement, distribution of axial force, displacement and skin resistance of single pile along the depth in layered soils can be easily attained. By contrast with the practically measure data, it can be seen that the method proposed in this paper is simply and comparatively accurate in calculating the pile settlement under working load.

A Nonlinear Numerical Analysis of Vertical Bearing Behavior of Bored Pile Foundations Including Defective Piles with Stem Shrinkage

In order to investigate the influence of the defective piles with stem shrinkage on the working behavior of pile foundations under vertical loadings, a numerical model was set up for the analysis of pile foundations. A series of contrastive analyses were made to a group piled foundations including a pile with defect of stem shrinkage in a shallow or a deeper depth and a pile foundation with normal piles with a three dimensional nonlinear finite-infinite element method. The basic working behavior of the pile foundation with a defective pile of stem shrinkage was initially revealed by the results of the analyses; and the basic rules of the affects of pile stem shrinkage defect on the distribution of axial forces among piles and the bending moments in pile caps were obtained. The results of this research are not only helpful for the understanding and rational judgment of the working mechanism, but also of practical importance in the assessment of the bearing behavior of pile foundations including defective piles with stem shrinkage and in the structural designs of piles and pile caps.

Field Tests on Bearing Characteristics of X-Section Pile Composite Foundation

To investigate the behavior of X-section cast-in-place concrete piles (XCC pile), a series of static load tests for piled foundation are conducted on the basis of a soft soil reinforcement engineering for a sewage treatment plant in the north of Nanjing, China. The testing results are presented in load-settlement curves, pile-soil stress ratios, distributions of skin friction (side friction) and axial force, and load-sharing between side resistance and end-bearing capacity. Comparative analysis between an XCC pile and a circular section concrete pile (circular pile) with the same cross-sectional area indicates that the XCC pile with its increased perimeter can improve the vertical-bearing capacity by 20% because of the larger skin friction. Also, the XCC pile shows increasing pile-soil stress ratio and reduces settlement. The existing design standards for traditional piles can be referenced by the XCC pile composite foundation, because the axial force and skin friction distribution are the same as those of the traditional pile. It has been found that pile spacing is an important factor for XCC piles, and the XCC pile should be considered as a special friction pile because of high skin friction sharing. Above all, the XCC pile can significantly increase ground-bearing capacity.

Optimization Strategy of the Long-Short-Pile Composite Foundation Based on the Settlement Control

By using finite difference software FLAC3D, the displacement field and stress field of the long-short-pile composite foundation were studied, as well as the distribution of axial force, neutral position and penetration amount. The effects of the main parameters of long-short-pile composite foundation on its working properties, such as the modulus and thickness of the cushion, the length and quantity of the long pile, are investigated in detail. The results show that the modulus and thickness of cushion have less effect on the foundation settlement, while they can affect the pile-soil stress ratio significantly. Moreover, increasing the number of piles can control the foundation settlement effectively. The stresses in upper soil layer can be transferred to lower soil layer effectively, with the increasing of the number of long piles. Then the foundation settlement can be reduced correspondingly. While the variation of the number of piles has less effect on the stress field when the number of piles reaches a certain extend, and the reduction of the foundation settlement tends to slow down. Further, the foundation settlement decreases with the increasing of long-pile length. Finally, based on the foundation settlement control, the recommended values of parameters are given.

Axial Response of HDPE Pipes as a Result of Installation by Directional Drilling

Abstract Axial stresses and strains develop in high density polyethylene (HDPE) pipes during installation by directional drilling. This paper examines the engineering design implications regarding these axial stresses resulting from three recent studies. First, the cyclic axial response of the leading end of a HDPE pipe is measured for the cyclic pulling force history experienced as it is pulled into place. Pulling force history measured in the field is approximated and used to measure the response of pipe samples. The study includes evaluation of simple creep modeling to estimate the axial strains, demonstrating that these provide useful, conservative estimates of maximum axial strain. Second, the development of axial tension in the leading section of the HDPE pipe after connection to appurtenances is modeled in the laboratory. It is demonstrated that the conventional 24 h time period over which the pipe is left to recover in length after installation ensures that the axial tensions that redevelop are at low levels. A calculation procedure is introduced to determine the axial force distribution along the pipe during installation and over its service life. Pulling force modeling similar to that outlined in ASTM 1962-05 is extended to consider the effects of pipe and soil deformations, so that cyclic response during installation and axial stress history after installation are determined. The study demonstrates that values of from one quarter to one third of the maximum pulling force can be used to estimate the long term axial stress in the pipe over a 50 year service life (for assessment of potential for slow crack growth). Strain measurements in the laboratory simulation of pipe installation and strain calculations for computed response over the service life of the pipe are found to be estimated effectively using time-dependent creep (secant) modulus for the HDPE.