Comparative Analysis of Pile-Soil Stress Ratio Calculation Methods for Composite Foundation Based on Lateral Resistance Distribution Assumptions
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摘要:
桩土应力比作为刚性桩复合地基承载力和沉降计算的重要参数,在复合地基优化设计中具有重要工程意义。现有模型多是基于特定的理论假设建立的半经验-半理论计算模型,其中输入参数的高度敏感性以及部分模型依赖有限实验数据的事实使得计算模型的普适性和可靠性大大降低。本研究通过总结复合地基桩土应力比影响因素,分析复合地基的荷载传递特性,明确桩侧摩阻力为桩土应力比主要影响因素。依据侧阻分布形式不同对现有桩土应力比计算模型进行分类总结,并结合具体工程案例对模型预测效果进行对比分析。结果表明,反映极限桩侧摩阻力的软化侧阻分布模型可以合理预测承载力特征值下桩土应力比,其误差范围在10%~20%。刚性桩复合地基的中性面深度及正、负摩阻力合力是影响桩土应力比的关键因素,具体曲线分布形式对预测结果影响有限。工程实践中可根据已有工程参数,结合侧阻分布变化趋势分阶段选用不同桩土应力比计算模型。
Abstract:The pile-soil stress ratio is a critical parameter for the bearing capacity and settlement calculations of rigid pile composite foundations and holds significant engineering importance in their optimization design. Current models are predominantly semi-empirical and semi-theoretical calculation models established on specific theoretical assumptions. The high sensitivity of input parameters and the reliance on limited experimental data for some models significantly reduce the universality and reliability of these computational models. This study summarizes the factors of influencing the pile-soil stress ratio and analyzes the load transfer characteristics of composite foundation. The final result shows that the distribution form of the pile shaft resistance is the main influencing factor of the pile-soil stress ratio. The existing pile-soil stress ratio calculation models are classified and summarized according to the different forms of pile shaft resistance distribution. The predictive performance of these models is compared and analyzed using specific engineering case studies. Comparative results show that the softened shaft resistance distribution model reflecting the ultimate pile shaft resistance can reasonably predict the pile-soil stress ratio at the bearing capacity eigenvalue with an error range of 10%~20%. The location of the neutral surface and the combined force of positive and negative pile shaft resistances are the main factors affecting the pile-soil stress ratio in rigid pile composite foundations. However, the specific form of the pile shaft resistances distribution curve has a limited effect on the predicted results. Based on the engineering parameters, different pile-soil stress ratio calculation models can be selected according to the variation trend of pile shaft resistance distribution during the loading process.
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刚性桩复合地基作为处理天然地基的一种形式,具有承载力高、调整幅度大、变形小和沉降稳定快等特点,因此在实际工程中得到广泛应用[1]。实际工程中,褥垫层可以将上部荷载分配给桩与桩间土,使得桩与土实现相互协同工作,进而使两者的承载力得到最大程度的发挥,达到控制复合地基沉降的目的。桩土应力比是指上部荷载作用下桩顶应力和桩间土应力的比值,作为复合地基承载力与沉降计算的重要参数之一,可以直接反映出桩土间荷载分配和应力分布特征,以及桩土的承载力发挥度,因此成为复合地基优化设计的重要内容。
由于复合地基的荷载传递机理复杂,现阶段复合地基的桩土应力比仍主要基于现场单桩复合静载试验确定。然而,现场试验耗时漫长且成本高昂,因此近年来相关学者开始通过总结室内和现场试验规律,明确影响复合地基桩土应力比的关键因素。大量研究[2 − 6]表明,刚性桩复合地基桩土应力比受桩土相对刚度、桩体截面形状、桩间距、褥垫层、荷载水平等众多因素的影响。相同荷载水平条件下,桩土应力比与桩长、桩间距及基础刚度系数成正比关系[7 − 8]。不同荷载水平条件下,桩土应力比随上部荷载的增大呈现先减小后增大的趋势[7]。
复合地基桩土应力比的主要计算模型包括荷载传递法、弹性理论法和剪切位移法。荷载传递法[9 − 11]将桩体离散为多个弹性单元,假定任一桩体单元的侧摩阻仅与该桩单元的桩土相对位移,而两者之间的相互作用关系采用非线性荷载传递函数计算;弹性理论法[12 − 14]将地基当作均质的各向同性体,考虑桩体和土体的应力与位移的边界条件,通过Mindlin解分析桩间土的应力和位移;剪切位移法[15 − 17]假定桩周土体主要产生剪切变形,而桩土界面不产生相对滑移,桩体位移只与桩周土体的剪切位移有关而进行分析。现有模型多基于特定的理论假设,这些假设在实际工程应用中可能存在局限性,导致预测结果与实际情况存在一定偏差。此外,模型对输入参数的高敏感性使得参数选取不当会显著影响预测精度。更为重要的是,部分半经验-半理论模型依赖于有限的实验数据,未能充分验证其普适性和可靠性。
本文首先对刚性桩复合地基桩土应力比计算理论的研究现状进行综述,基于理论假定讨论其适用范围;同时结合工程案例对模型的预测效果进行分析,讨论导致不同假定模型计算偏差的主要原因;最后分析对比结果,给出形式简洁且能够满足精度要求的桩土应力比预测模型选用建议,以期为刚性桩复合地基的优化设计提供参考依据。
1. 荷载传递机制与基本假定
由于褥垫层的调节作用以及桩和桩间土竖向变形模量的不同,上部荷载由桩和桩间土共同承担,且桩顶应力和桩间土顶应力会出现较大差别。桩体刚度和桩间土刚度随沉降变形的增大逐渐发挥,因此桩土应力比的变化过程同样是桩体刚度和桩间土刚度的发挥过程。承载力特征值是刚性桩复合地基设计计算的重要参数,在该荷载作用下桩和桩间土的承载力均得到充分利用,因此本文主要研究对象为承载力特征值下刚性桩复合地基的荷载传递机制。
图1显示了根据工程实践总结得到的刚性桩复合地基的荷载传递机制[7,9]。由图可见,桩体刚度主要由桩侧摩阻力和桩端承载力贡献,针对摩擦桩刚性桩复合地基来说,桩侧摩阻力的分布即桩土界面的相互作用成为影响桩体刚度发挥的决定性因素,同时也是桩土应力比的主要影响因素。
笔者将关于刚性桩复合地基桩土应力比(n)的计算公式进行了归纳总结,如表1所示。文献[7,9,18 − 23]计算中考虑桩顶和桩端“上下刺”变形,同时将加固区按等沉面划分为上(弹性和塑性)和下(弹性和塑性)两个区域,考虑了桩与土之间的相互作用;文献[24 − 25]计算中分析了褥垫层的受力状态和破坏模式与桩土应力比的相关性,未考虑垫层-桩-土的相互作用;文献[26 − 28]利用弹性力学的解析解对桩土应力比进行了分析。所有计算公式在桩土应力比计算时都要涉及桩顶、桩端“上下刺”和桩侧摩阻力假定,而假定是否合理将对计算结果产生较大影响。
表 1 桩土应力比计算公式Table 1. Calculation formula of pile-soil stress ratio序号 来源 公式 备注(参数含义) 1 朱世哲[21] α为荷载扩散系数,由压力扩散法确定;β与荷载大小、桩周土的性状等有关 2 武崇福[9] k1为桩土间被动土压力系数;φ为桩体与土体之间的摩擦角 3 缪林昌[20] k为桩侧摩阻力与相对位移比值 4 赵明华[22] τm为桩侧摩阻力极限值;z1、z2为负、正摩阻区桩土相对位移深度;λ/k为负/正摩阻力的侧阻传递系数 5 何腊平[23] 6 高翔[19] z0为等沉面深度;z1为负摩阻力塑性区深度;um为桩土极限相对位移 7 姜文雨[18] ,K0为静止土压力系数;φf为桩间土内摩擦角;wb为下卧层单位压力时的竖向刺入变形; 、 为中性点上、下桩土应力比计算值8 陆清元[7] l1为负摩阻区桩土相对位移深度;δu1为负摩阻区单位长度桩土相对位移 9 陈健[25] σS为桩间土应力;Pe为弹性极限载荷;τ0为最大负摩阻力;r0为桩体半径;μ为垫层泊松比;rp为塑性区半径;λ为中性面位置; 为弹性状态桩土应力比计算值; 为弹塑性状态下桩土应力比计算值10 刘俊飞[24] KP为桩身基床系数;α为应力折算系数 11 Baumann[26] ks/kp为桩间土/桩体的侧压力系数;re为桩体半径;
rp为加固半径12 Priebe[27] μs为桩间土泊松比 13 Rowe[28] ks/kp为桩间土/桩体的侧压力系数;μs/μp为桩间土/桩体泊松比 注:l为桩长/m;d为桩径/m;Ap为桩体截面积/m2;u为桩周长/m;Ep为桩体弹性模量/kPa;l0为桩体中性点位置/m;hc为垫层厚度/m;Ec为垫层弹性模量/kPa;Es为桩间土弹性模量/kPa;As为桩间土面积/m2;m为复合地基面积置换率;Ks为下卧层文克尔地基基床系数/kPa;P为上部荷载/kN;Cu、Cd为桩体顶/底面作用于垫层、下卧层单位压力时的竖向刺入变形量/m;φp为桩间土的内摩擦角/(°)。 1.1 桩顶、桩端“上下刺”假定
复合地基与桩基、复合桩基相比,其特点是在上部荷载增加时褥垫层可以使桩土荷载分担比发生变化,进而改变桩土协同变形和受力的状态。随着荷载的增大,桩顶的应力集中会使桩身上刺入褥垫层,而“上刺”进一步加大,也导致桩土相对位移随之发生变化,进而引起桩土应力比和荷载分担比改变,该情况对复合地基工作状态的影响不可忽略。为此,一些学者通过不同的理论假定对桩“上刺”问题进行了分析。李进军等[29]和周德泉[30]分别利用弹性地基梁理论和太沙基理论分析了“上刺”问题;周志军[31]将褥垫层分为压密和塑性流动两个受力变形阶段分析了“上刺”问题;池跃君[32]假定桩端土层坚硬且粗糙,利用Mandel-Salencon模型分析了“上刺”问题;毛前等[33]将褥垫层假定为弹塑性体,利用小孔扩张理论分析了“上刺”问题;陶景晖[34]假定桩顶面光滑,利用Meyerhof模型分析了“上刺”问题。除此之外,大多数学者对“上刺”问题进行研究时,将褥垫层假定为均质弹性体,利用虎克定律进行解析[35]。
桩端“下刺”问题与桩顶“上刺”问题分析的方法类似,而复合地基在设计时往往会优先考虑将桩端设置在承载力较高的地层中。桩侧摩阻力会随着上部荷载的增加而提高,虽然上部荷载向桩端传递的荷载在增加,但要远远小于桩顶荷载,这使得桩端“下刺”现象相比桩顶“上刺”现象弱很多。为此,多数学者在计算中忽略桩端“下刺”对复合地基桩土协同受力的影响,但对于下卧层为软土层且厚度较大的情况,则需要考虑桩体对下卧层的刺入。亓乐[36]将下卧层等效单元体作为分析对象,并将接触面分为“弹性段”和“弹塑性段”考虑;少数学者将下卧层考虑为Winkler地基梁[37],基于弹性力学相关理论分析桩端“下刺”情况;也有学者为了便于计算,采用经验系数法[38](即单位压力的桩端刺入量与桩土压力差值的乘积作为桩体的“下刺”量)计算桩端的“下刺”量。
1.2 桩侧摩阻力假定
目前在复合地基桩土应力比计算中能够体现桩土协同受力与相互作用的重要参数为桩侧摩阻力,而在摩阻力计算时,桩侧摩阻力的极限值、中性点位置和桩侧摩阻力的分布形式对计算结果均有直接影响。在这方面,常见的桩侧摩阻力计算假定大致分为两种。一种是桩侧摩阻力与桩土相对位移成非线性函数关系,随着桩土相对位移的增加,桩侧摩阻力逐渐增大,当桩土相对位移达到极限值时桩侧摩阻力达到最大值,之后桩侧摩阻力不变。基于此假定,郑俊杰[39]、黄炳权[40]等学者分别利用折曲线、非线性函数和双曲线等模型对桩土应力比进行了分析。另一种是桩侧摩阻力与桩长成线性函数关系,朱世哲[21]、武崇福[9]、王涛[41]等学者将桩侧摩阻力假定为线性函数和均布函数,对桩土应力比进行了分析。
以往学者通过试验研究,刚性桩复合地基中由于褥垫层的设置,桩体会产生“上刺”现象,因而桩顶出现负摩阻区,对应的桩侧摩阻力会在桩身一定深度l0(中性点)处发生改变,l0以上为负摩阻力,l0以下为正摩阻力,并得出理想状态下桩侧摩阻力曲线呈非线性分布如图2。表2给出了目前常用的桩侧摩阻力分布曲线模型。
表 2 各计算模型中桩侧摩阻力简化曲线Table 2. Simplified curves of lateral friction resistance of different model来源 分布曲线 分布模型 备注 朱世哲[21] 不计负摩阻力作用,假定桩侧摩阻力沿桩长均匀分布。 该假定直接以桩土的极限侧摩阻力值作为桩侧摩阻力代入计算,显然与实际工况不符。 武崇福[9] 将桩侧摩阻分布曲线简化为线性分布,并将桩顶处侧摩阻力作为最大负摩阻力。 此假定可以体现出桩侧摩阻力随桩土相对位移的变化情况,对于分析小荷载、小变形的桩土相互作用适用性良好。 缪林昌[20] 考虑负摩阻区作用,假定负/正摩阻力分别在中性点以上/下均匀分布。 此假定的计算结果往往与桩侧摩阻力极限值的选择有较大关系,但其值不易确定。 赵明华[22] 对刚性桩复合地基的桩土相互作用进行划分,建立塑性-弹性-塑性的三段桩侧摩阻力分布模型。假定桩顶与桩端处的桩侧摩阻力达到极限状态且沿深度均匀分布,分别对中间弹性阶段桩侧摩阻力分布按照线性或非线性分布进行假设。 该类型桩侧摩阻分布曲线在塑性区长度较小的弹-塑性桩-土相互作用分析中具有较好的结果。 何腊平[23] 高翔[19] 姜文雨[18] 考虑桩端处的桩土相互作用存在塑性区,即假定桩端处存在极限摩阻力。 线性模型能在一定程度上反映实际分布规律,但应用于桩身较长的桩体时计算结果存在较大偏差,对桩端侧摩阻力进行修正可在一定程度上减小计算误差。 陆清元[7] 针对柔性基础下桩体上、下部塑性区长度较大的特点,考虑桩土界面弹性区非线性、塑性区非均匀的实际发挥性状,建立塑性-弹性-塑性的三段桩侧摩阻力分布模型。 注:l0为中性面位置所在深度;τu为极限桩侧摩阻力;δu为τu对应的极限相对位移;δ1为负摩阻力对应的极限相对位移;δ2为正摩阻力对应的极限相对位移;ζ为负摩阻力侧阻传递系数λ与正摩阻力侧阻传递系数k的比值;τu1为桩侧负摩阻力的极限值;τu2为桩侧正摩阻力的极限值;Ss为深度z处桩间土的沉降量;Sp为深度z处桩的沉降量;ca、φa分别为桩-土界面的黏聚力和内摩擦角;K0为水平土压力系数;ps为作用于桩间土表面的均布荷载;γ为桩间土的重度。 以上假定多数基于复合地基在荷载作用下侧摩阻发挥情况,此时求出的桩土应力比n即为初始桩土应力比。在实际复合地基中,上部荷载的作用会导致瞬时沉降、固结沉降和次固结沉降的发生。随着桩间土的固结和蠕变过程,桩侧摩阻力和桩端阻力的发挥程度会不断变化,进而引起桩侧摩阻力分布形式的转变。武崇福[9]和周航[42]等通过室内模型试验,研究了不同截面和布桩形式下刚性桩复合地基桩土应力比的时效性。研究表明,不同截面类型的复合地基桩土应力比均表现出随时间先增大后减小,最终趋于稳定的趋势[9, 42]。因此,在复合地基沉降计算中,特别是对于软土地层,必须考虑桩土应力比n随时间的变化特性。余海强[43]利用ABAQUS软件对软土地基中被动排桩的土拱效应进行了有限元分析,结果显示,土拱效应随着固结时间的增长逐渐减弱,其对桩土应力比的减弱作用也逐渐减小。此外,现有的研究较少关注桩侧摩阻力分布形式随复合地基持荷状态变化的动态过程,更难以全面考虑桩、加固区、下卧层土体、基础和褥垫层等参数对这一转变过程的影响。
2. 计算实例分析与结果对比
以南京某住宅小区复合地基实际工程[44]为例,将表1中序号1—8文献中的桩土应力比试算结果进行对比分析,其余公式因为参数过多且取值的不确定性未进行分析。实际工程中桩身材料为C25素混凝土,桩径d=500 mm,桩长l=13.5 m,桩身弹性模量Ep =2.52×104 MPa;正方形布桩,面积置换率m=
0.0713 ;褥垫层材料为粗砂,厚度hc=150 mm,弹性模量Ec =72 MPa桩间土的弹性模量Es=40 MPa;桩间土的重度γ=18.2 kN/m3。顾勇[44]依据《建筑地基处理技术规范》(JGJ 79—2012)[45]得出复合地基承载力特征值为480 kPa,现场单桩复合地基静载荷试验最大加载量为800 kPa。按照表1中给出的部分计算模型,参考表3中的计算参数取值,对桩土应力比计算结果进行对比分析,其中下卧层winkle基床系数Ks取值为2.5×104 kN/m3。表 3 各计算模型中的参数Table 3. Parameters assumed of different computational formula序号 黏聚力/
kPa内摩擦角/(°) 单位长度桩土极限相对位移/‰ 侧摩阻传递系数/(kN∙m-3) 侧向土压力系数 桩-土界面黏聚力/kPa 桩-土界面摩擦角/(°) 负摩阻区 正摩阻区 1 15 25 — — — 0.58 9 19.8 2 25 12 2.35 2.1 5×104 0.6 15 11.4 3 15 25 — 1.56 5×104 0.58 9 19.8 4 15 25 — — — 0.58 9 19.8 5 15 25 — — — 0.58 9 19.8 6 25 12 1.85 1.1 5×104 0.6 15 11.4 7 20 18.3 — — — 0.01 12 17 8 25 12 1.02 1.87 5×104 — — — 注:不同公式中桩侧摩阻分布形式假定不同,故参数选取不同。 如图3所示,模型2、3、5、6的桩土应力比计算结果大于实测结果,计算误差值在10%~20%之间,其余模型的桩土应力比计算值均小于实测桩土应力比。究其原因,2、3、5、6模型均涉及对桩顶与桩端“上下刺”变形效应的考量,而各模型间桩侧摩阻力的极限值设定、中性点预设位置以及摩阻力沿桩身的分布模式存在差异,这些因素共同作用,致使计算结果出现偏差。尤其在假定中性面位置固定的情况下,正、负桩侧摩阻力的合力效应相较于摩阻力分布形式,对桩土应力比的计算结果产生更为显著的影响。这意味着,计算模型中对桩侧摩阻力方向与大小的综合评估准确性,直接关系到桩土应力比预测的精确程度。
对于计算得出的桩土应力比,按照《建筑地基处理技术规范》(JGJ 79—2012)[45]进行复合地基承载力的计算,结果对比发现不同计算模型计算结果均需要进行修正,具体的修正系数建议取0.8~0.9。具体计算结果见表4。
表 4 复合地基承载力计算结果Table 4. Calculation results of composite foundation bearing capacity序号 桩顶应力/kPa 桩间土顶应力/kPa 桩土应力比 复合地基承载力/kPa 1 6473.2 516.5 12.55 392.7 2 6644.6 355.4 18.70 523.6 3 6768.4 341.8 19.80 535.4 4 6528.3 471.7 13.84 418.7 5 6544.2 327.7 19.97 540.1 6 6660.9 339.1 19.64 511.5 7 6563.8 436.2 15.05 428.5 8 6243.6 756.4 8.25 250.9 3. 结论
本文对刚性桩复合地基桩土应力比的计算方法进行了归纳总结,同时对各计算理论与方法中存在的问题和导致计算结果偏差过大的原因进行了分析与探讨,通过研究分析提出如下几点建议:
(1)对桩侧摩阻力的分布形式的假定大致分为两种:一种考虑桩土相互作用为理想弹-塑性关系,将桩侧摩阻力假定为沿桩长非线性分布,并建立塑性-弹性-塑性三个区段,适合存在塑性区作用的桩土应力比的计算;一种考虑桩侧摩阻力与桩长成线性函数关系,将桩侧摩阻力假定为沿桩长线性分布,适用于上部加载量和复合地基沉降较小时的桩土应力比计算。
(2)利用桩土应力比进行刚性桩复合地基承载力和沉降设计时,应充分考虑桩侧摩阻力分布形式随上部持荷状态变化的转变,而对于软土地层还应要考虑到桩间土的固结变形导致桩土应力比变化的时间效应。
(3)文中所给文献的桩土应力比计算模型在复合地基工程实例的计算过程中计算偏差约10%~20%。这是由于分析了桩顶和桩端“上下刺”变形,并且将加固区按等沉面划分为上(弹性和塑性)和下(弹性和塑性)两个区域,并考虑了桩与土之间的相互作用不同时,桩侧摩阻力的极限值、中性点位置和桩侧摩阻力的分布形式导致了计算产生差异。
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表 1 桩土应力比计算公式
Table 1 Calculation formula of pile-soil stress ratio
序号 来源 公式 备注(参数含义) 1 朱世哲[21] α为荷载扩散系数,由压力扩散法确定;β与荷载大小、桩周土的性状等有关 2 武崇福[9] k1为桩土间被动土压力系数;φ为桩体与土体之间的摩擦角 3 缪林昌[20] k为桩侧摩阻力与相对位移比值 4 赵明华[22] τm为桩侧摩阻力极限值;z1、z2为负、正摩阻区桩土相对位移深度;λ/k为负/正摩阻力的侧阻传递系数 5 何腊平[23] 6 高翔[19] z0为等沉面深度;z1为负摩阻力塑性区深度;um为桩土极限相对位移 7 姜文雨[18] ,K0为静止土压力系数;φf为桩间土内摩擦角;wb为下卧层单位压力时的竖向刺入变形; 、 为中性点上、下桩土应力比计算值8 陆清元[7] l1为负摩阻区桩土相对位移深度;δu1为负摩阻区单位长度桩土相对位移 9 陈健[25] σS为桩间土应力;Pe为弹性极限载荷;τ0为最大负摩阻力;r0为桩体半径;μ为垫层泊松比;rp为塑性区半径;λ为中性面位置; 为弹性状态桩土应力比计算值; 为弹塑性状态下桩土应力比计算值10 刘俊飞[24] KP为桩身基床系数;α为应力折算系数 11 Baumann[26] ks/kp为桩间土/桩体的侧压力系数;re为桩体半径;
rp为加固半径12 Priebe[27] μs为桩间土泊松比 13 Rowe[28] ks/kp为桩间土/桩体的侧压力系数;μs/μp为桩间土/桩体泊松比 注:l为桩长/m;d为桩径/m;Ap为桩体截面积/m2;u为桩周长/m;Ep为桩体弹性模量/kPa;l0为桩体中性点位置/m;hc为垫层厚度/m;Ec为垫层弹性模量/kPa;Es为桩间土弹性模量/kPa;As为桩间土面积/m2;m为复合地基面积置换率;Ks为下卧层文克尔地基基床系数/kPa;P为上部荷载/kN;Cu、Cd为桩体顶/底面作用于垫层、下卧层单位压力时的竖向刺入变形量/m;φp为桩间土的内摩擦角/(°)。 表 2 各计算模型中桩侧摩阻力简化曲线
Table 2 Simplified curves of lateral friction resistance of different model
来源 分布曲线 分布模型 备注 朱世哲[21] 不计负摩阻力作用,假定桩侧摩阻力沿桩长均匀分布。 该假定直接以桩土的极限侧摩阻力值作为桩侧摩阻力代入计算,显然与实际工况不符。 武崇福[9] 将桩侧摩阻分布曲线简化为线性分布,并将桩顶处侧摩阻力作为最大负摩阻力。 此假定可以体现出桩侧摩阻力随桩土相对位移的变化情况,对于分析小荷载、小变形的桩土相互作用适用性良好。 缪林昌[20] 考虑负摩阻区作用,假定负/正摩阻力分别在中性点以上/下均匀分布。 此假定的计算结果往往与桩侧摩阻力极限值的选择有较大关系,但其值不易确定。 赵明华[22] 对刚性桩复合地基的桩土相互作用进行划分,建立塑性-弹性-塑性的三段桩侧摩阻力分布模型。假定桩顶与桩端处的桩侧摩阻力达到极限状态且沿深度均匀分布,分别对中间弹性阶段桩侧摩阻力分布按照线性或非线性分布进行假设。 该类型桩侧摩阻分布曲线在塑性区长度较小的弹-塑性桩-土相互作用分析中具有较好的结果。 何腊平[23] 高翔[19] 姜文雨[18] 考虑桩端处的桩土相互作用存在塑性区,即假定桩端处存在极限摩阻力。 线性模型能在一定程度上反映实际分布规律,但应用于桩身较长的桩体时计算结果存在较大偏差,对桩端侧摩阻力进行修正可在一定程度上减小计算误差。 陆清元[7] 针对柔性基础下桩体上、下部塑性区长度较大的特点,考虑桩土界面弹性区非线性、塑性区非均匀的实际发挥性状,建立塑性-弹性-塑性的三段桩侧摩阻力分布模型。 注:l0为中性面位置所在深度;τu为极限桩侧摩阻力;δu为τu对应的极限相对位移;δ1为负摩阻力对应的极限相对位移;δ2为正摩阻力对应的极限相对位移;ζ为负摩阻力侧阻传递系数λ与正摩阻力侧阻传递系数k的比值;τu1为桩侧负摩阻力的极限值;τu2为桩侧正摩阻力的极限值;Ss为深度z处桩间土的沉降量;Sp为深度z处桩的沉降量;ca、φa分别为桩-土界面的黏聚力和内摩擦角;K0为水平土压力系数;ps为作用于桩间土表面的均布荷载;γ为桩间土的重度。 表 3 各计算模型中的参数
Table 3 Parameters assumed of different computational formula
序号 黏聚力/
kPa内摩擦角/(°) 单位长度桩土极限相对位移/‰ 侧摩阻传递系数/(kN∙m-3) 侧向土压力系数 桩-土界面黏聚力/kPa 桩-土界面摩擦角/(°) 负摩阻区 正摩阻区 1 15 25 — — — 0.58 9 19.8 2 25 12 2.35 2.1 5×104 0.6 15 11.4 3 15 25 — 1.56 5×104 0.58 9 19.8 4 15 25 — — — 0.58 9 19.8 5 15 25 — — — 0.58 9 19.8 6 25 12 1.85 1.1 5×104 0.6 15 11.4 7 20 18.3 — — — 0.01 12 17 8 25 12 1.02 1.87 5×104 — — — 注:不同公式中桩侧摩阻分布形式假定不同,故参数选取不同。 表 4 复合地基承载力计算结果
Table 4 Calculation results of composite foundation bearing capacity
序号 桩顶应力/kPa 桩间土顶应力/kPa 桩土应力比 复合地基承载力/kPa 1 6473.2 516.5 12.55 392.7 2 6644.6 355.4 18.70 523.6 3 6768.4 341.8 19.80 535.4 4 6528.3 471.7 13.84 418.7 5 6544.2 327.7 19.97 540.1 6 6660.9 339.1 19.64 511.5 7 6563.8 436.2 15.05 428.5 8 6243.6 756.4 8.25 250.9 -
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