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条形浅基础极限承载力的滑移线解

彭明祥

彭明祥. 条形浅基础极限承载力的滑移线解[J]. 南方能源建设, 2019, 6(4): 13-28. DOI: 10.16516/j.gedi.issn2095-8676.2019.04.003
引用本文: 彭明祥. 条形浅基础极限承载力的滑移线解[J]. 南方能源建设, 2019, 6(4): 13-28. DOI: 10.16516/j.gedi.issn2095-8676.2019.04.003
PENG Mingxiang. Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip Footings[J]. SOUTHERN ENERGY CONSTRUCTION, 2019, 6(4): 13-28. DOI: 10.16516/j.gedi.issn2095-8676.2019.04.003
Citation: PENG Mingxiang. Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip Footings[J]. SOUTHERN ENERGY CONSTRUCTION, 2019, 6(4): 13-28. DOI: 10.16516/j.gedi.issn2095-8676.2019.04.003
彭明祥. 条形浅基础极限承载力的滑移线解[J]. 南方能源建设, 2019, 6(4): 13-28. CSTR: 32391.14.j.gedi.issn2095-8676.2019.04.003
引用本文: 彭明祥. 条形浅基础极限承载力的滑移线解[J]. 南方能源建设, 2019, 6(4): 13-28. CSTR: 32391.14.j.gedi.issn2095-8676.2019.04.003
PENG Mingxiang. Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip Footings[J]. SOUTHERN ENERGY CONSTRUCTION, 2019, 6(4): 13-28. CSTR: 32391.14.j.gedi.issn2095-8676.2019.04.003
Citation: PENG Mingxiang. Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip Footings[J]. SOUTHERN ENERGY CONSTRUCTION, 2019, 6(4): 13-28. CSTR: 32391.14.j.gedi.issn2095-8676.2019.04.003

条形浅基础极限承载力的滑移线解

详细信息
    作者简介:

    彭明祥(通信作者) 1964-,男,广东化州人,教授级高级工程师,注册岩土工程师,注册港口与航道工程师,硕士,主要从事水工结构和岩土力学与工程的研究工作(e-mail) pengmingxiang1964@qq.com。

  • 中图分类号: TU470

Slip-line Solution to Ultimate Bearing Capacity of Shallow Strip FootingsEn

  • 摘要:
      [目的]  基于极限平衡理论,提出了一种求解一般条件下条形浅基础极限承载力的精确方法。
      [方法]  地基土被视为服从Mohr-Coulomb屈服准则的理想弹塑性材料,并且假定它是各向同性的、均匀的以及不可压缩或不可膨胀的理想连续介质。通过分析基础与土之间的相对运动和相互作用,将条形浅基础极限承载力问题分为两类问题。建立一个以总竖向极限承载力为目标函数的最小值模型,进而采用滑移线法求解极限承载力而无需事先对塑性区和非塑性楔作任何假定,还提出一种工程上方便实用的简化方法。此外,重点研究了基础两侧均布荷载相同的第一类问题,推导出Terzaghi极限承载力方程的适用条件以及其三个承载力系数的理论精确解,提出一个新承载力方程替代Terzaghi方程,并且通过无量纲分析提出几何力学相似原理。
      [结果]  研究结果表明:当基础完全光滑时,研究得到的总竖向极限承载力与现有方法得到的结果相当吻合;然而当基础完全粗糙时,现有方法低估了极限承载力。
      [结论]  经典的Prandtl机构并不是无重土地基上完全光滑基础极限承载力问题的塑性破坏机构。
    Abstract:
      [Introduction]  Based on the limit equilibrium theory, an accurate approach is proposed to solve the ultimate bearing capacity of shallow strip footings under general conditions.
      [Method]  The foundation soil is considered to be an ideal elastic-plastic material, which obeys the Mohr-Coulomb yield criterion, and is assumed to be an ideal continuous medium that is isotropic, homogeneous and incompressible or non-expansive. Through analyzing the relative motion and interaction between the footing and soil, the problem of the ultimate bearing capacity of shallow strip footings is divided into two categories. A minimum model with the total vertical ultimate bearing capacity as its objective function is established to solve the ultimate bearing capacity using the slip-line method with no need to make any assumptions on the plastic zone and non-plastic wedge in advance. A convenient and practical simplified method is also proposed for practical engineering purposes. Furthermore, the first category of the problem in the case of the same uniform surcharges on both sides of footing is the focus of the study: the applicable conditions of Terzaghi′s ultimate bearing capacity equation as well as the theoretical exact solutions to its three bearing capacity factors are derived, and a new bearing capacity equation is put forward as a replacement for Terzaghi′s equation. The geometric and mechanical similarity principle is proposed by a dimensionless analysis.
      [Result]  The results show that for perfectly smooth footings, the total vertical ultimate bearing capacity obtained by the present method is in good agreement with those by existing methods; whereas for perfectly rough footings, the existing methods underestimate the ultimate bearing capacity.
      [Conclusion]  The classic Prandtl mechanism is not the plastic failure mechanism of the ultimate bearing capacity problem of perfectly smooth footings on weightless soil.
  • 液体电介质的绝缘性能对于电力系统的安全稳定运行具有重要意义。学者发现高纯水、硝基苯以及变压器油等液体电介质在不同电极材料情况下,其击穿特性有所不同[,,]。由此可见,电极材料是影响液体电介质击穿性能的重要因素,然而其影响机理目前尚不明确。液体电介质的绝缘性能与其内部的电场分布密切相关[]。研究表明在高电压作用下液体电介质中空间电荷的存在会畸变液体中的电场分布,对液体的绝缘性能产生重要的影响[,,]。测量液体电介质中的电场分布是研究其击穿机理以及降低击穿发生的可能性的前提。

    克尔电光效应法广泛应用于液体电介质的电场分布测量,具有测量精度高、抗电磁干扰能力强的优点[,]。文章中我们选用了无色透明,无毒性、克尔常数高的碳酸丙烯酯作为液体电介质,选用不锈钢、黄铜、铝三种金属材料组成电极对,利用克尔电光方法分别测量了冲击电压作用下碳酸丙烯酯不同电极材料下的击穿电压与电场分布情况。根据测量结果,我们分析得到了不同电极材料对碳酸丙烯酯冲击击穿特性的影响机理。

    文中选取了不锈钢、黄铜与铝三种金属制成的平行板电极材料,其尺寸为100 mm×12 mm×5 mm,电极之间的间距为3 mm。电极的边缘经过抛光处理以避免边缘放电。文章根据IEC60897标准进行了冲击击穿测试。对于平行板电极,击穿电压不存在极性效应,我们采用标准负极性操作冲击电压(250 μs/2 500 μs)对碳酸丙烯酯进行冲击击穿测试。测试时先从一个较低幅值的冲击电压开始施加,然后以1~2 kV的增幅增加冲击电压的幅值直至击穿发生。为了确保测量结果的准确性,每个幅值的冲击电压至少重复施加3次。相邻的冲击电压之间的时间间隔为2 min,通过示波器来记录击穿电压的幅值与时间,由于间隙为mm级,击穿发生时刻可能在波头或波尾,如果在波头击穿,击穿电压幅值取击穿时刻实际值,如果击穿发生在波尾,击穿电压幅值取峰值。对于每种电极材料,以上的测量过程重复10次,以此求得击穿电压的平均值。

    碳酸丙烯酯电场测量系统如图1所示,该测量系统由冲击电压装置、克尔电光测量装置以及光信号接收装置三部分组成。冲击电压波形由马克思发生器产生,经过分压器由示波器测量。由He-Ne激光器发出的波长为633 nm的激光经过扩束镜、起偏器、1/4波片、克尔盒、1/4波片、检偏器,由电荷耦合器件(Charge Coupled Device, CCD)接收。起偏器与检偏器的光轴平行,构成平行偏振。电极的材料、尺寸与击穿实验中相同。CCD的触发信号由冲击电压发生器提供。所有的光学元件放置于光学防震平台上。实验时,实验装置的周围为黑暗的环境以排除外界自然光对实验测量的影响。测量时施加的冲击电压波形为幅值为25 kV的负极性标准操作波。根据克尔效应的原理对由CCD接收得到的电光图进行反算[],可以得到碳酸丙烯酯在冲击电压作用下的电场分布。

    图 1 碳酸丙烯酯电场测量系统
    图  1  碳酸丙烯酯电场测量系统
    Figure  1.  Electric field measurement system for propylene carbonate

    表1中所示的为不同电极材料下碳酸丙烯酯的击穿电压性能。如表1中的数据所示,不同电极材料下碳酸丙烯酯的负极性冲击击穿电压不同,不锈钢电极情况下的击穿电压幅值比黄铜电极情况下高13.8%,比铝电极情况下则高21.2%。此外,黄铜电极的情况下击穿电压幅值比铝电极情况下高6.5%。不仅三种不同电极材料下的液体击穿电压不同,液体击穿的时间也不同,这是因为三种电极情况下液体中的空间电荷注入情况不同,导致电场寄畸变程度不同。

    表  1  碳酸丙烯酯负极性冲击击穿实验测量结果
    Table  1.  Test results of negative impulse breakdown for propylene carbonate
    极板材料 击穿电压均值/kV 标准差 击穿时间均值/μs
    不锈钢 44.6 1.4 425
    39.2 1.5 507
    36.8 1.1 420
    下载: 导出CSV 
    | 显示表格

    图2所示的是由克尔电光测量系统测量得到的CCD电光图,测量原理详见文献[]。图中的明暗条纹代表等势线。由图中可以看出,电极之间存在明暗条纹,这说明电极之间的电场是不均匀的,存在一定程度的电场畸变。铝、不锈钢与黄铜电极之间的条纹数量分别在1 150 μs、1 300 μs与1 500 μs时减少,这说明了不同的电极材料具有不同的电荷注入能力,这导致了电极之间的电场畸变程度的不同。

    图 2 不同电极材料下碳酸丙烯酯中克尔电光图
    图  2  不同电极材料下碳酸丙烯酯中克尔电光图
    Figure  2.  Kerr electric-optic images for propylene carbonate under different electric materials

    根据克尔效应的原理对图2中的电光图进行反算,可以得到不同电极材料下碳酸丙烯酯在冲击电压作用下电极之间的电场分布情况,如图3所示。对比三种电极材料下液体中的电场分布情况可以看出,相同时刻不同电极之间电场畸变程度有着明显的差异。

    图 3 不同电极材料下碳酸丙烯酯中电场分布
    图  3  不同电极材料下碳酸丙烯酯中电场分布
    Figure  3.  Electric field distribution of propylene carbonate under different electric materials

    在外施电压的作用下,液体电介质中电极之间存在着电子电场发射、电化学反应以及双电层等复杂的现象,一定量的空间电荷会从电极注入到液体当中[,]。这些空间电荷会畸变液体中原来的几何电场分布,减弱电极附近的电场强度而增大液体中的电场强度。根据高斯定理,平行板电极情况下液体中电场分布曲线的斜率与液体中注入的电荷成正比。而液体中空间电荷的存在会畸变液体中的电场分布,液体中空间电荷的量越大,液体中电场的畸变程度越高。因此,我们推断不同金属的电极材料在冲击电压作用下空间电荷的注入能力不同,由此导致了不同电极材料下液体中电场的畸变程度不同。文中定义液体中的电场畸变率D为某一时刻,液体中瞬时电场与平均电场的差值的最大值与平均电场之比,如公式(1)所示。

    ((1))

    根据此定义与图3中的电场分布,我们得到了不同电极材料下不同时刻碳酸丙烯酯中的电场畸变率,如表2所示。从表2可以看出,黄铜电极与不锈钢电极的情况下电场最大畸变发生在750 μs,而铝电极情况下发生在900 μs。大部分的时间范围内,铝电极情况下的电场畸变率最高,黄铜电极情况下次之,而不锈钢电极情况下最低。这意味着在相同的电场作用下,铝电极、黄铜电极与不锈钢电极情况下碳酸丙烯酯中的电场畸变率依次递减。这可能是三种不同材料下碳酸丙烯酯冲击击穿性能差异的原因。

    表  2  不同电极材料下碳酸丙烯酯中电场畸变率
    Table  2.  Electric field distortion rate for propylene carbonate under different electrodes
    时间/μs (电场畸变率/铝电极)/% (电场畸变率/黄铜电极)/% (电场畸变率/不锈钢电极)/%
    250 13.0 10.9 9.8
    500 20.3 17.2 13.5
    750 23.6 27.8 23.5
    900 29.2 25.0 23.4
    1 150 19.6 18.1 15.2
    1 300 19.1 12.4 7.1
    1 500 17.7 5.8 2.9
    下载: 导出CSV 
    | 显示表格

    文章分别测量了碳酸丙烯酯液体电介质在不锈钢、黄铜以及铝电极材料情况下的负极性冲击击穿性能与液体中的电场分布情况。根据实验测量结果,得到了以下结论:

    1)电极材料对碳酸丙烯酯的冲击击穿特性具有重要的影响,铝、黄铜以及不锈钢电极情况下,碳酸丙烯酯的冲击击穿电压依次增大。

    2)不同电极材料在冲击电压作用下空间电荷的注入能力不同,不锈钢、黄铜以及铝电极的电荷注入能力依次减小。

    3)由于电荷注入能力的不同,导致不同电极材料下碳酸丙烯酯中电场畸变程度不同,这是电极材料对碳酸丙烯酯冲击特性差异化的原因。

    郑文棠
  • 图  1   计算模型

    Figure  1.   Calculation models

    图  2   基本边值问题

    Figure  2.   Basic boundary value problem

    图  3   地基塑性破坏随q1变化

    Figure  3.   Variation of plastic failures with q1

    图  4   完全粗糙基础的非塑性楔

    Figure  4.   Non-plastic wedges for perfectly rough footing

    图  5    φ=30°无黏性土的地基塑性破坏

    Figure  5.   Plastic failures of cohesionless soil with φ=30°

    图  6   无非塑性楔的第一类问题

    Figure  6.   First category of problem without non-plastic wedge

    图  7   有非塑性楔的第一类问题

    Figure  7.   First category of problem with non-plastic wedge

    图  8   完全光滑基础的计算结果

    Figure  8.   Calculation results for perfectly smooth footings

    图  9   完全粗糙基础的计算结果

    Figure  9.   Calculation results for perfectly rough footings

    图  10   计算结果

    Figure  10.   Calculation results

    表  1   竖向承载力系数Nv0Nv1

    Table  1   Vertical bearing capacity factors Nv0 and Nv1

    工况 φ=25°,δ=-10° φ=25°,δ=10°
    η2/η1 -1 -0.5 0 0 0.5 1
    η1 Nv0 Nv1 Nv0 Nv1 Nv0 Nv1 Nv0 Nv1 Nv0 Nv1 Nv0 Nv1
    0.0 0 3.422 9 0 3.422 9 0 3.422 9 0 11.330 0 11.330 0 11.330
    0.2 2.551 7 7.442 1 2.798 1 7.945 1 3.013 3 8.407 9 5.225 5 21.239 5.327 4 21.515 5.422 3 21.784
    0.4 5.103 5 10.365 5.5962 11.187 6.026 6 11.936 10.451 27.988 10.655 28.426 10.845 28.851
    0.6 7.655 2 13.117 8.3943 14.228 9.0399 15.234 15.676 34.131 15.982 34.711 16.267 35.270
    0.8 10.207 15.797 11.192 17.183 12.053 18.433 20.902 39.992 21.309 40.703 21.689 41.385
    1.0 12.759 18.439 13.991 20.093 15.067 21.579 26.127 45.692 26.637 46.527 27.111 47.327
    1.2 15.310 21.059 16.789 22.975 18.080 24.693 31.353 51.288 31.964 52.243 32.534 53.156
    1.4 17.862 23.663 19.587 25.839 21.093 27.785 36.578 56.813 37.292 57.884 37.956 58.907
    1.6 20.414 26.256 22.385 28.689 24.106 30.861 41.804 62.286 42.619 63.471 43.378 64.602
    1.8 22.966 28.843 25.183 31.531 27.120 33.927 47.029 67.720 47.946 69.018 48.800 70.254
    2.0 25.517 31.423 27.981 34.365 30.133 36.984 52.255 73.123 53.274 74.533 54.223 75.873
    2.2 28.069 33.999 30.779 37.194 33.146 40.034 57.480 78.503 58.601 80.023 59.645 81.466
    2.4 30.621 36.572 33.577 40.019 36.160 43.080 62.706 83.864 63.928 85.493 65.067 87.039
    2.6 33.173 39.142 36.375 42.840 39.173 46.121 67.931 89.208 69.256 90.946 70.489 92.593
    下载: 导出CSV

    表  2   完全光滑基础结果比较

    Table  2   Comparison of results for perfectly smooth footings

    φ/(°) 本文方法 Martin(2004)[22] Bolton和Lau(1993)[16] Chen(1975)[24] Sokolovskii(1965)[14]
    Nv Nγ Quv/kN Nγ Quv/kN Error/ % Nγ Quv/kN Error/ % Nγ Quv/kN Error/ % Nγ Quv/kN Error/ %
    q=0
    5 0.085 0.085 0.85 0.084 0.84 -0.05 0.09 0.90 6.51 0.131 1.31 55.03 0.17 1.70 101.18
    10 0.281 0.281 2.81 0.281 2.81 0.07 0.29 2.90 3.28 0.461 4.61 64.17 0.56 5.60 99.43
    15 0.699 0.699 6.99 0.699 6.99 0.03 0.71 7.10 1.60 1.16 11.60 66.00 1.40 14.00 100.34
    20 1.578 1.578 15.78 1.579 15.79 0.06 1.60 16.00 1.39 2.68 26.80 69.83 3.16 31.60 100.25
    25 3.461 3.461 34.61 3.461 34.61 0.01 3.51 35.10 1.43 5.90 59.00 70.49 6.92 69.20 99.97
    30 7.655 7.655 76.55 7.653 76.53 -0.03 7.74 77.40 1.10 12.70 127.00 65.89 15.30 153.00 99.86
    35 17.599 17.599 175.99 17.577 175.77 -0.13 17.80 178.00 1.14 28.60 286.00 62.51 35.20 352.00 100.01
    40 43.293 43.293 432.93 43.187 431.87 -0.24 44.00 440.00 1.63 71.60 716.00 65.38 86.50 865.00 99.80
    q=20 kPa
    5 1.346 0.210 33.46 0.210* 33.46 0.00 0.09 32.25 -3.60 0.131 32.66 -2.38 0.17 33.05 -1.21
    10 3.562 0.619 55.62 0.619* 55.62 0.00 0.29 52.33 -5.92 0.461 54.04 -2.84 0.56 55.03 -1.06
    15 7.293 1.411 92.93 1.411* 92.93 0.00 0.71 85.92 -7.54 1.16 90.42 -2.70 1.40 92.82 -0.12
    20 13.767 2.968 157.67 2.968* 157.67 0.00 1.60 143.99 -8.68 2.68 154.79 -1.83 3.16 159.59 1.22
    25 25.462 6.138 274.62 6.138* 274.62 0.00 3.51 248.34 -9.57 5.90 272.24 -0.87 6.92 282.44 2.85
    30 47.723 12.921 497.23 12.921* 497.23 0.00 7.74 445.42 -10.42 12.70 495.02 -0.44 15.30 521.02 4.78
    35 93.059 28.467 950.59 28.467* 950.59 -0.00 17.80 843.92 -11.22 28.60 951.92 0.14 35.20 1017.92 7.08
    40 193.890 67.499 1 958.90 67.496* 1 958.86 -0.00 44.00 1 723.90 -12.00 71.60 1 999.90 2.09 86.50 2 148.90 9.70
    q=40 kPa
    5 2.496 0.225 64.96 0.225* 64.96 0.00 0.09 63.61 -2.08 0.131 64.02 -1.45 0.17 64.41 -0.85
    10 6.545 0.660 105.45 0.660* 105.45 0.00 0.29 101.76 -3.50 0.461 103.47 -1.88 0.56 104.46 -0.94
    15 13.264 1.499 172.64 1.499* 172.64 0.00 0.71 164.75 -4.57 1.16 169.25 -1.97 1.40 171.65 -0.58
    20 24.748 3.151 287.48 3.151* 287.48 0.00 1.60 271.98 -5.39 2.68 282.78 -1.64 3.16 287.58 0.03
    25 45.164 6.515 491.64 6.515* 491.64 -0.00 3.51 461.58 -6.11 5.90 485.49 -1.25 6.92 495.68 0.82
    30 83.336 13.732 873.36 13.732* 873.36 0.00 7.74 813.44 -6.86 12.70 863.04 -1.18 15.30 889.04 1.80
    35 159.508 30.324 1635.08 30.322* 1 635.06 -0.00 17.80 1 509.84 -7.66 28.60 1 617.84 -1.05 35.20 1 683.84 2.98
    40 324.929 72.148 3289.29 72.142* 3 289.23 -0.00 44.00 3 007.81 -8.56 71.60 3 283.81 -0.17 86.50 3 432.81 4.36

    注:*表示该Nγ值是基于Terzaghi方程由软件ABC计算的Quv值进行换算得到的。

    下载: 导出CSV

    表  3   完全粗糙基础的结果比较

    Table  3   Comparison of results for perfectly rough footings

    φ/(°) 本文方法 Martin(2004)[22] Bolton和Lau(1993)[16] Chen(1975)[24] Terzaghi(1943)[3]
    Nv Quv/ kN Nγ Quv/kN Error/ % Nγ Quv/kN Error/ % Nγ Quv/kN Error/% Nγ Quv/ kN Error/ %
    q=0
    5 0.114 1.14 0.113 1.13 -0.81 0.62 6.20 442.43 0.382 3.82 234.21 0.50 5.00 337.45
    10 0.447 4.47 0.433 4.33 -3.16 1.71 17.10 282.29 1.16 11.60 159.33 1.20 12.00 168.28
    15 1.267 12.67 1.181 11.81 -6.76 3.17 31.70 150.28 2.73 27.30 115.54 2.50 25.00 97.38
    20 3.183 31.83 2.839 28.39 -10.80 5.97 59.70 87.58 5.87 58.70 84.44 5.00 50.00 57.10
    25 7.618 76.18 6.491 64.91 -14.79 11.60 116.00 52.28 12.40 124.00 62.78 9.70 97.00 27.34
    30 18.083 180.83 14.754 147.54 -18.41 23.60 236.00 30.51 26.70 267.00 47.66 19.70 197.00 8.95
    35 43.677 436.77 34.476 344.76 -21.07 51.00 510.00 16.77 60.20 602.00 37.83 42.40 424.00 -2.92
    40 111.435 1 114.35 85.566 855.66 -23.21 121.00 1 210.00 8.58 147.00 1 470.00 31.92 100.40 1 004.00 -9.90
    q=20 kPa
    5 1.621 36.21 0.376* 35.11 -3.03 0.62 37.55 3.71 0.382 35.17 -2.86 0.50 37.84 4.49
    10 4.516 65.16 1.122* 60.65 -6.92 1.71 66.53 2.10 1.16 61.03 -6.34 1.20 65.87 1.09
    15 9.722 117.22 2.579* 104.61 -10.76 3.17 110.52 -5.71 2.73 106.12 -9.47 2.50 113.92 -2.81
    20 19.187 211.87 5.457* 182.56 -13.83 5.97 187.69 -11.41 5.87 186.69 -11.89 5.00 198.77 -6.18
    25 36.951 389.51 11.326* 326.50 -16.18 11.60 329.24 -15.47 12.40 337.24 -13.42 9.70 351.41 -9.78
    30 72.205 742.05 23.887* 606.89 -18.21 23.60 604.02 -18.60 26.70 635.02 -14.42 19.70 646.11 -12.93
    35 147.066 1 490.66 52.651* 1 192.43 -20.01 51.00 1 175.92 -21.11 60.20 1 267.92 -14.94 42.40 1 252.79 -15.96
    40 320.843 3 228.43 124.75* 2 531.45 -21.59 121.00 2 493.90 -22.75 147.00 2 753.90 -14.70 100.40 2 629.42 -18.55
    q=40 kPa
    5 2.951 69.51 0.418* 66.89 -3.77 0.62 68.91 -0.87 0.382 66.53 -4.29 0.50 70.67 1.68
    10 8.061 120.61 1.233* 111.19 -7.81 1.71 115.96 -3.86 1.16 110.46 -8.42 1.20 119.74 -0.72
    15 16.902 209.02 2.814* 185.78 -11.12 3.17 189.35 -9.41 2.73 184.95 -11.52 2.50 202.85 -2.95
    20 32.560 365.60 5.926* 315.23 -13.78 5.97 315.68 -13.66 5.87 314.68 -13.93 5.00 347.55 -4.94
    25 61.424 654.24 12.262* 549.10 -16.07 11.60 542.49 -17.08 12.40 550.49 -15.86 9.70 605.82 -7.40
    30 117.337 1 213.37 25.824* 994.29 -18.06 23.60 972.04 -19.89 26.70 1 003.04 -17.33 19.70 1 095.23 -9.74
    35 233.012 2 370.12 56.911* 1 900.95 -19.80 51.00 1 841.84 -22.29 60.20 1 933.84 -18.41 42.40 2 081.59 -12.17
    40 493.947 4 979.47 134.96* 3 917.45 -21.33 121.00 3 777.81 -24.13 147.00 4 037.81 -18.91 100.40 4 254.83 -14.55

    注:*表示该Nγ值是基于Terzaghi方程由软件ABC计算的Quv值进行换算得到的。

    下载: 导出CSV
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  • 收稿日期:  2019-09-30
  • 修回日期:  2019-11-19
  • 刊出日期:  2020-07-10

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