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§4 土中应力

§4 土中应力. 土中应力与建筑物安全. 汶川地震中的最牛学校. 安县桑枣中学 北川县刘汉希望小学. 地面沉降使房屋地面开裂 —— 常州武进县横林红联永利表玻璃厂. 地面沉降使房屋墙体开裂 —— 常州武进县横林红联永利表玻璃厂. 地面沉降使房屋墙面开裂 —— 常州武进县横林红联永利表玻璃厂. 地面沉降使围墙、地坪开裂 —— 常州武进县红联小学. 4 STRESSES IN SOIL. 4.2 effective overburden pressure. 4.1 Introduction 4.2 Effective Overburden Pressure

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§4 土中应力

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  1. §4 土中应力 土中应力与建筑物安全 汶川地震中的最牛学校 安县桑枣中学 北川县刘汉希望小学

  2. 地面沉降使房屋地面开裂 ——常州武进县横林红联永利表玻璃厂

  3. 地面沉降使房屋墙体开裂 ——常州武进县横林红联永利表玻璃厂

  4. 地面沉降使房屋墙面开裂 ——常州武进县横林红联永利表玻璃厂

  5. 地面沉降使围墙、地坪开裂 ——常州武进县红联小学

  6. 4 STRESSES IN SOIL 4.2 effective overburden pressure 4.1 Introduction 4.2 Effective Overburden Pressure in the Ground 4.3 Contact Pressure between the Foundation and the Ground 4.4 Stress Increase in the Ground 4.1 概述 4.2 自重应力 4.3 基底压力 4.4 地基附加应力

  7. CHAPTER 4 STRESSES IN SOIL 4.1 Introduction 4.2 Effective Overburden Pressure in the Ground 4.3 Contact Pressure between the Foundation and the Ground 4.4 Stress Increase in the Ground

  8. 4 STRESSES IN SOIL 4.1 Introduction Chapter 3 强度问题 地基中的应力状态 应力应变关系 土力学中应力符号的规定 变形问题 Chapter 4 Stress condition 应力状态 The stress due to the effective self-weight of the soil. Effective overburden pressure 自重应力 The stress between the foundation and the ground. Contact pressure 基底压力 The stress in the interior of the ground due to exterior (static or dynamic) load. Additional stress 地基附加应力 p89

  9. 4 STRESSES IN SOIL ∞ ∞ ∞ ∞ ∞ 4.2 Effective overburden pressure Nomenclature in soil mechanics 土力学中应力符号的规定 Foundation: elastic half-space 地基：半无限空间 o x y z Normal stresses in the x,y, and z direction Shear stresses in the xy,yz, and zx direction

  10. 4 STRESSES IN SOIL Δσ ε 土的应力-应变关系的假定 线弹性体 ①连续介质 （宏观平均） 加载 碎散体 非线性 弹塑性 ②线弹性体 （应力较小时） 卸载 成层土 各向异性 ③均匀一致各向同性体 （土层性质变化不大时） εp εe 理论 ——弹性力学解求解“弹性”土体中的应力 方法 ——解析方法优点：简单，易于绘成图表等 p90

  11. 4 STRESSES IN SOIL 4.2 effective overburden pressure in the ground 水平地基中的自重应力 Definition: effective self-weight of the ground soils 定义：在修建建筑物以前， 地基中由土体本身的有效重量而产生的应力。 Purpose: original conditions of foundation 目的：确定土体的初始应力状态 Assumption: semi-infinite, elastic half-space 假定：水平地基半无限空间体半无限弹性体 侧限应变条件一维问题 Calculation: bulk unit weight above the water table, buoyant unit weight below the water table 计算：地下水位以上用天然重度，地下水位以下用浮重度

  12. 4 STRESSES IN SOIL 4.2 effective overburden pressure Calculation Formulas 计算公式 竖直向： 均质地基 K0:coeficient of lateral earth pressure 侧压力系数 水平向： 成层地基 竖直向： γ1 水平向： γ2 γ3 重度：地下水位以上用天然重度γ 地下水位以下用浮重度γ’ p91

  13. 4 STRESSES IN SOIL 4.2 effective overburden pressure 分布规律 • 自重应力分布线的斜率是容重； • 自重应力在等重度地基中随深度呈直线分布； • 自重应力在成层地基中呈折线分布； • 在土层分界面处和地下水位处发生转折。 成层地基 均质地基

  14. 4 STRESSES IN SOIL 4.2 effective overburden pressure Example 4-1 O GL A ground consists of four layers of soil stratum with their thickness and unit weights shown in Figure. Try to determine the vertical effective overburden pressure at the interface level among the soil layers and plot its distribution curve. r1=18.23kN/m3 h1=2.5m 45.58kPa r2=18.62kN/m3 h2=2.0m 82.82kPa GWL h3=1.5m r3’=9.80kN/m3 97.52kPa h4=2.0m r4’=9.40kN/m3 116.32kPa Solution With the presented data, the vertical overburden pressure can be calculated as follows, σsz1 =γ1h1=18.23 x 2.5 = 45.58kPa σsz2 =σsz1+γ2h2= 45.58 + 18.62 x 2 = 82.82kPa σsz3 =σsz2+γ3’h3= 82.82 + 9.8 x 1 .5 = 97. 52kPa σsz4 =σsz3+γ4’h4 = 97.52 + 9.4 x 2 = 116.32kPa Z

  15. 4 STRESSES IN SOIL 4.2 effective overburden pressure 1.8m Gravel 1.2m Silt 4m Rock Example 4.2 Details of the subsoil conditions at a site are shown in Fig. 4.4 together with details of the soil properties. The ground surface is subjected to a uniform loading of 60 kPa and the groundwater level is 1.2 m below the upper surface of the silt. It can be assumed that the gravel has a degree of saturation of 50 percent and that the silt layer is fully saturated. Take γw = 10 kN/m3. Determine the vertical effective stress acting at a point 1 m above the silt/rock interface. P=60kPa GWL · Action Point 1m

  16. 4 STRESSES IN SOIL 4.2 effective overburden pressure Example 4.2 Solution Bulk unit weight of gravel = =18.03=l8kN/m3 Saturated weight of silt= =18.98=l9kN/m3 Effective vertical stress at 1 m above silt/rock interface= [Uniform pressure applied at ground surface]+[Total pressure due to weight of soils]-[Water pressure] =60 +(1.8×18+4.2×19)- 3×10= 142.2 kPa

  17. 4 STRESSES IN SOIL 4.2 effective overburden pressure 4.1 Introduction 4.2 Effective Overburden Pressure in the Ground 4.3 Contact Pressure between the Foundation and the Ground 4.4 Stress Increase in the Ground 4.1 概述 4.2 自重应力 4.3 基底压力 4.4 地基附加应力

  18. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground x o y z 1 Stress increase due to vertical concentrated (point) load P α r y M’ x R z β M （P；x,y,z；R, α,β） p99

  19. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground Vertical concentrated load – Boussinesq Solution K制表查阅 集中力作用下的 应力分布系数 p100

  20. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground P o α x r y x M’ β R z y M z Vertical concentrated load – Boussinesq Solution 0.5 0.4 0.3 0.2 0.1 0 特点 1.σz与K无关，应力呈轴对称分布 K 2.σz:τzy:τzx= z:y:x, 竖直面上合力过原点，与R同向 0.5 1.0 1.5 2.0 2.5 3.0 r/z

  21. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground 竖直集中力作用下的附加应力计算－布辛内斯克课题 特点 3.P作用线上，r=0, K=3/(2π）,z=0, σz→∞，z→∞，σz=0 4.在某一水平面上z=const，r=0, K最大，r↑，K减小，σz减小 5.在某一圆柱面上r=const，z=0, σz=0，z↑，σz先增加后减小 6.σz等值线－应力泡 P P 0.1P 球根 0.05P Stress bulb 应力 球根 0.02P 0.01P p101

  22. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground 4.4.1 矩形荷载作用时的地基附加应力 均布的矩形荷载 p M m=L/B, n=z/B 矩形竖直向均布荷载角点下的应力分布系数 （角点应力系数）Kc p102

  23. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground 任意点的垂直附加应力—角点法 荷载与应力间 满足线性关系 角点法 角点下垂直附加 应力的计算公式 叠加原理 地基中任意点的附加应力 两种情况： a.矩形面积内 b.矩形面积外

  24. Example 4.4 A 4.5 in square foundation exerts a uniform pressure of 200 kPa on a soil. Determine (i) the vertical stress increments due to the foundation load to a depth of 10 m below its centre and (ii) the vertical stress increment at a point 3 m below the foundation and 4 m from its centre along one of the axes of symmetry.

  25. 4.0m 4.5m A B A E B A B G k O 4.5m k F D C C C D D (c) (a) (b) Example 4.4 Fig. 4.6 Fig. 4.7

  26. Example 4.4

  27. 4 STRESSES IN SOIL 4.4 Stress Increase in the Ground Summary K= f（底面形状；荷载分布；计算点位置） K：附加应力系数表 • K——竖直集中荷载作用下 • Kc ——矩形面积竖直均布荷载作用角点下 • Kt——矩形面积三角形分布荷载作用角点下 • Ks ——条形面积竖直均布荷载作用时

  28. 4 STRESSES IN SOIL 4.3 contact pressure 4.3 Contact Pressure between the foundation and the ground 上部结构 上部结构的自重及各种荷载都是通过基础传到地基中的。 建筑物设计 基础 地基 基础结构的外荷载 基底压力：基础底面传递给地基表面的压力，也称基底接触压力。 基底反力 影响因素 计算方法 分布规律 基底压力 • 暂不考虑上部结构的影响，使问题得以简化； • 用荷载代替上部结构。 附加应力 地基沉降变形

  29. 4 STRESSES IN SOIL 4.3 contact pressure 4.3 Contact Pressure between the foundation and the ground • 大小 • 方向 • 分布 Contact pressure (基底压力) is the intensity of loading transmitted from the underside of a foundation to the ground soil. 荷载条件 • 刚度 • 形状 • 大小 • 埋深 基础条件 基底压力 地基条件 • The magnitude and the distribution pattern of the contact pressure depend on many factors such as the magnitude and distribution of the structure load applied, the rigidity and embedment depth of the foundation, and the soil properties, etc. • 土类 • 密度 • 土层结构等 p93

  30. 4 STRESSES IN SOIL 4.3 contact pressure 基底压力的分布规律 条形基础，竖直均布荷载 弹性地基，完全柔性基础 • 基础抗弯刚度EI=0 ； • 基础变形能完全适应地基表面的变形; • 基础上下压力分布必须完全相同，若不同将会产生弯矩。 弹性地基，绝对刚性基础 • 抗弯刚度EI=∞ ； • 反证法: 假设基底压力与荷载分布相同，则地基变形与柔性基础情况必然一致； • 分布: 中间小, 两端无穷大。

  31. 4 STRESSES IN SOIL 4.3 contact pressure 弹塑性地基，有限刚度基础 — 接近弹性解 — 马鞍型 — 抛物线型 — 倒钟型 — 荷载较小 —荷载较大 粘性土地基 砂性土地基

  32. 4 STRESSES IN SOIL 4.3 contact pressure 4.3.1 Contact pressure due to vertical centric load 垂直中心荷载下的基底压力 根据圣维南原理，基底压力的具体分布形式对地基应力计算的影响仅局限于一定深度范围；超出此范围以后，地基中附加应力的分布将与基底压力的分布关系不大，而只取决于荷载合力的大小、方向和位置。 基底压力的分布形式十分复杂 基础尺寸较小 荷载不是很大 简化计算方法： 假定基底压力按直线分布的材料力学方法

  33. 4 STRESSES IN SOIL 4.3 contact pressure B L x y 4.3.1 Contact Pressure due to Vertical Centric Load 垂直中心荷载的基底压力 P The length and width of a rectangular foundation are L and B, respectively, as shown in Fig. 3-7a). A vertical centric load P is applied on the foundation. According to the linear distribution assumption, the value of the contact pressure is p=P/A (3-5) where lowercase p represents the contact pressure (kPa); capital P represents the vertical total load on the underside of the foundation (kN); and A = B x L represents the area of the foundation. p95

  34. §4.3 基底压力 室内设计地面 室外设计地面 1. 中心荷载下的基底压力 4.3.2 基底压力的简化计算 F F 对于荷载沿长度方向均布的条形基础，应视为平面问题，沿长度方向截取一单位长度，计算平均基底压力。

  35. 4 STRESSES IN SOIL 4.3 contact pressure B ey L x ex y 4.3.2 Contact Pressure due to Vertical Eccentric Load 垂直偏心荷载的基底压力 P p96

  36. 4 STRESSES IN SOIL 4.3 contact pressure B B B e L L L x x x y y y 矩形面积单向偏心荷载 土不能承受拉应力 P P P 压力调整 e K e 基底压力合力与总荷载相等 K=B/2-e 3K e<B/6: 梯形 e=B/6: 三角形 e>B/6: 出现拉应力区 p97

  37. 4 STRESSES IN SOIL 4.3 contact pressure Vertical eccentric load on strip foundation 条形基础竖直偏心荷载 Inclined eccentric load 倾斜偏心荷载 e Pv P P Ph B 分解为竖直向和水平向荷载，水平荷载引起的基底水平应力视为均匀分布。 Pv=Pcosβ Ph=Psinβ

  38. 4 STRESSES IN SOIL Stress condition 应力状态 • 土力学中应力符号的规定 Summary 小结 • 地基中的应力状态 • 应力应变关系的假定 Effective overburden pressure 自重应力 计算 • 水平地基中的自重应力 • 影响因素 Contact pressure 基底压力计算 • 基底压力分布 • 实用简化计算 Foundation shape and load conditions 基础形状与荷载条件的组合 • 因素：底面形状；荷载分布；计算点位置

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