Stress-seepage coupled analysis of critical suction for installation of suction caissons in sand
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摘要: 临界负压是砂土中吸力桶沉贯施工的关键控制因素。现有方法多基于渗流分析确定临界负压,因不考虑土体变形而无法真实反映临界负压下土体破坏。利用应力-渗流耦合有限元方法,基于桶内土体位移发展确定临界负压。通过对比现场试验数据验证了方法的合理性,进一步比较了基于应力-渗流耦合和渗流计算的分析结果,探讨了临界负压下土体的破坏模式。主要结论包括：①临界负压下桶内土体竖向位移发展显著加速,土体位移和负压关系曲线出现明显拐点；②当插入比较大时,基于渗流分析可低估临界负压；③插入比较小和较大时,临界负压下桶内土体分别呈楔形体破坏和整体隆起破坏模型。Abstract: The critical suction is the key control factor for the installation of suction caissons in sand. The existing methods mainly rely on seepage analysis to determine the critical suction, which does not consider soil deformation and consequently might not realistically reflect soil failure under the critical suction. By using the stress-seepage coupled finite element method, the critical suction is determined based on soil displacements inside a caisson. After examined against the field tests, the model is utilized to study the differences between the critical suctions determined by stress-seepage coupled and seepage analyses, and the failure mode of soils under the critical suction is discussed. The main conclusions include: (1) The vertical displacements of the soils inside the caisson exhibit accelerating growth under critical suction, reflected by an inflection point in the soil displacement-suction curve. (2) When the embedment ratio is relatively large, the seepage-based methods might underestimate the critical suction. (3) The soils inside the caisson show wedge-shaped failure mode and uniform upheaval failure mode under the critical suction when the embedment ratio is relatively small and large, respectively.
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0. 引言
吸力桶是一种上端封闭、底端开口的桶形基础（见图1）[1]。沉贯时,吸力桶切入海床,内部形成封闭空间,抽水形成负压。桶内渗流场会降低沉贯阻力,且桶内外压差形成向下的额外沉贯力可帮助桶体继续下沉。但当渗流力增大到一定程度时会导致桶外土体塑性流动进入桶内部引起土塞加速隆起,使吸力桶无法沉贯到预定深度,此时的负压值称为临界负压[2-3]。
现有方法对临界负压的预测主要基于单纯渗流分析[4-6],通过比较桶内特征水力梯度与管涌发生的临界水力梯度icrit=
γ′/γw ,判定是否到达临界负压；其所面临的两个最主要的难题是判定准则及其验证。目前有多种判定方法。如Houlsby等[4]将沿桶内壁的平均水力梯度iave（见图1）作为特征水力梯度进而判定临界负压,而Senders等[5]则选择桶内地表处的水力梯度iexit（见图1）作为特征梯度。但是,渗流分析因为无法考虑土体变形和破坏,导致较难验证上述判定准则。应力-渗流耦合有限元具有可以计算渗流作用下土体变形的优势,可以获得不同沉贯负压下土体位移,进而可以通过土体位移开始加速发展判定到达临界负压。这种方法可以更自然地确定临界负压,避免了上述渗流分析中判定准则选取上的随意性。本文旨在基于应力-渗流耦合有限元确定吸力桶沉贯临界负压,对比其与渗流分析结果,探讨单纯渗流分析可能潜在的问题,并借助应力-渗流耦合方法可以考虑土体变形的优势,分析了临界负压下土体破坏模式。
1. 应力-渗流耦合临界负压计算模型
1.1 有限元模型及边界条件
取桶轴线为对称轴,建立轴对称有限元模型。网格划分及边界条件如图2所示。吸力桶内径D为4 m,入土深度L,桶壁厚度t为0.02 m（t/D=0.5%,典型设计取值为0.3%～0.5%[7]）。土体建模区域直径为84 m,深度为25 m。土体采用轴对称变形孔压耦合单元（CAX8P）。对称轴及土体右边界处无水平位移且不可透水；土体下边界无水平和竖向位移且不可透水。建立厚度t=0.02 m的不透水钢制环形挡板作为吸力桶壁,其上端固定,与对称轴的水平距离为2 m (D/2)。
1.2 本构模型及材料参数
土体采用莫尔库仑模型,参数取值参照Houlsby等[4]案例1b中给出的数据,有效摩擦角
φ 为40°,剪胀角ψ 为20°。土体与桶界面摩擦系数μ 为0.48。土体渗透系数为0.0003 m/s,孔隙比为0.66,浮重度γ′ 为8.5 kN/m3。1.3 模拟过程及临界负压确定
如图2所示,初始时,在吸力桶壁两侧土体上表面设置100 kPa的孔压并设置100 kPa的表面压力（P1和P2）。地应力平衡后减小P2,以模拟负压作用下的桶内水头降低。参考Pratama等[8]判定临界水头差的方法,本文取桶内土体表面一特征点（图2中A点）,分析其位移与负压的关系,如图3所示。其中,土体竖向位移为u,桶内土体上表面负压为p,且均进行归一化处理。从图中可知,当p/
γ′D =0.91时,u/L迅速增大,将具有这一特征的点称为位移拐点,并可将位移拐点对应的负压值定义为临界负压pcrit。![]()
图 3 归一化土体位移与负压关系及临界负压确定Figure 3. Relationship between normalized soil displacement and suction and determination of critical suction2. 计算结果与分析
2.1 有限元模型验证
为验证上述有限元模型的合理性,将计算所得临界负压与Houlsby等[4]汇报的现场沉贯试验数据对比。有限元计算使用的吸力桶尺寸和土体参数见1.1节。如图4所示,计算临界负压与现场实测沉贯负压随吸力桶入体深度变化的趋势一致,一定程度上说明有限元计算的合理性。另一方面,图4表明实测负压倾向于小于计算的临界负压。造成这一现象的可能原因是,临界负压对应极限状态（即桶内土体发生破坏、快速隆起）,然而正常沉贯施工中（如图4的现场试验中吸力桶可以顺利贯入至设计标高）,实际负压一般小于上述极限值。对于图4中B点,实测负压较大程度地超过了计算临界值,其可能原因是吸力桶盖已经与地表接触,此时负压只要小于气化值仍可升高。
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图 4 不同入土深度下实测沉贯负压与计算临界负压的比较Figure 4. Comparison between measured suctions and computed critical suctions at different penetration depths2.2 基于应力-渗流耦合和渗流计算的临界负压对比
Houlsby等[4]基于纯渗流分析得到归一化临界负压
pcrit /γ′D 与插入比L/D之间的关系：pcritγ'D=LD1−{0.45−0.36[1−exp(−L0.48D)]}。 (1) Senders等[5]基于纯渗流分析提出归一化临界负压
pcrit /γ′D 与插入比L/D之间的关系：pcritγ′D={π−arctan[5(LD)0.85](2−2π)}LD。 (2) 图5对比了上述渗流分析和本文方法计算的临界负压。不同方法得到的临界负压随插入比L/D的变化趋势一致,且当L/D较小（L/D<0.5）时,各方法计算的临界值接近,表明现有渗流分析具有合理性。另一方面需要注意,当L/D较大（L/D>0.5）时,渗流分析可能会低估临界负压。结合图6中水力梯度分布,分析上述现象原因：当L/D较小时（见图6（a））,水力梯度高的区域主要在桶壁附近,与Houlsby等[4]和Senders等[5]的基本假定相符；而当L/D较大时（见图6（b））,整个桶内土体都可承担较大的水力梯度作用。此时仅关注桶壁附近土体水力梯度（如上述渗流分析方法）就可能低估临界负压。
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图 5 基于应力-渗流耦合和单纯渗流分析所确定的临界负压Figure 5. Comparison between critical suctions determined by stress-seepage coupled and seepage analyses![]()
图 6 临界负压下桶内土体竖向水力梯度分布Figure 6. Distribution of vertical hydraulic gradient of soils inside caisson upon reaching critical suction2.3 临界负压下土体破坏模式
如图7（a）所示,当插入比较小时,桶内土体破坏呈楔形体模式。当插入比较大时,如图7（b）所示,桶内土体竖向位移差距不大,呈整体向上隆起破坏。这与Ragni等[9]在吸力桶沉贯离心试验所得结论一致。且上述土体破坏模式与图6中所示竖向水力梯度分布相吻合。在渗流力的作用下,土体竖向有效应力会显著降低,因此也会产生了较大的竖向位移。
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图 7 临界负压下吸力桶内土体竖向位移分布Figure 7. Distribution of vertical displacement of soils inside caisson upon reaching critical suction3. 结论
本文通过应力-渗流耦合有限元方法分析了吸力桶沉贯过程中的临界负压。基于现场沉贯试验数据验证了本文方法的合理性。进而,对比了基于应力-渗流耦合和单纯渗流计算所确定的临界负压,探讨了临界负压下土体的破坏模式,得到以下3点结论。
（1）达到临界负压状态时,桶内土体竖向位移呈现显著加速特征,土体位移和负压关系出现明显拐点。
（2）当插入比较小时,应力-渗流耦合与单纯渗流分析给出相近的临界负压；当插入比较大时,单纯渗流分析可能造成对临界负压的显著低估。
（3）临界负压下,插入比较小时,桶内土体呈楔形体破坏；插入比较大时,桶内土体呈整体隆起破坏。
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图 3 归一化土体位移与负压关系及临界负压确定
Figure 3. Relationship between normalized soil displacement and suction and determination of critical suction
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图 4 不同入土深度下实测沉贯负压与计算临界负压的比较
Figure 4. Comparison between measured suctions and computed critical suctions at different penetration depths
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图 5 基于应力-渗流耦合和单纯渗流分析所确定的临界负压
Figure 5. Comparison between critical suctions determined by stress-seepage coupled and seepage analyses
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图 6 临界负压下桶内土体竖向水力梯度分布
Figure 6. Distribution of vertical hydraulic gradient of soils inside caisson upon reaching critical suction
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