Shaking Table Model Test on Dynamic Response Characteristics and Failure Mechanism of Three Sections Locked Rock Slope
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摘要:
设计和制作了三段式锁固型岩质边坡模型，并进行了大型振动台试验，对三段式锁固型岩质边坡在地震作用下的动力响应和变形破坏模式进行了分析.研究结果表明：三段式锁固型边坡模型的自振频率随振动次数的增加而逐渐降低，阻尼比则随振动次数的增加而逐渐增大；边坡模型水平加速度放大系数表现出明显的高程放大效应和趋表效应；在不同类型输入波的作用下，边坡加速度响应存在着明显的差异；加速度放大系数随着输入波频率的增加表现出先增加后减小的变化规律，且在频率为15 Hz时峰值加速度放大系数达到最大值；随着输入波振幅的增加，坡体加速度放大系数总体上表现为先增加后减小的变化趋势；在地震波的作用下，位于坡体顶部裂缝和底部软弱夹层之间的锁固段出现多条裂缝，并不断发展呈X型贯通，最终在坡体内部形成3级滑面，并在持续的振动作用下，边坡沿着3级滑面发生滑动破坏.
Abstract:A three sections locked rock slope model was designed and produced, and a large-scale shaking table test was carried out to analyze the dynamic response and deformation failure mode of the three sections locked rock slope under earthquake action. The research results show that the natural vibration frequency of the three sections locked slope model decreases gradually with the increase of vibration times, and the damping ratio increases gradually with the increase of vibration times; the horizontal acceleration amplification factor of the slope model shows obvious elevation amplification effect and surface effect. Under the action of different types of input waves, there are obvious differences in the slope acceleration response: the acceleration amplification coefficient increases first and then decreases with the increase of input wave frequency, and the peak acceleration amplification coefficient reaches the maximum value when the frequency is 15 Hz. With the increase of the amplitude of the input wave, the acceleration amplification coefficient of the slope increases first and then decreases. Under the action of seismic wave, multiple cracks appear in the locking section between the crack at the top of the slope and the weak interlayer at the bottom, and continue to develop in an X-shaped connection. Finally, a 3-level slip surface is formed in the slope, and the slope slides along the 3-level slip surface under the action of continuous vibration.
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堤防工程或水库坝基渗流模拟中, 要取得符合实际的模拟结果, 计算模型的建立与计算参数的选取同等重要.计算参数又可划分为几何尺寸参数和水力学参数两大类, 其中, 尺寸参数大多为人工控制参数, 易于量测; 而水力学参数, 如渗透系数等, 则因介质的不均一性和测量手段的不合理等原因, 往往具有离散性大、不易准确确定的特点.因此如何确定合理的渗透系数一直是一个困扰工程界的难题.目前比较成熟的做法是通过反演的手段确定合理的渗透系数组合.反演是以一定的实际水位观测资料为基础的, 通过调整计算模型各部分的渗透系数, 使模拟结果最终与实际观测结果吻合, 此时模型各部分的渗透系数即可用作实际模拟时的计算参数.然而, 对于那些尚处于规划设计阶段的水库工程, 显然不具备反演的条件, 此时, 即可采用敏感性分析的方法.
1. 敏感性分析的一般思路
敏感性分析(谭晓慧, 2001) 是系统分析方法的一种, 它以一定的数学模型为基础.对于一固定系统, 可设其影响变量的集合为(x1, x2, …, xn), 系统特征用变量Z表示; 影响变量的基准值集合为(x1′, x2′, …, xn′), 与之对应的系统特征变量取值为z′.分析变量xk对系统特征的影响时, 可令其余变量取基准值且固定不变, xk在其可能的范围内变动, 进而可得变量xk对系统特征的影响曲线
(1) 由此可得变量的敏感度函数
(2) 取xk=xk′, 即得变量xk的敏感因子Sk′
(3) 上述理论应用于水库坝基渗流分析中, 可令坝基最大水力比降J为系统特征值, 其影响变量则为计算模型各部分的渗透系数(k1, k2, …, kn).对于第i部分的渗透系数ki, 套用式(3) 可得其敏感性因子Si′
(4) 其中: ki′为第i部分渗透系数基准值(可取试验值的均值或大值均值); J′为各部分渗透系数取基准值时的坝基最大水力比降; φi′ (ki′) 为坝基最大水力比降表达式对ki取偏导后, 再令ki=ki′时的计算结果; 对于难以作微分处理的复杂系统而言, 可按以下差分格式作近似处理
(5) 由式(4)、式(5) 结合有限元分析方法, 即可确定计算模型各部分渗透系数对整个坝基渗流场的敏感性因子, 进而找出最不利的参数组合.
2. 计算模型及相关试验参数
燕山水库位于淮河流域支流沙颍河主要支流澧河上游甘江河上, 其不仅是历次淮河流域规划所选定的以防洪为主的大型水库, 而且还是南水北调中线引汉工程所选定的反调节水库之一.该坝基存在大规模顺河断层带, 宽100余m, 具渗透变形问题, 是人们关心的重要隐患.
于河槽位置选一垂直于坝轴线的剖面为计算剖面, 上游水位取一期工程正常蓄水位108.14 m, 下游水位取河床地表高程85.48 m.结合《燕山水库项目建议书》中的一期工程坝体结构和现场所作的勘查工作, 得计算模型, 如图 1所示.
模型中坝基各层的渗透系数由试验确定, 坝体各部分的渗透系数为设计控制值, 具体取值如表 1; 依此可确定敏感分析时的取值范围和基准值.
表 1 计算模型各部分渗透系数试验值Table Supplementary Table Calculation model's testing penetration parameters
3. 渗透系数敏感性分析
编制有限元计算程序(毛昶熙, 1990; 陈崇希和唐仲华, 1993), 按前述敏感性分析思路对模型各部分渗透系数逐一作敏感性分析, 结果如下:
图 2对比列出了粘土斜墙取3种不同渗透系数时的渗流场模拟结果: 点划线对应渗透系数最小值6×10-7 cm/s, 虚线对应大值均值1×10-6 cm/s, 实线对应最大值3×10-6 cm/s.模拟中其他部分的渗透系数均取大值均值.不难看出, 当粘土斜墙渗透系数取3个不同值时, 其所对应的水头等值线模拟结果基本重合, 说明粘土斜墙只要达到了一定的密实度, 其渗透系数的改变对渗流场状态不会再产生明显的影响.
图 2 粘土斜墙渗透系数敏感性分析结果(3组等值线基本重合)Fig. 2. Sensitivity analyzing results of clay wall's penetration parameters (the three groups are almost overlapped)图 3对比列出了排水体取3种不同渗透系数时的渗流场模拟结果(对应关系如图 3); 模拟时其他部分的渗透系数亦取大值均值.可以看出, 随着排水体渗透系数的加大, 水头等值线在坝底的水平渗流段会向上游偏移, 但任意2组等值线间的间隔却变化甚小; 也就是说, 排水体渗透系数在其变化范围内的改变会影响水头值的分布, 但不会造成水力比降的显著提高或降低.
图 3 排水体渗透系数敏感性分析结果Fig. 3. Sensitivity analyzing results of the drainage part's penetration parameters图 4对比列出的是任意料区渗透系数分别取5×10-5cm/s (填料方案1的大值均值)和3.5×10-1 cm/s (填料方案2) 时的水头等值线.虽然2个渗透系数间隔几个数量级, 但从图 4中可以看出, 渗流场的变化并不十分明显.而且与图 4的规律类似, 任意料区渗透系数的改变只会影响水头的分布, 而不会造成水力比降的提高或降低.
图 4 任意料区渗透系数敏感性分析结果Fig. 4. Sensitivity analyzing results of the discretionarily filled part's penetration parameters图 5为Q42卵石混合土渗透系数敏感性分析结果.从图 5中不难看出, 虽然其渗透系数只在同一数量级中变化(2.0×10-1~6.0×10-1 cm/s), 但整个坝基的渗流场却发生了显著的改变: 随着渗透系数的加大, 水头等值线间隔明显减小, 即对应位置的水力比降会有明显的提高.
图 5 Q42卵石混合土渗透系数敏感性分析结果Fig. 5. Sensitivity analyzing results of Q42's penetration parameters图 6为Q3卵石混合土渗透系数敏感性分析结果.该层渗透系数的改变对整个坝基渗流场(尤其是坝头与坝脚部位) 亦会有较大的影响, 渗透系数的加大会导致坝基平均水力比降的提高.
图 6 Q3卵石混合土渗透系数敏感性分析结果Fig. 6. Sensitivity analyzing results of Q3's penetration parameters图 7为断层破碎带渗透系数的敏感性分析结果.从图 7中可以看出3组等值线基本重合, 这说明破碎带渗透系数在其变化范围内的取值对整个坝基渗流场无显著影响.
图 7 破碎带渗透系数敏感性分析结果(3组等值线基本重合)Fig. 7. Sensitivity analyzing results of fault area's penetration parameters (the three groups are almost overlapped)为更好地指导设计, 还进行了垂直防渗体渗透系数的敏感性分析.模拟时, 上游水位取校核洪水位116.78 m, 下游水位仍取河床地表高程85.48 m; 防渗体厚4 m, 打入Q3卵石混合土层底部.当防渗体渗透系数取10-4, 10-5和10-8 cm/s时, 其水头等值线模拟结果如图 8所示, 当渗透系数小于10-5 cm/s后, 再减小其渗透系数, 防渗效果不再有明显改变, 图 8中10-5 cm/s所对应的等值线(虚线) 与10-8 cm/s所对应的等值线(点划线) 基本重合.表 2中, ki′为渗透系数基准值; J′为各部分渗透系数取基准值时坝基最大水力比降; φi′ (ki′) 为比降表达式对ki偏导后再令ki=ki′时的计算结果; Si′为敏感性因子.
图 8 垂直防渗体渗透系数敏感性分析结果Fig. 8. Sensitivity analyzing result of seepage-proof body's penetration parameters表 2 计算模型各部分渗透系数敏感性分析结果Table Supplementary Table Sensitivity analyzing results of penetration parameters
4. 结论
堤防工程及水库坝基渗流模拟时, 如不具备反演条件, 可在试验参数的基础上, 采用敏感性分析的方法确定计算模型各部分渗透系数的最不利组合, 然后以此作为实际渗流模拟时的计算参数.
计算模型不同部位渗透系数的改变对整个坝基渗流场的影响差异很大, 所以在模拟计算时其各自渗透系数的取值标准也应有所不同.对于燕山水库, 有如下分析结论: (1) 粘土斜墙及断层破碎带的渗透系数在其变化范围内发生改变时, 对整个坝基的渗流场特征不会产生显著影响.计算时其渗透系数可取大值均值. (2) 随排水体或任意料区的渗透系数的加大, 在坝底水平渗流段, 水头等值线会发生向上游的整体偏移, 但其偏移幅度很小.这说明排水体和任意料区渗透系数的改变亦不会对坝基渗流场特征产生显著影响, 在具体计算时其渗透系数亦可取大值均值. (3) 坝基覆盖层Q42及Q3卵石混合土渗透系数的改变对整个坝基渗流场会产生较大的影响.其中, Q42渗透系数的加大主要导致了坝基水平渗流段水力比降的大幅度增加, 而Q3渗透系数的加大则会导致坝前和坝后部分水力比降的提高.为了使评价结果偏安全, 在具体计算时两部分的渗透系数均应取最大值. (4) 就粘土斜墙和垂直防渗体而言, 只要它们的渗透系数小于一定值之后, 再降低其渗透系数, 其防渗效果不再会有明显提高.
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图 6 不同白噪声激励下模型边坡第一阶自振频率和阻尼比变化曲线
Fig. 6. First order natural frequency and damping ratio curve of model slope under different white noise excitation
图 7 加速度放大系数的等值线图
a.压缩4倍卧龙波0.1 g; b.压缩4倍卧龙波0.2 g; c.压缩4倍El波0.1 g; d.压缩4倍El波0.2 g; e.20 Hz正弦波0.1 g; f.20 Hz正弦波0.2 g
Fig. 7. Contour maps of acceleration amplification coefficient
图 8 边坡模型的加速度动力响应
a.坡面; b.坡体内部竖直方向上; c.坡体内部水平方向上
Fig. 8. Acceleration dynamic response of slope model
图 9 不同频率正弦波输入下坡面水平加速度放大系数
a.幅值0.1 g; b.幅值0.2 g
Fig. 9. Horizontal acceleration amplification factor of slope surface under different frequency sine wave inputs
图 10 输入波幅值对坡面加速度放大系数的影响
Fig. 10. Effect of input wave amplitude on slope acceleration amplification coefficient
图 11 输入波幅值对坡面测点加速度放大系数的影响
Fig. 11. Effect of input wave amplitude on slope acceleration amplification coefficient
图 12 水平方向上正弦波输入下加速度放大系数(A22~A19)
Fig. 12. Acceleration amplification factor (A22-A19) under sine wave input in horizontal direction
图 13 竖直方向上不同频率正弦波输入下加速度放大系数(A4⁃A10⁃A15⁃A19)
Fig. 13. Acceleration amplification factor under different frequency sine wave input in vertical direction (A4⁃A10⁃A15⁃A19)
图 14 试验中边坡模型的变形破坏情况输入
a.软弱夹层末端出现拉裂(卧龙波0.3 g); b.锁固段出现竖直拉裂缝(正弦波0.3 g); c.锁固段处裂缝贯通(卧龙波0.4 g); d.坡体浅部出现裂纹(正弦波0.4 g); e.坡体浅部现块体滑落(卧龙波0.5 g); f.预制裂缝后部岩体出现破碎(正弦波0.5 g); g.形成3级滑面(卧龙波0.6 g); h.坡体沿着3级滑面滑动破坏(正弦波0.6 g)
Fig. 14. Input of deformation and failure of model slope in test
表 1 模型试验主要相似常数
Table 1. Main similarity constants in model test
物理量 相似关系 相似常数 密度(ρ) Cρ 1 长度(L) CL 16 时间(t) Ct 4 弹性模量(E) CE = CρCL2Ct-2 16 泊松比(μ) Cμ 1 内摩擦角(φ) Cφ 1 黏聚力(c) Cc = CE 16 加速度(a) Ca = CECρ-1CL-1 1 频率(f) Cf = Ct-1 0.25 应力(σ) Cσ = CECε 16 
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表 2 相似材料物理力学参数
Table 2. Physical and mechanical parameters of similar materials
位置 密度(g/cm3) 抗压强度(MPa) 抗拉强度(MPa) 弹性模量(MPa) 泊松比 内摩擦角(°) 黏聚力(kPa) 坡体 2.50 0.853 0.099 124.46 0.12 34.8 294.0 软弱层 2.32 - - 4.8 0.35 10.0 10.0
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表 3 试验加载方案
Table 3. Physical and mechanical parameters
工况 激励方式 加速度峰值(m/s2) 频率(Hz) 时间压缩比 1~3 卧龙波 1 - 4, 2, 1 4~6 El波 1 - 4, 2, 1 7~14 正弦波 1 5, 10, 15, 20, 25,
30, 35, 40- 15 白噪声 0.05 - - 16~18 卧龙波 2 - 4, 2, 1 19~21 El波 2 - 4, 2, 1 22 白噪声 0.05 - - 23~30 正弦波 2 5, 10, 15, 20, 25,
30, 35, 40- 31 白噪声 0.05 - - 32 卧龙波 3 - 4 33 正弦波 3 10 - 34 白噪声 0.05 - - 35 卧龙波 4 - 4 36 正弦波 4 10 - 37 白噪声 0.05 - - 38 卧龙波 5 - 4 39 正弦波 5 10 - 40 白噪声 0.05 - - 41 卧龙波 6 - 4 42 正弦波 6 10 - 43 白噪声 0.05 - - 44 卧龙波 7 - 4 45 正弦波 7 10 - 46 白噪声 0.05 - - 47 卧龙波 8 - 4 48 正弦波 8 10 - 49 白噪声 0.05 - -
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