Analysis of crack development in loess deep filled ground based on physical modelling tests
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摘要:
裂缝是高填方工程中常见病害,常规手段难以精准预测裂缝的发育情况。为指导黄土高填方工程的抗裂缝设计,以陕北某黄土高填方工程中的典型沟谷断面为原型,采用土工离心模型试验预测黄土高填方场地潜在裂缝,结合现场监测方法,揭示裂缝产生机制,并调查分析工程场地内裂缝的孕裂环境、启裂条件、破裂过程,评估离心模型试验预测裂缝发育的有效性,提出适用于黄土高填方场地的裂缝防控措施。离心模型试验结果显示,不均匀沉降、水平位移会引起沟谷地形中的黄土高填方场地在挖填交界带内发育裂缝;离心模型试验与原型现场监测结果显示,原型与离心模型试验的裂缝分布位置相对应,填土厚度差异引起的不均匀沉降和朝向沟谷中心的水平位移产生的拉剪联合作用是裂缝产生的主要原因。
Abstract:Cracks are a common issue in deep filled construction projects, and conventional methods often struggle to accurately predict their development. To guide the anti-crack design for deep-filled loess projects, a prototype of a typical gully section from a northern Shaanxi project was selected. Geotechnical centrifuge model tests were utilized to predict potential cracks in the loess fill, with the cracking mechanisms elucidated through combined field monitoring. The study also investigates the conditions conducive to cracking, the fracture initiation of cracks, and the fracture processes within the project site. The effectiveness of using centrifuge model tests for predicting crack development was evaluated, and measures suitable for preventing and controlling cracks in high loess fill sites were proposed. The results indicate that uneven settlement and horizontal displacement cause cracks to develop in the excavation-fill boundary zone within gully terrain. Both centrifuge model tests and prototype field monitoring demonstrate that crack distributions in the prototype correspond to those in the tests, with differential fill thickness and horizontal displacement towards the center of the gully primarily responsible for the formation of cracks.
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Keywords:
- loess /
- deep filled ground /
- cracks /
- centrifuge model test /
- field monitoring
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0. 引言
近年来,我国工程建设逐步向西部推进,泥石流灾害对居民生活、工程建设的危害日益增显,不仅威胁工程的建设及运营,严重的甚至可以导致人员伤亡[1 − 5]。川西藏东交通廊道位于青藏高原东南缘,东起成都,向西经康定、昌都终至拉萨,是西藏自治区与外省的重要通道[6 − 7]。该地区地形起伏大,地质条件复杂,新构造运动活跃发育,河流冰川发育,气候湿润,为泥石流高发地区,因泥石流活动导致公路、铁路交通阻断、施工事故的案例屡见不鲜[8 − 10]。在此地区的工程建设中,受复杂地形地貌影响,铁路、公路选线常常出现无法绕避泥石流沟的情况,因此科学评价泥石流的发育特征并快速准确揭示泥石流动力学特性,对于川西藏东交通廊道安全建设具有重要意义。
前人针对川西藏东交通廊道泥石流灾害发育特征和对工程影响研究众多。王运生等[11]分析了川藏铁路泸定段的地质环境条件,提出该地区泥石流主要以堵河-溃决的危害形式影响工程设施。向兵等[9]认为丰富物源是川西地区低频泥石流危害性大的关键,并提出了川西地区针对公路泥石流防控的要点。袁东等[12]分析了西部山区交通廊道泥石流的发育类型和分布规律,指出了工程建设中防控难点和对策建议。
泥石流流量、流速等动力学特性分析对于防治工程的设计起重要作用。对于流速,现阶段的计算公式:弯道超高公式、基于量纲分析的经验公式、基于运动模型的半经验公式和改进的曼宁公式,而在工程实际中最多采用的一般为第二种[13 − 15]。流量计算方法包括:配方法、形态调查法、综合成因法和经验公式法,其中考虑堵塞因素的雨洪修正法也是配方法的一种,目前应用最广泛[16]。另外,胡卸文等[18 − 19]对火后泥石流、冰湖溃决型泥石流、震后泥石流等特殊泥石流的流量计算方法也进行了探讨论述。近年来,GIS技术在泥石流防控工作的应用也逐渐增多[20],传统泥石流参数计算方法在量取流域参数时效率较低,计算位置局限于某一特定断面。如何提升计算效率以满足日益增加的工程需求成为了现阶段泥石流灾害防治工作的新挑战。
毛家沟位于甘孜藏族自治州康定市境内,为典型的“宽缓沟道型泥石流”。G4218线康定—新都桥段高速公路(以下简称“康新高速”)拟设选线方案都以桥隧形式穿越毛家沟及其支沟磨子沟、野人沟。本文通过现场调查、遥感解译,分析了毛家沟泥石流的孕灾环境和发育特征,基于雨洪修正法,提出了利用GIS、Matlab揭示毛家沟沟道各点动力学特征参数的方法,为康新高速的线路方案选取和灾害防控及川西藏东交通廊道地质灾害防控提供了理论科学依据。
1. 研究区泥石流孕灾环境
1.1 地形地貌
毛家沟位于四川盆地青藏高原东南缘过渡区的川西高原,为大渡河支流折多河右岸支沟,地形切割强烈,高山峡谷地貌,河谷宽缓,山体陡峻(图1)。高程
3201 ~5487 m,最大相对高差2286 m,沟谷岸坡坡度15°~77°主支沟沟口泥石流堆积扇明显,多有挤压主河道现象。毛家沟流域面积144.29 km2,主沟长23.48 km,形态顺直,平均纵坡降75.3‰,共发育14条支沟,其中野人沟和磨子沟流域面积最大,沟道与主沟大角度相交,在下游交汇,流域特征参数见表1。
表 1 毛家沟主、支沟流域特征参数Table 1. Basin characterization parameters of main and branch ditches basins in Maojia gully沟域 流域江水面积/km2 江水沟长/km 平均纵坡降/‰ 毛家沟 144.29 23.48 75.30 磨子沟 20.73 8.18 174.85 野人沟 42.54 11.73 182.50 3#支沟 1.19 1.82 472.79 4#支沟 4.75 3.24 223.86 5#支沟 4.40 2.95 279.51 6#支沟 4.84 3.18 235.62 7#支沟 5.97 3.75 163.83 8#支沟 6.91 4.53 169.08 9#支沟 3.13 1.98 228.49 10#支沟 4.76 2.42 174.81 1-1#支沟 6.56 3.20 155.96 2-1#支沟 5.75 3.69 199.59 2-2#支沟 8.67 3.80 189.96 8-1#支沟 0.68 0.60 381.43 1.2 水源条件
泥石流暴发的主要水源条件是降雨、融雪和冰湖溃决[22]。研究区属青藏高原亚湿润气候区,年平均降雨量约
1100 mm,集中在5~9月,降水强度大,历时短,易形成暴雨型泥石流。上游海拔高,常年积雪,夏季冰雪融水量大,为泥石流起动提供一定水源条件。上游发育一处冰湖,根据遥感解译,现状面积约5.7×104 m2,历史变化不显著,周围无明显冰崩、冰滑坡,溃决可能性较小,形成冰湖溃决型泥石流可能性小。近30年,康定地区由短时强降雨引发泥石流共记录到40次[22],因此,短时暴雨仍是毛家沟泥石流最主要的水源激发条件。1.3 物源储量
流域内主要出露地层为燕山晚期似斑状黑云花岗岩($ {\gamma}_{\text{βn5}}^{\text{3}} $)、上三叠统居里寺组板岩、石英砂岩(T1j)。在多期强烈地震作用下,流域内岩体破碎、风化强烈,滑坡崩塌不良地质现象发育。上游山地冰川发育,冰碛物堆积体分布广泛。构造及冰川活动导致沟内第四系松散堆积物种类丰富,涵盖第四系更新统(${\mathrm{Q}}{\mathrm{p}}^{fgl} $)冰水堆积层,全新统崩坡积层(${\mathrm{Q}}{\mathrm{h}}^{col+dl}$)、冲洪积层(${\mathrm{Q}}{\mathrm{h}}^{al+pl} $)、泥石流堆积层(${\mathrm{Q}}{\mathrm{h}}^{sef} $)和人工填筑层(${\mathrm{Q}}{\mathrm{h}}^{ml} $)等。
根据野外调查及遥感解译,沟域内发育物源主要有5类:崩滑物源、沟道物源、坡面物源、早期冰碛物源、冻融物源。沟域内共发育294处物源,估算物源总静储量2.7×108 m3,动储量7.7×106 m3,典型物源照片见图2。
1.4 泥石流活动历史
根据走访调查,毛家沟主沟四十年来未暴发大规模泥石流,1995年曾暴发山洪。部分支沟沟口堆积扇发育,且沟道侵蚀作用明显,呈泥石流堆积特征,历史暴发泥石流频率较高(图3)。
2. 泥石流动力学特性
泥石流的流量、流速、泥深、整体冲击力等动力学参数是泥石流灾害防控中的重要依据。本文基于雨洪修正法对上述参数计算,流程见图4。
2.1 计算参数
研究区处于川西山地,相对高差200 m以上,故在确定流域产流参数(μ)、汇流参数(m)时,皆采用“川西南山地”分区对应公式。假定暴雨历时1~6 h,暴雨参数选取n2,N是暴雨公式指数,n=1+1.285log(SP/H6P),Ψ是洪峰径流系数,Ψ=1−(1.1μ/SP·$\tau_0^n $)。
泥石流容重(γc)及泥深修正系数(φ)由数量化得分获取,根据《泥石流灾害防治工程勘查规范》(DZ/T0220—2006)[23],对毛家沟、野人沟及磨子沟进行泥石流易发性评价,分别得分84,90,98,为轻度、中度、中度易发,查附录G可知,容重(γc)分别为1.579,1.676,1.621 g/cm3;泥沙修正系数(φ)分别为0.549,0.710,0.611。根据四川省暴雨统计参数图集,研究区所处位置10 min、1 h、6 h、24 h暴雨均值分别为5,9,24,37 mm,变差系数分别为0.55,0.43,0.39,0.38。本文中分别取降雨频率P=5%、2%、1%。
根据调查在毛家沟内发现7处潜在堵塞点,分布位置见图5a,引发堵塞的原因包括支沟泥石流暴发、崩塌滑坡失稳挤压主沟道等,毛家沟、野人沟、磨子沟沟道总体较顺直,河段宽窄较均匀,陡坎、卡口不多;主支沟交角多小于60°,形成区不大集中;河床堵塞情况一般,堵塞系数取值1.5~2.5,沟床糙率系数取值10~20。从上游至下游随堵塞点变多逐步变大。例如,堵溃点D5处沟道左岸发育一处中型崩塌,如图5b,体积约2.5×104m3,沟道内多崩塌碎块石,堵沟较严重,堵塞系数(Dc)取值由1.6变为1.7,沟床糙率系数(M)取值由16变为18;堵溃点D1处主沟沟道受两支沟沟口挤压,如图5c,沟口堆积体体积约9×104m3,沟道堵塞程度较严重,堵塞系数(Dc)取值由1.8变为1.9,沟床糙率系数(M)取值由18变为20。堵塞系数(Dc)、沟床糙率系数(M)沿沟道分段赋值结果见表2。
表 2 堵溃点位置及成因Table 2. The location and cause of the plugging point沟道 堵溃点 距沟口位置/km 堵塞系数 沟床糙率系数 堵塞原因 毛家沟 D1 4.2 1.9 20 磨子沟、野人沟
挤压主沟1.8 18 D2 6.9 左岸崩滑体 1.7 16 D3 9.5 6#、7#支沟
挤压主沟1.6 14 D4 16.2 大块石 1.5 12 野人沟 D5 5.3 1.7 18 左岸崩滑体 1.6 16 D6 8.1 支沟挤压 1.5 14 磨子沟 D7 4.2 1.6 16 支沟挤压 1.5 14 沟道宽度(D)指泥石流行进过程中流经轨迹的宽度,是计算泥石流流速(Vc)的主要控制参数,一般可在现场观察泥石流、洪水痕迹测量获取。定义沟谷宽度(W)为沟道岸坡坡度突增处间距,获取过程如下:选取沟道内一点做垂直于沟道的剖面线,读取剖面线上各点高程,沟道线与剖面线交点即为沟底,高程最低,由此点向剖面线左右两侧,以一定间距x0(由DEM精度确定,本文中取12.5 m)为间隔,计算高差ΔHi及高差增率δi,如式(1)—(3),寻找高差增率(δi)第一次超过50%的地形点,所得左右两侧两点至对岸水平距离平均值为沟谷宽度(W),示意图见图6。此过程可基于DEM数据,利用Python代码库GDAL、Shapely实现。
$$ \mathrm{\Delta}{H}_{{i}}{=H}_{{i+1}}{-H}_{{i}} $$ (1) $$ {\delta}_{{i}}=(\Delta{H}_{{i+}\mathrm{1}}\mathrm{-\Delta}{H}_{{i}})/\Delta{H}_{i} $$ (2) $$ {W}=({W}_{\mathrm{L}}+{W}_{\mathrm{R}})/2 $$ (3) 式中:Hi——岸坡某处海拔高程/m;
ΔHi——间隔x0内岸坡高差/m;
δi——相邻间隔高差增率/m;
WL(R)——左(右)侧δi首次超过50%的地形点至对 岸水平距离/m;
W——泥石流沟谷宽度/m。
毛家沟作为典型“宽缓沟道型泥石流沟”,沟道长,高差大,泥石流暴发不频繁,痕迹不明显,直接测量沟道宽度难度大。因此本文结合遥感影像及现场调查,获取了16处泥石流沟道宽度(表3),与处理DEM数据得到的沟谷宽度对比拟合,得出幂函数拟合关系如式(4),函数曲线见图7。通过拟合公式计算反推得到沟道宽度(D)栅格,进行泥石流流速等参数计算。
表 3 沟道宽度、沟谷宽度统计Table 3. Statistics of the width of the ditch and valley沟道 距沟口距离/km 沟谷宽度/m 沟道宽度/m 毛家沟 1.09 62 37 2.38 99 47 2.99 112 53 4.32 87 45 6.82 110 51 9.23 99 48 11.70 136 62 13.36 87 44 野人沟 0.72 112 53 1.72 150 67 2.84 161 75 4.54 100 45 磨子沟 1.17 112 52 2.37 124 52 2.88 113 56 3.80 137 54 $$ {D}\mathrm{=1.467}{W}^{\mathrm{0.758}},\;{R}^{\mathrm{2}}\mathrm{=0.866} $$ (4) 式中:D——泥石流沟道宽度/m;
W——泥石流沟谷宽度/m。
利用ArcGIS:Hydrology模块提取毛家沟、野人沟、磨子沟流域参数。其中,数字高程数据(DEM)来源于日本ALOS卫星相控阵型L波段合成孔径雷达(PALSAR),精度12.5m。首先利用ArcMAP水文分析模块中的填洼(fill)对DEM数据修正,并使用流向(flow direction)确定流域沟道汇水范围,使用河网链接(stream link)、河网分级(stream order)和河网栅格矢量化(stream to feature)确定毛家沟内汇水沟道,重分类后保留毛家沟主沟、野人沟、磨子沟沟道,之后使用流量(flow accumulation)和栅格字段计算器确定沟道各点的汇水面积(F)、汇水沟长(L)、平均纵坡降(J),流域参数提取流程见图8。
2.2 计算结果
分别计算毛家沟、野人沟、磨子沟降雨频率在P=5%、P=2%、P=1%下的泥石流流量、流速、泥深、整体冲击力等动力学特征参数。结果显示,在不同降雨频率下,毛家沟暴发泥石流的最大峰值流量分别为420,566,676 m3/s;最大流速分别为6.1,5.7,7.2 m/s;最大泥深为2.1,2.3,2.5 m;最大整体冲击力7.4,8.5,9.6 tF/m2;动力学参数最大点均位于毛家沟沟口。
各项动力学参数均呈现由上游到下游数值逐渐增大、在主支沟交汇点陡增两个特点,分析动力学参数变化与潜在堵溃点分布位置关系,以P=1%时为例,毛家沟、磨子沟、野人沟内的泥石流峰值流量随距沟口距离减小而增大,分别在7个潜在堵溃点处陡增20.8%~122.9%,在D1处,流量由293 m3/s陡增至655 m3/s;D3处由193 m3/s陡增至250 m3/s;D5处148 m3/s陡增至198 m3/s(图9)。另外,流量在陡增后,流域和沟道形态变化明显,汇水面积和汇水沟长增加,沟道纵坡降降低,故峰值流量呈现小幅下降的趋势。毛家沟的各项动力学特征参数计算结果见图10 − 13。
3. 泥石流对拟设线路的影响评价
拟建康新高速公路两种比选方案皆以桥隧形式通过毛家沟。K线服务区设于毛家沟下游右岸山坡,通过1#桥以隧道形式穿越毛家沟,通过2#桥进入磨子沟左岸山体,两处大桥桥面最低高程分别为
3447.24 ,3577.40 m。N3线1#大桥设于野人沟沟口,2#桥设于毛家沟、磨子沟与野人沟交汇处上游500 m处,两处大桥桥面最低高程分别为3439.54 ,3574.97 m。考虑10 m的安全高度及泥石流爬高过程中受沟床阻力的影响,分析4处拟设桥位处的泥石流影响高度,其中泥石流爬高∆Hc、影响高度(H)计算公式如式(5)—(6)。K线服务区(1#桥)与N3线1#桥位置重合,取相同的泥石流动力学参数。拟设桥位处各动力学参数见表4。
表 4 拟设桥位处泥石流动力学参数Table 4. Dynamic parameters of debris flow at the proposed bridge site动力学参数 设计频率/% N3线1#桥/K线服务区 N3线2#桥 K线2#桥 泥石流流量/(m3·s−1) 5 124.57 181.58 91.52 2 169.71 247.71 124.28 1 203.71 298.34 148.73 泥石流流速/(m·s−1) 5 4.41 3.05 3.83 2 4.62 3.55 4.43 1 4.78 4.06 4.70 泥石流泥深/m 5 0.48 1.11 0.36 2 0.56 1.20 0.44 1 0.89 1.34 0.51 泥石流整体冲击力/(tF·m−2) 5 6.22 2.60 4.71 2 7.27 3.58 8.08 1 8.20 9.41 9.55 泥石流影响高度/m 5 11.47 11.58 11.11 2 11.65 11.84 11.44 1 12.06 12.18 11.64 注:tF是吨力,为1吨质量产生的力,工程单位制中力的主单位,1 tF=9.8×103 N。 $$ \Delta{H_{\mathrm{c}}}=V_{\mathrm{c}}^{\mathrm{2}}\mathrm{/2}{g} $$ (5) $$ {H}\mathrm={H_{\mathrm{c}}}{+\Delta}{H_{\mathrm{c}}}+{H'} $$ (6) 式中:∆Hc——泥石流爬高/m;
Vc——泥石流流速/(m·s−1);
g——重力加速度/(m·s−2);
H——泥石流影响高度/m;
Hc——泥石流泥深/m;
H'——安全高度,取10 m。
根据线路与沟道相对位置,分析拟设桥面高度与P=1%时的泥石流影响高度(图14—15),泥石流不会直接对桥面直接冲击淤埋,但可能对桥墩产生直接威胁,危害方式包括:(1)裹挟大块石冲击损坏桥墩;(2)堵塞桥涵导致桥墩侧向变形倾斜,影响桥体安全;(3)桥墩基础受冲刷掏蚀导致桥体不均匀沉降。
2种方案均受毛家沟泥石流暴发的威胁,为保证线路运营安全,需建立完善的泥石流预警系统,必要时可根据动力学参数结果采取相应治理措施。此外,为避免增加毛家沟内可启动物源,需加强工程建设弃渣、土石料的安全管理。
4. 结论
(1)毛家沟位于川西藏东交通廊道的高山峡谷地区,流域面积大,地形高差大,沟道长缓,支沟发育,属于典型的“宽缓沟道型泥石流沟”。受构造活动影响,沟内山体风化强烈,岩体破碎,为泥石流发育提供了丰富的物源,同时充足的降雨及冰雪融水为泥石流的起动提供了触发条件。
(2)基于GIS,在研究区DEM栅格数据的基础上,提取了沟道各点的汇水面积(F)、汇水沟长(L)、平均纵坡降(J)、沟谷宽度(W)等流域参数栅格。同时根据统计分析,得到了沟道宽度(D)与沟谷宽度(W)的函数关系(D=1.467W0.758)。
(3)利用Matlab和Python,对获取的流域参数栅格进行矩阵运算,揭示了毛家沟在降雨概率P=5%、2%、1%时的沟道各点的泥石流峰值流量、流速、泥深、整体冲击力。各项动力学参数最大值均出现在毛家沟沟口,流量在堵溃点处陡增20.8%~122.9%。
(4)分析拟设康新高速两种方案4处桥址处的泥石流动力学参数,采用高架桥的方案可避免泥石流对线路的直接冲淤,但桥墩会存在受泥石流冲击损坏的可能。建议合理选取桥基桥墩位置,必要设置治理措施,同时加强工程建设土石材料与弃渣的堆放管理。
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表 1 模型对应原型的表面沉降统计结果
Table 1 Statistical results of surface settlement for the model corresponding to the prototype
值 别 LDS1 LDS2 LDS3 LDS4 LDS5 LDS6 LDS7 原型填土厚度/m 112 112 86.4 67.2 48 32 32 总沉降/mm 2609 2806 2671 1961 1174 284 354 施工期沉降占比/% 77.1 79.1 79.8 75.9 77.3 51.4 77.4 变形倾度/% / LDS1~LDS2 LDS2~LDS3 LDS3~LDS4 LDS4~LDS5 LDS5~LDS6 LDS6~LDS7 0.82 0.53 3.70 4.10 5.56 0.44 表 2 离心模型试验中土压力观测结果
Table 2 Observations of soil pressure during the centrifuge model experiment
测点编号 E1 E2 E4 E5 E6 E7 模型中水平方向距离/cm 20 20 90 20 50 20 对应原型中水平方向距离/m 32 32 144 32 80 32 模型中埋深/cm 10 20 40 60 对应原型中埋深/m 16 32 64 96 计算值/kPa 296 591 591 1183 1183 1774 观测值/kPa 352 564 720 920 1225 1545 -
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