Predicting the critical drainage induced by soil seepage failure during pumping in foundation pit construction
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摘要:
在地下水水位埋深较浅的基坑施工过程中,常因抽水强度控制不当导致土体渗透破坏引起工程事故,造成人员伤亡及财产损失。目前,已有研究主要针对抽水诱发土体渗透破坏的土层条件、沉降变形预测、施工抽水措施等方面,较少涉及抽水诱发土体渗透破坏的临界抽水量。然而,临界抽水量是基坑施工抽水安全的关键参数,当前无有效的方法计算测试该参数。基于《水电工程钻孔抽水试验规程》(NB/T 35103—2017)推荐的抽水试验渗透系数计算公式,结合达西定理及等价无穷小公式,推导得出潜水非完整孔、潜水完整孔、承压水非完整孔和承压水完整孔4种工况条件下土体渗透破坏的临界抽水量表达式,并引入修正系数对推导的表达式进行修正。结果表明:(1)4种工况下,诱发土体渗透破坏的临界抽水量表达式是关于临界渗透速率的一次函数,说明通过测算场地土体渗透破坏的临界渗透速率可求出临界抽水量;(2)以呼和浩特某基坑为例,场地内最大可能发生抽水渗透破坏的地层为圆砾层,通过室内试验得出它的破坏临界渗透速率为7.1×10−4 m/s。为了确保场地圆砾层不受抽水破坏,设计的潜水完整抽水井SJ1临界抽水量为174.45 m3/d。实际抽水量控制在150 m3/d内未出现渗透破坏现象,说明提出的方法具有可应用性。因此,相比于基坑施工中临界抽水量预测的现有定性经验方法,文章提出的定量计算方法更具有实践应用价值。
Abstract:In the construction of foundation pits with shallow groundwater levels, improper control of pumping strength often leads to soil penetration failure, resulting in engineering accidents, casualties, and property losses. Currently, existing research mainly focuses on soil conditions, settlement deformation prediction, construction pumping measures, etc., and rarely involves the critical pumping quantity. However, the critical pumping quantity is a key parameter for pumping safety in foundation pit construction and there is no effective method to calculate or test this parameter. Based on Darcy’s law and the equivalent infinitesimal formula, and the formula for calculating the permeability coefficient of pumping tests recommended by the specification for borehole pumping test of hydropower projects (NB/T 35103—2017), this study deduced the expressions of critical pumping quantity of the seepage failure under four conditions, including submersible incomplete hole, submersible integral hole, confined water incomplete hole and confined water integral hole. To ensure that the calculated result is more effective, the calculated expression was modified by introducing correction coefficient. The results indicate that the relationship between the critical drawdown volume for inducing soil permeability failure in the four cases and the critical permeability velocity is linear, suggesting that measuring the critical permeability velocity of the soil at the site can determine the critical drawdown volume. In a case study of basement excavation in Hohhot, it is found that the cobble layer has the highest potential for water permeability failure. Laboratory measurements revealed a critical permeability velocity for its failure of 7.1×10−4 m/s. To prevent damage to this layer during pumping, an artesian well SJ1 with a designed critical drawdown volume of 174.45 m3/d was used, and actual pumping volumes were controlled within 150 m3/d without observing any permeability failures, demonstrating applicability of the proposed method. Therefore, compared to existing qualitative experience-based methods for predicting critical drawdown volumes in basement excavation, the quantitative calculation method holds greater practical application value.
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基坑工程中,为了施工安全且方便通常通过抽水将地下水水位降低至施工区域以下。实际施工中若抽水强度过大,容易引发地面沉降变形[1 − 2]、地面塌陷[3]、基坑边坡失稳[4]等工程事故。事故发生的主要原因是抽水导致地下水强径流,从而诱发土体渗透变形破坏 [5 − 7]。
一些学者分析了基坑施工抽水诱发渗透变形的土层条件[8],基于理论分析建立了多种土层变形分析模型[9 − 12],形成了不同的土层沉降计算方法[13 − 15]。为了防范抽水诱发土体渗透变形破坏所引起的工程地质问题,大量工程实践中多采用变形监测、优化抽水方式相结合的技术方案,如粉质砂土层的轻型井点降水法[16]、富水砂层悬挂式止水帷幕降水法[17]、富水厚砂层洞桩降水法[18]、复杂环境超深基坑降水采用“多点排水”“缓慢降水”以及“设置滤层”的多维降水法[19]等。当前,针对抽水诱发土体渗透变形破坏的工程地质问题,已有的理论分析及工程技术措施并未涉及抽水强度,即临界抽水量问题。在具体的场地中,研究抽水强度与土体渗透变形的关系,得出临界抽水量是解决该问题的关键。
关于基坑施工临界抽水量的计算,一些学者在这方面做了尝试,如刁钰等[20]基于天津市十余个典型基坑工程提出井流量计算法、体积计算法和电量推测法3种地下水抽排量估算方法。笔者团队为了防范南宁地铁基坑施工抽水诱发黏土层地面塌陷,推导出潜水非完整孔、承压水非完整孔安全抽水量数学表达式[21 − 22]。然而,实际基坑抽水过程中地下水运动非常复杂,目前无有效的方法计算实际基坑抽水诱发土体渗透破坏的临界抽水量,主要原因是其受抽水地层非均质、过水断面渗透系数差异、地层结构组合条件、地层渗透破坏条件等多种因素的影响。
笔者团队在基坑抽水实践中,发现基于行业标准《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23]推荐的抽水地层渗透系数计算公式以及达西定理和等价无穷小公式,可推导基坑施工抽水诱发土体渗透变形的临界抽水量。本文针对具体的工程场地,计算诱发土体渗透破坏的临界抽水量,解决施工抽水临界抽水量预测问题,这对基坑安全施工具有重要的实际意义。
1. 临界抽水量表达式推导
按照钻孔抽水位置的含水层性质和抽水孔的结构类型划分,土层抽水孔可划分为:潜水非完整孔、潜水完整孔、承压水非完整孔和承压水完整孔。本文采用高等数学常用的等价无穷小公式对4种抽水孔中抽水诱发土体渗透破坏的临界抽水量进行推导。
1.1 潜水非完整孔
《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23]中,潜水非完整孔抽水渗透系数为:
K=0.16Ql(s1−s2)[arshlr1−arshlr2]=0.16Ql(s1−s2)[ln(lr1+√l2r21)−ln(lr2+√l2r22)]=0.16Ql(s1−s2)lnr2(l+√l2+r21)r1(l+√l2+r22) (1) 式中:K——渗透系数/( m·d−1);
Q——抽水孔抽水量/(m3·d−1);
r1——第1个观测孔与抽水孔的距离/m;
r2——第2个观测孔与抽水孔的距离/m;
l——过滤器长度/m;
s1——第1个观测孔的水位降深/m;
s2——第2个观测孔的水位降深/m。
式(1)由巴布什金提出,适用条件为潜水含水层、过滤器在含水层底部,过滤器长度(l)和第2个观测孔与抽水孔距离(r2)均小于0.3倍的含水层厚度(H),即l<0.3H、r2≤0.3H。
假设地下水渗透速率为V,水力坡降为I,依据达西定理V=KI,2个观测孔间的地下水渗流的平均速度(Va)为:
Va=KI=0.16Ql(s1−s2)lnr2(l+√l2+r21)r1(l+√l2+r22)×s1−s2r2−r1=0.16Ql(r2−r1)lnr2(l+√l2+r21)r1(l+√l2+r22) (2) 假设2个观测井无限趋近,则r1无限趋近于r2,数学表达为r1→r2。设2个观测井无限趋近于抽水井,数学表达为r1→r2→r,那么2个观测孔间平均渗流速度(Va)即为距抽水井中心距离为r点的渗透速率(Vr):
Vr=limr1→r2→r0.16Ql(r2−r1)lnr2(l+√l2+r21)r1(l+√l2+r22) (3) 根据高等数学常用的等价无穷小公式,当x→1时,lnx=x−1。式(3)中,r2(l+√l2+r21)r1(l+√l2+r22)→1,因此可得:
Vr=limr1→r2→r0.16Ql(r2−r1)[r2(l+√l2+r21)r1(l+√l2+r22)−1]=limr1→r2→r0.16Ql(r2−r1)[r2(l+√l2+r21)−r1(l+√l2+r22)r1(l+√l2+r22)]=limr1→r2→r0.16Ql(r2−r1)[l(r2−r1)+r2√l2+r21−r1√l2+r22r1(l+√l2+r22)]=limr1→r2→r0.16Ql(r2−r1)[l(r2−r1)+l2(r22−r21)r2√l2+r21+r1√l2+r22r1(l+√l2+r22)]=limr1→r2→r0.16Ql(r2−r1){l(r2−r1)[1+l(r2+r1)r2√l2+r21+r1√l2+r22]r1(l+√l2+r22)}=limr1→r2→r0.16Q[(r2√l2+r21+r1√l2+r22)+l(r2+r1)r2√l2+r21+r1√l2+r22r1(l+√l2+r22)]=0.16Q[2r√l2+r2+2lr2r√l2+r2r(l+√l2+r2)]=0.16Q[√l2+r2+l√l2+r2r(l+√l2+r2)]=0.16Qr√l2+r2 (4) 式(4)中,由于Vr是r的单调递减函数,即当r越小时,渗透速率Vr越大。在抽水井中,井壁处距离抽水中心最近,因此井壁位置达到最大渗透速率(Vmax):
Vmax=0.16Qr0√l2+r20 (5) 式中:r0——孔壁至孔中心的距离/m。
当Vmax等于临界渗透速率(Vcr)时,土体达到渗透破坏的临界条件,可得潜水非完整孔临界抽水量:
Qcr=Vcrr0√l2+r200.16 (6) 式中:Qcr——抽水引起土体渗透破坏的临界抽水量/ (m3·d−1)。
式(6)推导过程中假设了r1→r2→r,因此推导得出的公式与实际情况存在一定偏差。为了与实际情况相符合,引入修正系数(k1),修正后潜水非完整孔临界抽水量为:
Qxcr=k1Vcrr0√l2+r200.16 (7) 式中:Qxcr——修正后的临界抽水量/ (m3·d−1);
k1——潜水非完整孔临界抽水量修正系数,可通 过现场抽水渗透破坏试验确定。
1.2 潜水完整孔
依据《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23],针对使用条件为潜水含水层,裘布依潜水完整孔抽水渗透系数计算公式为:
K=0.732Q(2H−s1−s2)(s1−s2)×lgr2r1 (8) 依据达西定理,2个观测孔间地下水渗流的平均速度为:
Va=KI=0.732Q(2H−s1−s2)(s1−s2)×lgr2r1×s1−s2r2−r1=0.732Q(2H−s1−s2)(r2−r1)×lgr2r1 (9) 假设r1→r2→r,那么2个观测孔水位无限趋近于抽水孔水位降深(s1→s2→s),Va则为距抽水井中心距离为r点的渗透速率Vr:
Vr=lim (10) 式中:s——抽水孔中地下水水位降深/m。
式(10)中,\dfrac{{{r_2}}}{{{r_1}}} \to 1,则{\text{ln}}\dfrac{{{r_2}}}{{{r_1}}}{\text{ = }}\dfrac{{{r_2}}}{{{r_1}}}{{ - }}1,由此可得:
{V_r} = \mathop {{\mathrm{lim}}}\limits_{{r_1} \to {r_2} \to r} \dfrac{{0.16Q}}{{(H - s)({r_2} - {r_1})}} \times \dfrac{{{r_2}-{r_1}}}{{{r_1}}} = \dfrac{{0.16Q}}{{(H - s)r}} (11) 式(11)中,Vr是关于r的单调递减函数,并在井壁处达到最大渗透速率:
{V_{{\text{max}}}} = \dfrac{{0.16Q}}{{(H - s){r_0}}} (12) 当Vmax=Vcr时,土体达到渗透破坏的临界条件,可得潜水完整孔临界抽水量:
Q_{\mathrm{cr}} = \dfrac{V_{\mathrm{cr}}(H - s){r_0}}{{0.16}} (13) 为了与实际情况相符合,引入修正系数(k2),那么修正后潜水完整孔临界抽水量为:
{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_2}{V_{\mathrm{cr}}}(H - s){r_0}}}{{0.16}} (14) 式中:k2——潜水完整孔临界抽水量修正系数,可通过 现场抽水渗透破坏试验确定。
1.3 承压水非完整孔
依据《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23],针对适用条件为承压水含水层和过滤器在含水层顶板、l<0.3M、r2≤0.3M、 r1=0.3r2(M为承压水层厚度),吉林斯基承压水非完整孔抽水渗透系数计算公式为:
K = \dfrac{{0.16Q}}{{l({s_1} - {s_2})}}\left[{\rm{arsh}}\dfrac{l}{{{r_1}}} - {\rm{arsh}}\dfrac{l}{{{r_2}}}\right] (15) 由于式(15)和式(1)函数形式一致,采用潜水非完整孔临界抽水量相同的计算方法,解得距抽水井中心距离为r点的渗透速率为:
{V_r} = \dfrac{{0.16Q}}{{r\sqrt {({l^2} + {r^2})} }} (16) Vr是关于r的单调递减函数,在井壁处达到最大值:
{V_{\mathrm{max}}} = \dfrac{{0.16Q}}{{{r_0}\sqrt {{l^2} + r_0^2} }} (17) 当Vmax=Vcr时,土体达到渗透破坏的临界条件,可得承压水非完整孔临界抽水量:
Q_{{\mathrm{cr}}} = \dfrac{{V_{\mathrm{cr}}}{r_0}\sqrt {{l^2} + r_0^2} }{{0.16}} (18) 承压水非完整孔吉林斯基渗透系数公式适用条件之一为r1=0.3r2。但式(18)推导过程中假设了r1→r2→r,为了与实际情况相符合,引入修正系数(k3),那么修正后承压水非完整孔临界抽水量为:
{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_3}{V_{\mathrm{cr}}}{r_0}\sqrt {{l^2} + r_0^2} }}{{0.16}} (19) 式中:k3——承压水非完整孔临界抽水量修正系数,可 通过现场抽水渗透破坏试验确定。
1.4 承压水完整孔
依据《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23],针对适用条件为承压水含水层、多孔完整井,裘布依承压水完整孔抽水渗透系数计算公式为:
K = \dfrac{{0.366Q}}{{M({s_1} - {s_2})}} \times \lg \dfrac{{{r_2}}}{{{r_1}}} (20) 由于式(20)和式(8)函数形式一致,采用潜水完整孔抽水判据相同的计算方法,解得距抽水井中心距离为r点渗透速率为:
{V_r} = \dfrac{{0.16Q}}{{Mr}} (21) 式(21)中,Vr是关于r的单调递减函数,在井壁处达到最大值:
{V_{\mathrm{max}}} = \dfrac{{0.16Q}}{{M{r_0}}} (22) 当Vmax=Vcr时,土体达到渗透破坏的临界条件,可得承压水完整孔临界抽水量:
Q_{\mathrm{cr}} = \dfrac{{{V_{\mathrm{cr}}}M{r_0}}}{{0.16}} (23) 为了与实际情况相符合,引入修正系数(k4),修正后承压水完整孔临界抽水量为:
{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_4}{V_{\mathrm{cr}}}M{r_0}}}{{0.16}} (24) 式中:k4——承压水完整孔临界抽水量修正系数,可通 过现场抽水渗透破坏试验确定。
2. 实例应用
在4类临界抽水量的推导公式中,除了临界渗透速率外,其余参数均可通过现场监测、勘察、测量等获取,这些参数可认为是已知参数。因此,可以认为上述4种类型的临界抽水量数学表达式均是关于临界渗透速率的一次函数。如果通过试验测算出土体渗透破坏的临界渗透速率,那么代入临界抽水量函数即可算出临界抽水量。基于此思路,以呼和浩特市某地铁车站基坑为例,测算该场地土层破坏的临界渗透速率,并计算设计的抽水井临界抽水量。
2.1 工程概况
呼和浩特市某地铁车站基坑主体长400 m,宽约20 m,结构底板埋深约16.2 m。场地位于大黑河冲湖积平原区。场地土层为:深度0~1.5 m为素填土,1.5~3.3 m为粉土,3.3~5.4 m为粉质黏土,5.4~6.3 m为细砂,6.3~11.5 m为圆砾,11.5~13.4 m为粉土,13.4~15.0 m为粉砂,15.0~17.8 m为粉质黏土(图1)。根据室内渗透试验,各单层的渗透系数见表1。
表 1 土层渗透系数Table 1. Permeability coefficients of rock strata层底
深度/m厚度/
m地层岩性 单层渗透
系数/(m·d−1)1.5 1.5 素填土:褐色,稍密 3.3 1.8 粉土:褐色,稍湿,稍密 0.3 5.4 2.1 粉质黏土:黑褐色,可塑 0.005 6.3 0.9 细砂:黑褐色,潮湿,中密 10 11.5 5.2 圆砾:黄褐色,磨圆度一般,
潮湿至饱和,中密至密实80 13.4 1.9 粉土:褐黄色,潮湿,中密 0.3 15.0 1.6 粉砂:褐黄色,饱和,中密 5 17.8 2.8 粉质黏土:灰色,可塑 0.005 23.8 6.0 中砂:褐黄色,饱和,中密至密实 20 场地地下水主要为第四系土层孔隙水,含水地层主要为圆砾及砂土,厚约13~20 m,富水性较好。地下水水位常年埋深5.3~7.5 m,枯水与丰水期的水位变化幅度小于2.0 m。地下水主要接受大气降水补给,总体流向为从东北流向西南。
2.2 抽水层
该车站基坑开挖底板埋深为16.2 m,位于下部粉质黏土层中(图1)。场地地下水水位常年在圆砾层中波动,基坑施工时,地下水水位埋深需降至基坑底板以下。由于粉质黏土渗透系数很小,通常认为它是隔水层,因此可将地下水水位控制在粉质黏土层内。这说明基坑底部以上施工抽水层是圆砾层、粉土层和粉砂层。
按照设计标高,粉质黏土层(厚2.8 m)需要开挖厚度1.2 m,仅剩下1.6 m厚的薄层。该薄层很可能由于上覆土层的开挖或局部超挖,形成贯通性卸荷裂隙。而粉质黏土下部中砂层为含水层,该含水层的地下水可通过贯通性裂隙流入基坑中,导致工程事故。另外,开挖后的粉质黏土薄层也容易受到底部承压水的作用而发生破坏。因此,为了避免该类型事故发生,基坑开挖施工中基坑底部以下抽水层为中砂层。
2.3 渗透变形试验
为了得到场地内土层的临界渗透破坏条件,进行室内渗透变形试验。采用自行设计的渗透变形试验装置(图2)进行试验,试样高度(L)为15 cm。试验过程为:(1)调节上升板的位置达到预定高度,水管开关处于关闭状态;(2)向水箱中持续注入自来水,待水箱水满后,打开水管开关;(3)水渗入土样流出至烧杯;(4)利用浊度计测试烧杯中水的浊度;(5)观测记录土样上下面观察管的水位差(△h);(6)调节上升板的位置在另一设计高度,重复上述步骤,直至试验结束。
当试样未发生渗透破坏时,烧杯中水的浊度较小,一般小于5 NTU(国家标准)。若试验发生渗透破坏,则烧杯中水的浊度远大于5 NTU。因此,通过渗出水的浊度判断土体是否发生渗透破坏,并取浊度突变前的水力坡降为临界坡降(Icr=Δh /L)。
2.4 临界渗透速率
取基坑施工降水涉及的4个含水层原状样进行渗透破坏试验,试验结果见表2。 根据试验结果计算得到渗透破坏临界水力坡降,圆砾层为0.77,粉土层为3.96,粉砂层为1.43,中砂层为1.03。根据达西定理计算得出破坏的临界渗透速率,圆砾层为7.1×10−4 m/s,粉土层为1.4×10−5 m/s,粉砂层为8.3×10−5 m/s,中砂层为2.4×10−4 m/s。
表 2 场地土体渗透破坏临界渗透速率Table 2. Critical velocity of soil infiltration failure in the site土层 试样
编号破坏时
浊度/NTU临界
水头差/cm平均临界
水力坡降临界
渗透速率/(m·s−1)圆砾 YL1 62 11.2 0.77 7.1×10−4 YL2 46 12.0 YL3 55 11.6 粉土 FT1 123 56.5 3.96 1.4×10−5 FT2 168 60.2 FT3 98 61.6 粉砂 FS1 105 21.7 1.43 8.3×10−5 FS2 67 21.2 FS3 86 21.3 中砂 ZS1 77 16.0 1.03 2.4×10−4 ZS2 42 15.1 ZS3 58 15.4 尽管粉土和粉砂的临界渗透速率小于圆砾,但圆砾优先破坏,主要基于以下原因。
(1)渗透速率与孔隙尺寸大小有关,一般孔隙越大,地下水的渗透速率越快,因此圆砾达到临界速度的条件低于粉土、粉砂。
(2)圆砾层的临界水力坡降小于粉土、粉砂,水力坡降越小越容易破坏。
(3)由于圆砾层渗透系数远大于粉土、粉砂,所抽的水主要来源于圆砾层,这说明含水层中圆砾层优先破坏。
2.5 降水井设计
为了工程施工安全,该基坑主要对粉质黏土上部的潜水层(圆砾层、粉土层、粉砂层)进行抽水及对粉质黏土下部承压水层(中砂层)进行抽水。在施工过程中,将对粉质黏土层上部的影响范围内潜水进行疏干,因此设置一个潜水完整降水井SJ1,其进水的有效过滤器从圆砾层顶部至粉砂层底部(图1)。
由于承压水层抽水的目的是防止过高的水压向上顶破粉质黏土层,因此在中砂层内设置一个降压降水井SJ2,其进水的有效过滤器从粉质黏土底部至中砂层1 m深位置(图1)。
2.6 临界抽水量预测
SJ1井设计直径为325 mm,r0为162.5 mm。抽水前,地下水水位埋深为7.3 m。由于SJ1井中抽取的地下水主要来源于圆砾层,因此仅计算圆砾层的临界抽水量。对于圆砾层,它的潜水含水层厚度(水位以下厚度,H)为4.2 m,临界渗透速率为7.1×10−4 m/s。为了避免抽水速度过快,引起土体有效应力快速增加,导致土体沉降。圆砾层内设计3 次逐步抽水,每次降深(s)1.4 m,相关参数代入式(14)。计算过程中,由于无工程经验,修正系数(k2)取值为1.0,最后计算得出SJ1井中临界抽水量为174.45 m3/d。在实际施工过程中,圆砾层实际抽水量控制在150 m3/d,未出现渗透变形现象,这表明本文的临界抽水量计算值偏安全。
SJ2井抽水是为了降低中砂层承压水位,因此其水位降至粉质黏土底部即可。因此,当SJ2井中水位高于粉质黏土层底部时进行低强度的抽水,否则不抽水。由于SJ2所降水位幅度较小且不常抽水,依据当地工程经验,SJ2井实际抽水量控制在72 m3/d。为了确保SJ2井低强度抽水的安全,在进水过滤器底部采用过滤布包裹防止中砂层颗粒流入,并在该井中粉砂层与粉质黏土层界面上设置止水阀防止上部含水层地下水流入(图1)。直至施工结束,依据SJ2井安全抽水措施,在中砂层抽水过程中未出现砂土颗粒流出。这说明SJ2井安全抽水措施具有可行性。
3. 讨论
基坑抽水常引发边坡失稳、坑内涌水、地面塌陷等灾害,造成工程事故。这些事故由多方面因素引起,其中土体渗透破坏是一个重要的因素。目前,土体渗透破坏条件主要通过水力坡降判断,若达到临界水力坡降值,则发生渗透破坏。
水力坡降临界值测试及计算理论方法较成熟,但场地内水力坡降较难监测。一方面,场地内水力坡降是一个变量值,与距抽水井的距离有关。一般情况下,越靠近抽水井,水力坡降越大,反之亦然。另一方面,场地内通过孔间水位差及其距离比值计算水力坡降。该水力坡降值代表了两孔间土层的平均值,非最大值,而渗透破坏优先在水力坡降最大值处发生。因此,这些原因导致水力坡降作为土体渗透破坏判据,在实际工程中运用存在一定困难。
本文基于《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23]推荐的抽水渗透系数计算公式,运用达西定理,计算抽水条件下任意点的地下水渗透速率。通过数学推导运算,建立了潜水完整孔、非完整孔和承压水完整孔、非完整孔4种抽水方式下诱发渗透破坏的临界抽水流量数学表达式,这些表达式均是关于临界渗透速率的一次函数。因此,只需测算土体渗透破坏的临界渗透速率则可求得临界抽水量值。由于场地内抽水量具有可控性,也可以监测,本文求解的临界抽水量在实践中具有可行性及应用性。
本文求解的临界抽水量表达式中,临界抽水量与孔径大小成正比,这说明孔径越大临界抽水量越大,可见采用大孔径抽水有利于防范土体渗透破坏带来的工程事故。实际上,大孔径管井降水方法是深基坑中应用较为成熟的抽水控制措施,如济南西客站地铁 6号线基坑工程[24],成都地铁2号线东门大桥车站基坑工程[25]、江阴—靖江过江通道长江北岸盾构井基坑工程[26],北京地铁亦庄线次渠南站[27]等均采用大口径管井抽水方案。这些工程实例佐证了本文计算结果在一定程度上符合工程实践。
但是,本文是基于特定理想条件下提出的基坑抽水诱发的土体渗透破坏临界抽水量计算。与实际情况比较,本文计算的结果存在以下不足:(1)直接将2口观测井与抽水井距离取极限,相当于3口井重合,这与实际情况有差距;(2)计算的临界抽水量是基于均质地层,但实际地层多为非均质,如易发生渗透破坏的砂砾层、圆砾层土颗粒差距较大;(3)渗透破坏临界抽水量计算方法是基于单一层,未考虑综合地层对计算结果的影响;(4)临界抽水量计算方法未考虑不同透水层与非透水层的组合条件,未考虑施工等其他因素对土体渗透破坏条件的影响。
以往基坑抽水实践中,技术人员根据经验定性预估某个抽水量,如遇问题再进行调整。尽管本文提出的临界抽水量预测存在一些不足,但相比现有的定性方法,这种定量方法仍然更具有实践参考价值。此外,土体渗透破坏的实际值(N)属于某一个区间范围[a, b],本文的计算值(n)也属于某一个区间范围[c, d],因此实际值和计算值必然存在一个相乘的系数区间[e, f]。这个系数区间值[e, f]可通过大量的工程实践获得。因此,本文提出的计算方法仍然需要大量的工程实践修正其中的不足。
4. 结论
(1)本文基于《水电工程钻孔抽水试验规程》(NB/T 35103—2017)[23]推荐的抽水渗透系数计算公式,运用达西定理,通过数学推导运算,得出潜水非完整孔抽水诱发土体渗透破坏临界抽水量表达式为{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_1}{V_{\mathrm{cr}}}{r_0}\sqrt {{l^2} + r_0^2} }}{{0.16}},潜水完整孔为{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_2}{V_{\mathrm{cr}}}(H - s){r_0}}}{{0.16}},承压水非完整孔为{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_3}{V_{\mathrm{cr}}}{r_0}\sqrt {{l^2} + r_0^2} }}{{0.16}},承压水完整孔为{Q_{{\mathrm{xcr}}}} = \dfrac{{{k_4}{V_{\mathrm{cr}}}M{r_0}}}{{0.16}},其中修正系数可通过现场抽水渗透破坏试验确定。
(2)在4类临界抽水量的推导公式中,除了临界渗透速率外,其余参数均可通过现场监测、勘察、测量等获取。因此,4种类型的临界抽水量数学表达式均是关于临界渗透速率的一次函数,只需测算土体渗透破坏的临界渗透速率,即可求得临界抽水量值。
(3)以呼和浩特某基坑为例,测算场地内不同地层破坏临界渗透速率,圆砾层为7.1×10−4 m/s,粉土层为1.4×10−5 m/s,粉砂层为8.3×10−5 m/s,中砂层为2.4×10−4 m/s,其中最大可能(或优先)发生抽水渗透破坏的地层为圆砾层。
(4)为了确保场地圆砾层不受抽水破坏,设计直径325 mm的潜水完整抽水井SJ1,单次水位降深1.4 m,含水层厚度4.2 m,修正系数取值1.0,计算得出临界抽水量为174.45 m3/d。实际抽水施工中,圆砾层抽水量控制在150 m3/d以内,未出现渗透破坏现象。这说明文章提出的定量计算方法具有应用价值。
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表 1 土层渗透系数
Table 1 Permeability coefficients of rock strata
层底
深度/m厚度/
m地层岩性 单层渗透
系数/(m·d−1)1.5 1.5 素填土:褐色,稍密 3.3 1.8 粉土:褐色,稍湿,稍密 0.3 5.4 2.1 粉质黏土:黑褐色,可塑 0.005 6.3 0.9 细砂:黑褐色,潮湿,中密 10 11.5 5.2 圆砾:黄褐色,磨圆度一般,
潮湿至饱和,中密至密实80 13.4 1.9 粉土:褐黄色,潮湿,中密 0.3 15.0 1.6 粉砂:褐黄色,饱和,中密 5 17.8 2.8 粉质黏土:灰色,可塑 0.005 23.8 6.0 中砂:褐黄色,饱和,中密至密实 20 表 2 场地土体渗透破坏临界渗透速率
Table 2 Critical velocity of soil infiltration failure in the site
土层 试样
编号破坏时
浊度/NTU临界
水头差/cm平均临界
水力坡降临界
渗透速率/(m·s−1)圆砾 YL1 62 11.2 0.77 7.1×10−4 YL2 46 12.0 YL3 55 11.6 粉土 FT1 123 56.5 3.96 1.4×10−5 FT2 168 60.2 FT3 98 61.6 粉砂 FS1 105 21.7 1.43 8.3×10−5 FS2 67 21.2 FS3 86 21.3 中砂 ZS1 77 16.0 1.03 2.4×10−4 ZS2 42 15.1 ZS3 58 15.4 -
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