泥石流啟動(dòng)臨界土體含水量及其預(yù)警應(yīng)用

胡凱衡+馬超

基金項(xiàng)目：中國(guó)科學(xué)院重點(diǎn)部署項(xiàng)目(KZZDEW0501)；國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目(41030742)；中國(guó)科學(xué)院水利部成都山地災(zāi)害與環(huán)境研究所青年百人團(tuán)隊(duì)項(xiàng)目(110900K235)

摘要：傳統(tǒng)的泥石流預(yù)警方法多基于前期和實(shí)時(shí)降雨量等間接指標(biāo)，但實(shí)際上直接影響泥石流啟動(dòng)的關(guān)鍵物理參數(shù)是土體含水量，通過(guò)分析土體含水量的變化來(lái)判斷泥石流啟動(dòng)更為直接可靠。首先定義了泥石流啟動(dòng)的臨界土體含水量的概念，然后基于國(guó)內(nèi)外泥石流啟動(dòng)的觀測(cè)試驗(yàn)數(shù)據(jù)，采用逐步回歸分析方法，建立了臨界土體含水量與土體滲透系數(shù)、孔隙度和顆粒曲率系數(shù)的經(jīng)驗(yàn)關(guān)系，進(jìn)而提出一種基于臨界土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法。最后，以云南東川蔣家溝1999年7月16日發(fā)生的一場(chǎng)泥石流為實(shí)例進(jìn)行演算和驗(yàn)證。結(jié)果表明：該方法在可靠性和準(zhǔn)確性上優(yōu)于傳統(tǒng)利用臨界線(xiàn)和暴發(fā)線(xiàn)判別泥石流的預(yù)測(cè)模型。

關(guān)鍵詞：泥石流；預(yù)警；臨界土體含水量；孔隙度；滲透系數(shù)；曲率系數(shù)；降雨

中圖分類(lèi)號(hào)：P642.23文獻(xiàn)標(biāo)志碼：A

Critical Soil Moisture for Debris Flow Initiation and Its Application in Forecasting

HU Kaiheng1,2, MA Chao1,2,3

(1. Key Laboratory of Mountain Hazards and Earth Surface Processes, Chinese Academy of Sciences, Chengdu 610041,

Sichuan, China; 2. Institute of Mountain Hazards and Environment, Chinese Academy of Sciences

and Ministry of Water Resources, Chengdu 610041, Sichuan, China; 3. University of

Chinese Academy of Sciences, Beijing 100049, China)

Abstract: Most of traditional debris flow forecasting methods are based on indirect variables such as antecedent and realtime rainfalls. But the key factor influencing directly the debris flow initiation is soil moisture, which is more reliable for debris flow forecasting. Firstly, the concept of critical soil moisture for debris flow initiation was defined; secondly, based on the experimental and observation data of debris flow initiation at home and abroad, the empirical relationships between critical soil moisture and permeability coefficient, porosity, coefficient of paritcle curvature were obtained by the means of stepwise regression analysis; finally, the forcasting method for debris flow based on critical soil moisture and realtime rainfall was proposed. The method was tested and verified by the debris flow happened at Jiangjiagou of Dongchuan, Yunnan on 16 July, 1999. The results show that the reliability and accuracy of new forcasting method is better than the traditional forecast method for debris flow based on critical line and occurrence line.

Key words: debris flow; forecasting; critical soil moisture; porosity; permeability coefficient; coefficient of curvature; rainfall

0引言

自然界中，泥石流往往由上游溝岸或坡面的固體物質(zhì)失穩(wěn)進(jìn)入溝道，并在溝道水流的動(dòng)力作用下形成。初始形成的泥石流規(guī)模不大，在運(yùn)動(dòng)過(guò)程中通過(guò)侵蝕、裹挾松散物質(zhì)，規(guī)模才逐漸增長(zhǎng)［12］。

一般而言，坡面土體要達(dá)到一定的含水量(體積比，下同)才能啟動(dòng)形成泥石流。坡面土體的含水量是反映泥石流形成的直接參數(shù)。目前常用的前期降雨和當(dāng)期降雨量預(yù)警指標(biāo)，間接體現(xiàn)了降雨使土體含水量增加，抗剪強(qiáng)度和土體穩(wěn)定性降低，從而使泥石流發(fā)生的可能性增大［36］。國(guó)內(nèi)外許多泥石流預(yù)警模型多以“前期有效雨量雨強(qiáng)/雨強(qiáng)歷時(shí)”為基本模式［710］。但是前期有效雨量與流域下墊面特性、巖土體物理特性等有關(guān)，其計(jì)算過(guò)程中涉及的遞減系數(shù)、前期降水衰減系數(shù)等重要常數(shù)的確定需要長(zhǎng)時(shí)間的土體含水量和降雨量觀測(cè)，且不同學(xué)者使用的計(jì)算方法以及得到的結(jié)果可能不一樣［1114］。不同泥石流溝的有效前期雨量衰減規(guī)律也不同。因此，前期降雨量預(yù)警模式存在局地性強(qiáng)、預(yù)警精度不高、參數(shù)不易確定等缺點(diǎn)。

針對(duì)“有效前期雨量雨強(qiáng)/雨強(qiáng)歷時(shí)”預(yù)警模型所存在的不足，筆者通過(guò)分析國(guó)內(nèi)外大量泥石流形成過(guò)程中的土體含水量變化數(shù)據(jù)，直接以土體含水量為預(yù)警指標(biāo)，提出泥石流啟動(dòng)臨界土體含水量的概念和經(jīng)驗(yàn)計(jì)算公式；經(jīng)過(guò)云南東川蔣家溝泥石流觀測(cè)數(shù)據(jù)的驗(yàn)證，所得到的方法和公式可應(yīng)用于泥石流預(yù)警工作中。

1泥石流臨界土體含水量

1.1泥石流形成過(guò)程中土體含水量變化

Cannon等對(duì)美國(guó)加利福利亞、科羅拉多火災(zāi)地區(qū)大量野外土體含水量和泥石流暴發(fā)時(shí)間監(jiān)測(cè)表明，不同深度坡面土體(一般監(jiān)測(cè)最大深度為60 cm)在泥石流暴發(fā)時(shí)的含水量都未達(dá)到飽和［1517］。以加利福尼亞南部桑加布里埃爾山區(qū)2009年發(fā)生的泥石流為例，167 mm的累積雨量共造成7條流域產(chǎn)生泥石流，而流域中的土體含水量卻始終維持在22%，遠(yuǎn)小于飽和度40%［18］。這些地區(qū)的泥石流在較好的地表植被條件下（比如火災(zāi)過(guò)后植被逐漸恢復(fù)后），可由徑流觸發(fā)轉(zhuǎn)變?yōu)榛录ぐl(fā)，1 h激發(fā)雨量也逐漸增大［19］；蔣家溝暴雨泥石流的多年監(jiān)測(cè)也表明：降雨過(guò)程中，雨水在坡面松散土體最大可以下滲60~80 cm，斜坡坡腳位置的土體含水量最大，但是都未超過(guò)孔隙度 ［2021］；一些模型試驗(yàn)結(jié)果也表明，在土體啟動(dòng)時(shí)大部分土體處于未飽和狀態(tài)［2224］。這與傳統(tǒng)認(rèn)識(shí)的泥石流形成理論并不一致，尤其從非飽和土力學(xué)角度來(lái)看，泥石流啟動(dòng)的原因應(yīng)是土體飽和后短歷時(shí)雨強(qiáng)造成孔隙水壓力劇增、有效應(yīng)力下降或喪失。事實(shí)上，降雨過(guò)程中土體含水量空間分布不均勻，垂直深度上土體含水量是非線(xiàn)性關(guān)系。對(duì)孔隙度大、強(qiáng)度低、顆粒間黏結(jié)程度差的坡面松散物源體來(lái)說(shuō)，土體失穩(wěn)不僅僅是由于含水量增加、抗剪強(qiáng)度減小、下滑力增加導(dǎo)致的，土體失穩(wěn)在泥石流形成過(guò)程中只是初步階段也是必不可少的階段，降雨下滲在土體中形成壤中流以及表面形成地表徑流也是非常重要的原因。在一些地區(qū)甚至徑流作用在泥石流形成作用中更是起主導(dǎo)作用。例如，根據(jù)蔣家溝流域坡面徑流和溝道匯流匯集過(guò)程的觀測(cè)，大多是清水變成泥石流體的過(guò)程，在很多情況下，在坡面上就初步形成了小泥石流體或漿體［25］。美國(guó)加利福尼亞南部、科羅拉多地區(qū)火災(zāi)后的泥石流多是流域坡面土體含水量達(dá)到一定值后，由峰值降雨時(shí)段在引發(fā)一定水力條件的坡面徑流激發(fā)形成的［26］。

1.2臨界土體含水量定義和經(jīng)驗(yàn)計(jì)算公式

無(wú)論是土力類(lèi)還是水力類(lèi)的泥石流，暴發(fā)時(shí)刻大多在峰值降雨時(shí)段附近。隨著雨水入滲，土體含水量逐漸增加，當(dāng)含水量達(dá)到某個(gè)臨界值時(shí)，源區(qū)坡面土體達(dá)到極限平衡狀態(tài)，或者坡面土體入滲和失水達(dá)到動(dòng)態(tài)平衡。后續(xù)的降雨強(qiáng)度如果能夠達(dá)到或者超過(guò)滲透率，坡面產(chǎn)生地表徑流而且土體失穩(wěn)下滑，形成最初的泥石流。這一臨界含水量稱(chēng)為泥石流啟動(dòng)的臨界土體含水量。國(guó)內(nèi)外研究中有關(guān)臨界土體含水量的概念已有所涉及。例如，在Brocca等提出的一些降雨徑流模型中，土體水分平衡主要考慮了降雨入滲率、雨強(qiáng)、蒸發(fā)率以及因壤中流和深層土體滲透的土體排水率，臨界土體含水量與飽和度并不一致［27］。楊大文等將遂川江流域?qū)崪y(cè)土體含水量與不同時(shí)間的雨量結(jié)合起來(lái)，建立流域內(nèi)不同點(diǎn)土體飽和度和警戒雨量的關(guān)系［28］。該結(jié)果間接反映了含水量越大，警戒雨量越小。實(shí)測(cè)的土體飽和度中也反映了臨界土體含水量的概念。

通過(guò)對(duì)國(guó)內(nèi)外大量降雨激發(fā)淺表層滑坡、泥石流過(guò)程中土體含水量變化與土體物理參數(shù)的分析（表1），發(fā)現(xiàn)泥石流暴發(fā)時(shí)的土體含水量與土體滲透系數(shù)、孔隙度以及顆粒級(jí)配存在正相關(guān)關(guān)系，用Matlab的Stepwise函數(shù)作交互式逐步回歸分析，得到多重線(xiàn)性關(guān)系式

Wa =-1.12K+0.46n+0.12Cc-0.165(1)

式中：Wa為臨界土體含水量；K為土體滲透系數(shù)；n為土體孔隙度；Cc為土體顆粒的曲率系數(shù)，Cc=d230/(d10d60)，其中d10、d30和d60分別是土體顆粒質(zhì)量累計(jì)含量（質(zhì)量分?jǐn)?shù)，下同）為10%、30%和60%時(shí)的粒徑。

式（1）擬合所用數(shù)據(jù)如表1，判定系數(shù)為0.896 5，調(diào)整判定系數(shù)為0.883，均方根誤差為0.055 6。對(duì)該方程顯著性進(jìn)行F檢驗(yàn)，查表得到F0.05(3,23)值為3028，遠(yuǎn)小于統(tǒng)計(jì)量F值（66.4），因此，回歸公式顯著。

從式(1)可以看出，臨界土體含水量與滲透系數(shù)成負(fù)相關(guān)關(guān)系，與孔隙度和土體顆粒曲率系數(shù)成正相關(guān)關(guān)系。滲透系數(shù)越大，說(shuō)明土體在一定水力梯度下可以很快下滲并在短時(shí)間內(nèi)轉(zhuǎn)化為壤中流。因內(nèi)部壤中流流動(dòng)和深層滲漏的土體排水速度與雨強(qiáng)大小接近時(shí)，土體含水量才達(dá)到臨界值，并短時(shí)間維持在相對(duì)穩(wěn)定的水平。孔隙度越大，說(shuō)明水、氣兩相占據(jù)土體內(nèi)部空間越大。一般而言，在非飽和階段，土體內(nèi)部顆粒之間具有一定的黏聚力和咬合力并使土體具備一定的抗剪強(qiáng)度，從而保持穩(wěn)定。國(guó)內(nèi)外許多研究證明土體啟動(dòng)時(shí)是非飽和的，土體內(nèi)部需要更多的水才能使抗剪強(qiáng)度下降，下滑力增加。因此，臨界土體含水量與孔隙度成正相關(guān)關(guān)系說(shuō)明水分在松散碎屑坡面體穩(wěn)定性中具有重要作用。土體顆粒的曲率系數(shù)反映了土顆粒粒徑分布曲線(xiàn)形態(tài)。從表1中曲率系數(shù)可以看出，泥石流源區(qū)粒徑級(jí)配累計(jì)曲線(xiàn)斜率比較連續(xù)，細(xì)顆粒在泥石流源區(qū)土體仍占很大部分。盡管級(jí)配連續(xù)，但是泥石流源區(qū)土體是不均勻的，存在不連續(xù)粒徑，且均勻系數(shù)變化較大。由此說(shuō)明臨界土體含水量與曲率系數(shù)成正相關(guān)關(guān)系，曲率系數(shù)越大，土體內(nèi)部存在不連續(xù)粒徑，土顆粒間的存水空間越多，臨界土體含水量越大。

另外，式(1)中的3個(gè)變量綜合反映了流域內(nèi)土體的平均最大蓄水量。臨界土體含水量實(shí)際上與平均最大蓄水量物理涵義一致。超過(guò)臨界土體含水量或者平均最大蓄水量的降水將從地表流走，形成地表徑流，并聚集形成足夠水動(dòng)力條件的溝道水流。坡面匯流而來(lái)的初步小規(guī)模泥石流漿體與溝道水流

表1泥石流形成時(shí)的土體含水量、滲透系數(shù)、孔隙度以及曲率系數(shù)

Tab.1Soil Moisture, Permeability Coefficient, Porosity and

Coefficient of Curvature when Debris Flow Formed

編號(hào)WaK/(mm·s-1)nCc

1

2

30.500 00.023 5100.753.333 333

0.590 00.014 4930.763.333 333

0.660 00.004 6670.693.333 333

0.540 00.007 6190.723.333 333

0.480 00.003 7040.763.333 333

0.540 00.005 0720.763.333 333

0.240 00.005 6260.542.000 000

0.133 00.005 6260.450.408 333

0.120 00.010 2600.580.888 889

0.113 00.087 7600.580.888 889

0.124 00.010 2600.580.888 889

0.103 60.087 7600.580.888 889

0.161 80.010 2600.580.888 889

0.152 60.005 6260.450.408 333

0.117 40.010 2600.580.888 889

0.152 90.005 6260.451.125 000

0.326 00.003 8190.691.481 481

0.310 00.003 8190.691.481 481

0.357 00.003 8190.691.481 481

0.237 00.003 8190.691.481 481

0.340 00.003 8190.691.481 481

0.340 00.003 8190.691.481 481

0.352 00.003 8190.691.481 481

0.378 00.003 8190.691.481 481

0.313 00.003 8190.691.481 481

0.347 00.003 8190.691.481 481

0.347 00.003 8190.691.481 481

注：編號(hào)1的數(shù)據(jù)引自文獻(xiàn)［29］；編號(hào)2的數(shù)據(jù)引自文獻(xiàn)［30］；編號(hào)3的數(shù)據(jù)引自文獻(xiàn)［24］。

匯集增大了其中的含沙量和攜帶固體物質(zhì)能力。溝道水流在流經(jīng)泥石流動(dòng)床時(shí)強(qiáng)烈侵蝕固體物質(zhì)并形成泥石流。由于式（1）中的3個(gè)參數(shù)是泥石流源區(qū)土體物理特征值，所以該公式主要針對(duì)泥石流形成區(qū)的土體，尤其是細(xì)顆粒含量多的泥石流物源體。

2基于臨界土體含水量和實(shí)時(shí)降雨的預(yù)警方法

根據(jù)臨界土體含水量的定義以及泥石流預(yù)警模式中有效前期降雨難以精確計(jì)算的問(wèn)題，筆者提出一種基于臨界土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法(圖1)，該方法的具體流程如下。

圖1基于土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法實(shí)施過(guò)程

Fig.1Flow Chart of Debris Flow Forecasting System Based on Critical Soil Moisture and Realtime Rainfall

(1)計(jì)算泥石流啟動(dòng)的臨界土體含水量。根據(jù)泥石流形成區(qū)的巖土體特征，利用式（1）計(jì)算對(duì)應(yīng)臨界土體含水量Wa。

(2)計(jì)算當(dāng)前土體含水量與臨界土體含水量的差值。在得到臨界土體含水量的情況下，通過(guò)土壤含水量傳感器，以太陽(yáng)能板和蓄電池作為電源，運(yùn)用GPRS無(wú)線(xiàn)網(wǎng)絡(luò)信息傳輸和室內(nèi)數(shù)據(jù)接收終端，得到降雨過(guò)程中t時(shí)刻的土體含水量Wt。通過(guò)室內(nèi)數(shù)據(jù)處理系統(tǒng)反復(fù)計(jì)算差值含水量ΔW，其表達(dá)式為

ΔW=Wa-Wt(2)

(3)根據(jù)當(dāng)前雨強(qiáng)計(jì)算達(dá)到臨界土體含水量所需要的時(shí)間T。具體計(jì)算方法為：通過(guò)雨量傳感器，以無(wú)線(xiàn)網(wǎng)絡(luò)方式發(fā)出和接收雨量值，通過(guò)室內(nèi)系統(tǒng)判定t時(shí)刻雨強(qiáng)Rt和土體滲透系數(shù)K的大??；并選擇大于滲透系數(shù)的計(jì)算公式和小于滲透系數(shù)的計(jì)算公式對(duì)達(dá)到臨界土體含水量所需要的時(shí)間進(jìn)行計(jì)算。

T＝(Wa-Wt)/KRt>K

(Wa-Wt)/RtRt≤K(4)

(4)根據(jù)計(jì)算的T值進(jìn)行預(yù)警，并每隔一定時(shí)間重復(fù)第(3)、(4)步直至達(dá)到臨界土體含水量或降雨結(jié)束。

如果T>0，則多通道數(shù)據(jù)反復(fù)確認(rèn)降雨過(guò)程中土體含水量是否達(dá)到臨界土體含水量，并每隔一定時(shí)間(比如10 s)重復(fù)第(2)、(3)步操作內(nèi)容。如果降雨一直持續(xù)且T≤0，那么安排現(xiàn)場(chǎng)查看或發(fā)出泥石流即將發(fā)生的警報(bào)。如果降雨結(jié)束，則停止泥石流預(yù)警。

3實(shí)例分析

筆者利用提出的基于臨界土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法，對(duì)云南東川蔣家溝1999年7月16日泥石流進(jìn)行演算。

3.1臨界土體含水量確定

蔣家溝角礫土密度為1.954 g·cm-3，孔隙度n為0.381 8，滲透系數(shù)k為0.008 07 mm·s-1，d10為0.01 mm，d30為0.25 mm，d60為3 mm，角礫土顆粒級(jí)配曲線(xiàn)的曲率系數(shù)Cc為3.125(圖2)。由此得到蔣家溝泥石流暴發(fā)的臨界土體含水量為401%。陳曉清等在蔣家溝人工降雨激發(fā)滑坡失穩(wěn)形成泥石流的試驗(yàn)中發(fā)現(xiàn)，盡管不同深度的土體含水量不同，但每一組試驗(yàn)中土體含水量最大值都介于45%和35%之間，且土體破壞前的土體含水量大致在40%上下劇烈波動(dòng)［23］。土體在降雨作用下達(dá)到破壞前狀態(tài)，其含水量劇烈變動(dòng)，但是變動(dòng)的幅度基本在40%左右。這與通過(guò)式(1)計(jì)算得到的土體含水量值基本相同。因此，蔣家溝源區(qū)土體含水量接近越該值，泥石流暴發(fā)的可能性就越大。

圖2云南東川蔣家溝角礫土的顆粒級(jí)配曲線(xiàn)

Fig.2Particle Grading Curve of Breccia Soil in Jiangjiagou of Dongchuan, Yunnan

3.2演算過(guò)程

根據(jù)東川泥石流觀測(cè)站提供的降雨數(shù)據(jù)，激發(fā)蔣家溝1999年7月16日泥石流的降雨過(guò)程見(jiàn)圖3。

圖31999年7月16日泥石流暴發(fā)前的降雨過(guò)程和前20 d的雨量過(guò)程

Fig.3Rainfall Processes Before Occurrence of

Debris Flow on 16 July, 1999 and During the 20 Days Before the Debris Flow

(1)計(jì)算差值含水量。初始時(shí)土體含水量為4%，未達(dá)到臨界土體含水量(40.1%)，因此，在此時(shí)沒(méi)有泥石流發(fā)生，差值含水量ΔW為36.1%。

(2)比較雨強(qiáng)、滲透系數(shù)大小并計(jì)算每單位時(shí)間的土體含水量。蔣家溝角礫土的滲透系數(shù)為0008 07 mm·s-1，相當(dāng)于每10 min降雨484 mm，與該溝的始發(fā)雨強(qiáng)（5 mm）非常接近。滲透系數(shù)0008 07 mm·s-1是經(jīng)過(guò)原位滲透試驗(yàn)得到的參數(shù)，即土體達(dá)到穩(wěn)定滲透階段時(shí)的滲透系數(shù)。滲透系數(shù)是隨時(shí)間和土體含水量變化的，但無(wú)論滲透系數(shù)在降雨過(guò)程中如何變化，穩(wěn)定滲透階段的滲透系數(shù)在不同測(cè)試手段下差異不是很大。比如陳寧生等經(jīng)人工降雨試驗(yàn)測(cè)得降雨開(kāi)始時(shí)的土體初始滲透系數(shù)為0009 2 mm·s-1 ［31］，相當(dāng)于每10 min降雨552 mm的等效雨強(qiáng)。

通過(guò)實(shí)際10 min雨量(R10)與滲透系數(shù)的對(duì)比，以單位面積和單位垂直深度的土體作為分析對(duì)象得到每單位10 min末的含水量

Wt=WtΔt+ΔtRAHA(5)

式中：WtΔt為tΔt時(shí)刻(對(duì)應(yīng)t時(shí)刻之初)的土體含水量；t為實(shí)際降雨記錄時(shí)刻；Δt為單位雨量記錄持續(xù)時(shí)間(這里為10 min)；R為雨強(qiáng)；

A為土體面積；ΔtRA為時(shí)間Δt內(nèi)進(jìn)入土體的降水體積；HA為土體的總體積，H為一般含水量傳感器的探針長(zhǎng)度（60 mm)。

(3)根據(jù)筆者提出的預(yù)警方法演算。由于蔣家溝沒(méi)有實(shí)測(cè)的泥石流暴發(fā)過(guò)程土體含水量變化，這里在得到臨界土體含水量、確定基本土體含水量和實(shí)際雨量過(guò)程后，根據(jù)提出的方法具體流程進(jìn)行演算。演算結(jié)果見(jiàn)表2。

表2基于臨界土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法演算過(guò)程

Tab.2Calculation Process by the Forcasting

Method for Debris Flow Based on Critical Soil Moisture and Realtime Rainfall

編號(hào)時(shí)間段R10/mmWtΔtWa-WtΔtT/min

121:50~22:000.50.040 00.361 0433.200 0

222:00~22:101.70.048 30.352 7124.482 4

322:10~22:201.60.076 70.324 3121.612 5

422:20~22:301.10.103 30.297 7162.381 8

522:30~22:400.80.121 70.279 3209.475 0

622:40~22:500.90.135 00.266 0177.333 3

722:50~23:001.30.150 00.251 0115.846 2

823:00~23:102.00.171 70.229 368.790 0

923:10~23:204.40.205 00.196 026.727 3

1023:20~23:301.40.278 30.122 752.585 7

1123:30~23:401.10.301 70.099 354.163 6

1223:40~23:503.00.320 00.081 016.200 0

1323:50~次日00:002.30.370 00.031 08.087 0

14次日00:00~次日00:101.30.408 3<0.000 0<0.000 0

注：次日01:12:34時(shí)刻，監(jiān)測(cè)到泥石流；R10值始終小于滲透系數(shù)。

3.3精度比較

將本文提出的預(yù)警方法與蔣家溝泥石流預(yù)報(bào)臨界線(xiàn)和暴發(fā)線(xiàn)判別式進(jìn)行結(jié)果對(duì)比，得到以下結(jié)果

R10=5.5-0.098(Pa0+h)>0.5 mm(6)

R10=6.9-0.123(Pa0+h)>1.0 mm(7)

式中：Pa0為泥石流暴發(fā)前某一天的指數(shù)；h為泥石流暴發(fā)前的當(dāng)日降雨量。

臨界線(xiàn)式(6)的物理意義是：在10 min雨強(qiáng)大于0.5 mm的降水過(guò)程中，某10 min降水量只要等于5.5-0.098(Pa0+h)，則蔣家溝泥石流就可能暴發(fā)；暴發(fā)線(xiàn)式(7)的物理意義為：在10 min雨強(qiáng)大于1 mm的降水過(guò)程中，某10 min降水量只要等于69-0.123(Pa0+h)，則蔣家溝就會(huì)暴發(fā)泥石流。

利用該次泥石流過(guò)程之前的降雨量過(guò)程和蔣家溝前期雨量計(jì)算公式，得到臨界線(xiàn)和暴發(fā)線(xiàn)10 min雨量分別為2.26、2.86 mm(圖3)。從該次降雨過(guò)程來(lái)看，23:10~23:20時(shí)段4.4 mm的降雨是造成該次泥石流的主要原因。但泥石流暴發(fā)時(shí)并不與該次降雨過(guò)程的峰值雨量時(shí)段重合，滯后近1 h。表1演算結(jié)果表明，該時(shí)段土體含水量并未達(dá)到臨界土體含水量。而泥石流暴發(fā)時(shí)段雨強(qiáng)僅0.9 mm，大于臨界線(xiàn)而小于暴發(fā)線(xiàn)。從達(dá)到臨界土體含水量和泥石流暴發(fā)時(shí)間上來(lái)看，達(dá)到臨界土體含水量和泥石流暴發(fā)之間相差約1 h，而原方法可提前預(yù)警17~200 min［8］。因此，從臨界土體含水量結(jié)合實(shí)時(shí)降雨過(guò)程來(lái)判別泥石流的發(fā)生更準(zhǔn)確。筆者提出的基于臨界土體含水量和實(shí)時(shí)降雨的預(yù)警方法比傳統(tǒng)利用臨界線(xiàn)和暴發(fā)線(xiàn)判別泥石流的物理意義更明確，方法更可靠。

4結(jié)語(yǔ)

（1）在泥石流形成過(guò)程中，一般理論認(rèn)為前期降雨使源區(qū)土體飽和，短歷時(shí)雨強(qiáng)造成飽和后的土體產(chǎn)生高孔隙水壓力使土體失穩(wěn)并轉(zhuǎn)化為泥石流。但是國(guó)內(nèi)外大量泥石流形成過(guò)程監(jiān)測(cè)表明，源區(qū)坡面土體降雨過(guò)程和泥石流形成過(guò)程中土體都未達(dá)到飽和，且土體含水量存在一個(gè)臨界值。由此，本文提出了臨界土體含水量的概念，并通過(guò)擬合國(guó)內(nèi)外野外監(jiān)測(cè)數(shù)據(jù)得到計(jì)算臨界土體含水量的經(jīng)驗(yàn)公式。

（2）基于臨界土體含水量的概念和經(jīng)驗(yàn)公式，發(fā)展了一種基于臨界土體含水量和實(shí)時(shí)降雨的泥石流預(yù)警方法。通過(guò)云南東川蔣家溝1999年7月16日暴發(fā)的泥石流的實(shí)際觀測(cè)資料，對(duì)該方法進(jìn)行了實(shí)例演算。演算結(jié)果表明，該場(chǎng)泥石流暴發(fā)時(shí)刻并未與峰值降雨時(shí)段重合，而是在達(dá)到臨界土體含水量后約1 h。

（3）由于臨界土體含水量計(jì)算公式是經(jīng)驗(yàn)性的，在后續(xù)研究中有必要從土體降雨入滲以及激發(fā)坡面土體失穩(wěn)的物理過(guò)程并結(jié)合泥石流形成區(qū)監(jiān)測(cè)進(jìn)行深入研究，提出更具有物理意義的臨界土體含水量概念，建立以水文學(xué)、水力學(xué)、泥沙運(yùn)動(dòng)學(xué)等為基礎(chǔ)的預(yù)警模型。

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［25］李椷,吳濟(jì)難.云南東川蔣家溝泥石流形成條件的初步分析［C］∥中國(guó)科學(xué)院水利部成都山地災(zāi)害與環(huán)境研究所.泥石流論文集(1).重慶:科學(xué)技術(shù)出版社重慶分社,1981:8792.

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［26］LARSEN I J,MACDONALD L H,BROWN E,et al.Causes of Postfire Runoff and Erosion:Water Repellency,Cover,or Soil Sealing?［J］.Soil Science Society of America Journal,2007,73(4):13931407.

［27］BROCCA L,BARBETTA S,MELONE F,et al.A Continuous Rainfallrunoff Model Derived from Investigations in a Small Experimental Basin［C］∥SCHUMANN S A,HOLKO L.Status and Perspectives of Hydrology in Small Basins.GoslarHahnenklee:IAHS Press,2010:179185.

［28］楊大文,龔偉,劉志雨,等.基于分布式模型土壤含水量評(píng)估的山洪預(yù)警指標(biāo)體系［C］∥中國(guó)水利學(xué)會(huì).中國(guó)水利學(xué)會(huì)2010學(xué)術(shù)年會(huì)論文集:上冊(cè).鄭州:黃河水利出版社,2010:464473.

YANG Dawen,GONG Wei,LIU Zhiyu,et al.An Fooding Forecasting Method Based Distributed Model of Estimating Soil Moisutre［C］∥Chinese Hydraulic Engineering Society.2010 Annual Conference Proceedings of Chinese Hydraulic Engineering Society:The First Volume.Zhengzhou:Yellow River Water Conservancy Press,2010:464473.

［29］GRECO R,GUIDA A,DAMIANO E,et al.Soil Water Content and Suction Monitoring in Model Slopes for Shallow Flowslides Early Warning Applications［J］.Physics and Chemistry of the Earth,Parts A/B/C,2010,35(3/4/5):127136.

［30］COE J A,KINNER D A,GODT J W.Initiation Conditions for Debris Flows Generated by Runoff at Chalk Cliffs,Central Colorado［J］.Geomorphology,2008,96(3/4):270297.

［31］陳寧生,張軍.泥石流源區(qū)弱固結(jié)礫石土的滲透規(guī)律［J］.山地學(xué)報(bào),2001,19(1):169171.

CHEN Ningsheng,ZHANG Jun.The Research of Permeability on Lose Gravelly Soil in Debris Flow Original Area［J］.Journal of Mountain Science,2001,19(1):169171.

CHEN Xiaoqing,CUI Peng,FENG Zili,et al.Artificial Rainfall Experimental Study on Landslide Transition to Debris Flow［J］.Chinese Journal of Rock Mechanics and Engineering,2006,

25(1):106116.

［24］CHAE B G,KIM M I.Suggestion of a Method for Landslide Early Warning Using the Change in the Volumetric Water Content Gradient Due to Rainfall Infiltration［J］.Environmental Earth Sciences,2012,66(7):19731986.

［25］李椷,吳濟(jì)難.云南東川蔣家溝泥石流形成條件的初步分析［C］∥中國(guó)科學(xué)院水利部成都山地災(zāi)害與環(huán)境研究所.泥石流論文集(1).重慶:科學(xué)技術(shù)出版社重慶分社,1981:8792.

LI Jian,WU Jinan.Preliminary Analysis on the Formation Conditions of Debris Flows in Jiangjia Ravine,Dongchuan,Yunnan Province［C］∥Institute of Mountain Hazards and Environment,Chinese Academy of Sciences and Ministry of Water Resources.Proceedings of Debris Flows:The First Volume.Chongqing:Chongqing Branches of Science and Technology Press,1981:8792.

［26］LARSEN I J,MACDONALD L H,BROWN E,et al.Causes of Postfire Runoff and Erosion:Water Repellency,Cover,or Soil Sealing?［J］.Soil Science Society of America Journal,2007,73(4):13931407.

［27］BROCCA L,BARBETTA S,MELONE F,et al.A Continuous Rainfallrunoff Model Derived from Investigations in a Small Experimental Basin［C］∥SCHUMANN S A,HOLKO L.Status and Perspectives of Hydrology in Small Basins.GoslarHahnenklee:IAHS Press,2010:179185.

［28］楊大文,龔偉,劉志雨,等.基于分布式模型土壤含水量評(píng)估的山洪預(yù)警指標(biāo)體系［C］∥中國(guó)水利學(xué)會(huì).中國(guó)水利學(xué)會(huì)2010學(xué)術(shù)年會(huì)論文集:上冊(cè).鄭州:黃河水利出版社,2010:464473.

YANG Dawen,GONG Wei,LIU Zhiyu,et al.An Fooding Forecasting Method Based Distributed Model of Estimating Soil Moisutre［C］∥Chinese Hydraulic Engineering Society.2010 Annual Conference Proceedings of Chinese Hydraulic Engineering Society:The First Volume.Zhengzhou:Yellow River Water Conservancy Press,2010:464473.

［29］GRECO R,GUIDA A,DAMIANO E,et al.Soil Water Content and Suction Monitoring in Model Slopes for Shallow Flowslides Early Warning Applications［J］.Physics and Chemistry of the Earth,Parts A/B/C,2010,35(3/4/5):127136.

［30］COE J A,KINNER D A,GODT J W.Initiation Conditions for Debris Flows Generated by Runoff at Chalk Cliffs,Central Colorado［J］.Geomorphology,2008,96(3/4):270297.

［31］陳寧生,張軍.泥石流源區(qū)弱固結(jié)礫石土的滲透規(guī)律［J］.山地學(xué)報(bào),2001,19(1):169171.

CHEN Ningsheng,ZHANG Jun.The Research of Permeability on Lose Gravelly Soil in Debris Flow Original Area［J］.Journal of Mountain Science,2001,19(1):169171.

CHEN Xiaoqing,CUI Peng,FENG Zili,et al.Artificial Rainfall Experimental Study on Landslide Transition to Debris Flow［J］.Chinese Journal of Rock Mechanics and Engineering,2006,

25(1):106116.

［24］CHAE B G,KIM M I.Suggestion of a Method for Landslide Early Warning Using the Change in the Volumetric Water Content Gradient Due to Rainfall Infiltration［J］.Environmental Earth Sciences,2012,66(7):19731986.

［25］李椷,吳濟(jì)難.云南東川蔣家溝泥石流形成條件的初步分析［C］∥中國(guó)科學(xué)院水利部成都山地災(zāi)害與環(huán)境研究所.泥石流論文集(1).重慶:科學(xué)技術(shù)出版社重慶分社,1981:8792.

LI Jian,WU Jinan.Preliminary Analysis on the Formation Conditions of Debris Flows in Jiangjia Ravine,Dongchuan,Yunnan Province［C］∥Institute of Mountain Hazards and Environment,Chinese Academy of Sciences and Ministry of Water Resources.Proceedings of Debris Flows:The First Volume.Chongqing:Chongqing Branches of Science and Technology Press,1981:8792.

［26］LARSEN I J,MACDONALD L H,BROWN E,et al.Causes of Postfire Runoff and Erosion:Water Repellency,Cover,or Soil Sealing?［J］.Soil Science Society of America Journal,2007,73(4):13931407.

［27］BROCCA L,BARBETTA S,MELONE F,et al.A Continuous Rainfallrunoff Model Derived from Investigations in a Small Experimental Basin［C］∥SCHUMANN S A,HOLKO L.Status and Perspectives of Hydrology in Small Basins.GoslarHahnenklee:IAHS Press,2010:179185.

［28］楊大文,龔偉,劉志雨,等.基于分布式模型土壤含水量評(píng)估的山洪預(yù)警指標(biāo)體系［C］∥中國(guó)水利學(xué)會(huì).中國(guó)水利學(xué)會(huì)2010學(xué)術(shù)年會(huì)論文集:上冊(cè).鄭州:黃河水利出版社,2010:464473.

YANG Dawen,GONG Wei,LIU Zhiyu,et al.An Fooding Forecasting Method Based Distributed Model of Estimating Soil Moisutre［C］∥Chinese Hydraulic Engineering Society.2010 Annual Conference Proceedings of Chinese Hydraulic Engineering Society:The First Volume.Zhengzhou:Yellow River Water Conservancy Press,2010:464473.

［29］GRECO R,GUIDA A,DAMIANO E,et al.Soil Water Content and Suction Monitoring in Model Slopes for Shallow Flowslides Early Warning Applications［J］.Physics and Chemistry of the Earth,Parts A/B/C,2010,35(3/4/5):127136.

［30］COE J A,KINNER D A,GODT J W.Initiation Conditions for Debris Flows Generated by Runoff at Chalk Cliffs,Central Colorado［J］.Geomorphology,2008,96(3/4):270297.

［31］陳寧生,張軍.泥石流源區(qū)弱固結(jié)礫石土的滲透規(guī)律［J］.山地學(xué)報(bào),2001,19(1):169171.

CHEN Ningsheng,ZHANG Jun.The Research of Permeability on Lose Gravelly Soil in Debris Flow Original Area［J］.Journal of Mountain Science,2001,19(1):169171.