陳陸望,彭智宏,王迎新,葛如濤,李蕊瑞
松散承壓含水層滲透系數(shù)變化規(guī)律與估算模型研究
陳陸望,彭智宏,王迎新,葛如濤,李蕊瑞
(合肥工業(yè)大學(xué) 資源與環(huán)境工程學(xué)院,安徽 合肥 230009)
我國(guó)華北隱伏型煤田的煤系普遍被第四系松散層覆蓋,其中的松散承壓含水層在煤礦生產(chǎn)中常帶來(lái)礦井突水、地表沉降、井筒變形破壞等水文地質(zhì)災(zāi)害,造成巨大經(jīng)濟(jì)損失和人員傷亡。滲透系數(shù)是反映松散承壓含水層土體介質(zhì)滲透能力的重要參數(shù),其數(shù)值的合理估算,對(duì)該類煤礦水文地質(zhì)災(zāi)害的防治具有重要指導(dǎo)意義。目前,華北隱伏型煤田松散承壓含水層滲透系數(shù)往往僅通過(guò)現(xiàn)場(chǎng)抽水試驗(yàn)確定,基于地質(zhì)勘探鉆孔信息與數(shù)據(jù)估算松散承壓含水層滲透系數(shù)的模型研究較少。通過(guò)收集淮北煤田祁東煤礦松散承壓含水層已有抽水試驗(yàn)的鉆孔信息與數(shù)據(jù),選取承壓含水層厚度、泥層砂層比、最厚砂層占比、有效應(yīng)力與底礫層厚比作為影響指標(biāo),分別與滲透系數(shù)進(jìn)行相關(guān)性分析。最終確定底礫層厚比、有效應(yīng)力、泥層砂層比為關(guān)鍵影響指標(biāo),并分析其對(duì)滲透系數(shù)的影響規(guī)律。結(jié)果表明,松散承壓含水層滲透系數(shù)隨底礫層厚比的增加而增大,隨有效應(yīng)力和泥層砂層比的增加而減小。在此基礎(chǔ)上,采用多元線性回歸分析,提出了基于底礫層厚比、有效應(yīng)力、泥層砂層比的滲透系數(shù)估算模型。并將該估算模型應(yīng)用于淮北煤田祁南、朱仙莊、青東煤礦松散承壓含水層的滲透系數(shù)估算,結(jié)果顯示估算結(jié)果與試驗(yàn)值一致。
松散承壓含水層;滲透系數(shù);底礫層厚比;有效應(yīng)力;泥層砂層比;多元線性回歸
我國(guó)華北隱伏型煤田含煤地層普遍被第四系松散層覆蓋,該松散層內(nèi)普遍發(fā)育多層以非膠結(jié)砂土、砂礫、礫石為骨架的承壓含水層,且各含水介質(zhì)各向異性明顯。鄰近松散承壓含水層的煤層開(kāi)采,常發(fā)生礦井突水、地表沉降、井筒變形破壞等煤礦水文地質(zhì)災(zāi)害,造成巨大經(jīng)濟(jì)損失和人員傷亡[1-4]。開(kāi)展此類煤礦水文地質(zhì)災(zāi)害的防治,很大程度上取決于對(duì)該類松散承壓含水層滲透系數(shù)的合理估算。目前,華北隱伏型煤田松散承壓含水層滲透系數(shù)往往僅通過(guò)現(xiàn)場(chǎng)抽水試驗(yàn)確定,且受人力、物力與財(cái)力的限制,能進(jìn)行抽水試驗(yàn)的鉆孔有限,無(wú)法反映研究區(qū)范圍內(nèi)松散承壓含水層現(xiàn)場(chǎng)實(shí)際滲透系數(shù)的變化規(guī)律及其空間效應(yīng)。已有的研究表明,滲透系數(shù)是分析松散含水層各向異性必不可少的參數(shù),若將研究區(qū)內(nèi)整個(gè)含水層滲透系數(shù)作為常值處理,必然會(huì)造成較大誤差,因此,開(kāi)展松散承壓含水層滲透系數(shù)變化規(guī)律的研究具有重要的工程應(yīng)用價(jià)值[5]。
近年來(lái),不少國(guó)內(nèi)外學(xué)者對(duì)土體滲透系數(shù)的變化規(guī)律進(jìn)行了研究。D. W. Taylor[6]指出滲透系數(shù)對(duì)數(shù)值隨孔隙比的變化呈線性關(guān)系;Jiang Xiaowei等[7]用應(yīng)力控制孔隙率來(lái)解釋滲透系數(shù)隨深度衰減的規(guī)律,提出滲透系數(shù)與深度的半經(jīng)驗(yàn)方程;吳婧[8]考慮顆粒級(jí)配和密實(shí)度對(duì)土體孔隙尺寸的影響,提出了基于孔隙尺寸的滲透系數(shù)估算模型;張改玲等[9]研究了同一水力梯度下滲透系數(shù)隨圍壓大小的變化規(guī)律;曾玲玲等[10]提出能反映重塑黏土滲透系數(shù)變化規(guī)律的數(shù)學(xué)模型;劉維正等[11]通過(guò)固結(jié)滲透聯(lián)合試驗(yàn),提出適用于天然沉積飽和黏土滲透系數(shù)預(yù)測(cè)模型。但目前已有的估算模型大都是基于室內(nèi)實(shí)驗(yàn)提出,并不適用于計(jì)算華北隱伏型煤田松散承壓含水層現(xiàn)場(chǎng)實(shí)際滲透系數(shù),且該類松散承壓含水層介質(zhì)組成復(fù)雜、埋深大,室內(nèi)實(shí)驗(yàn)很難再現(xiàn)其實(shí)際的地質(zhì)與環(huán)境。
淮北煤田祁東煤礦在第四系松散承壓含水層下開(kāi)采,煤層頂板突水頻發(fā),如3221、3222、7130等工作面在開(kāi)采過(guò)程中均發(fā)生了大面積突水。根據(jù)礦井水質(zhì)分析表明,突水水源主要來(lái)自松散承壓含水層第四含水層(簡(jiǎn)稱四含)。因此,研究四含的滲透性具有重要的工程應(yīng)用價(jià)值。鑒于此,筆者以淮北煤田祁東煤礦四含為研究對(duì)象,基于淮北煤田祁東煤礦松散承壓含水層大量抽水鉆孔信息與數(shù)據(jù),采用多元線性回歸分析,篩選關(guān)鍵影響指標(biāo),分析其對(duì)滲透系數(shù)的影響規(guī)律,建立松散承壓含水層滲透系數(shù)與關(guān)鍵影響指標(biāo)的估算模型,并開(kāi)展該估算模型的驗(yàn)證分析,為松散承壓含水層滲透系數(shù)的確定提供一種新的科學(xué)有效手段。
祁東煤礦位于典型的華北隱伏型煤田—淮北煤田宿南礦區(qū)境內(nèi)?;幢泵禾锏靥幇不帐”辈?,華北板塊東南緣、郯廬斷裂左側(cè),以宿北斷裂為界分為南北2個(gè)構(gòu)造分區(qū)。主體構(gòu)造線有近EW向和NNE向2組,正、逆斷層主要為NE和NNE方向,褶皺方向則較多變[12-13],如圖1所示?;幢泵禾飪?nèi)煤礦含煤地層普遍被第四系松散層覆蓋,研究區(qū)祁東煤礦在松散承壓含水層下開(kāi)采過(guò)程中曾發(fā)生多次突水事故,具有比較典型的研究和參考價(jià)值。
祁東煤礦以魏廟斷層為界劃分為南北2個(gè)采區(qū)。魏廟斷層以北采區(qū)松散層厚度為330~450 m,魏廟斷層以南采區(qū)松散層厚度為360~440 m[13]。
祁東煤礦松散層厚度變化明顯,自上而下可劃分為4個(gè)含水層(組)及3個(gè)隔水層(組),如圖2所示。第1含水層(簡(jiǎn)稱一含)為近地表的潛水含水層,2—4層含水層(分別簡(jiǎn)稱二含、三含、四含)為承壓含水層[14-15]。其中,四含直接覆蓋在煤系之上,是礦井開(kāi)采的直接充水水源。各含水層巖性多以黏土質(zhì)砂、粉細(xì)砂和中砂為主,垂向上呈交替沉積,一般單層厚度較小,含水層內(nèi)含有黏土夾層。隔水層多由鈣質(zhì)黏土與砂質(zhì)黏土組成,第1、第2隔水層厚度較小,普遍小于25 m,隔水性能一般;第3隔水層厚度大,平均厚度達(dá)80 m,隔水性能強(qiáng)。
現(xiàn)場(chǎng)鉆孔抽水試驗(yàn)確定含水層滲透系數(shù)是野外水文地質(zhì)工作中經(jīng)常采用的較為行之有效的方法之一[16-17]。松散承壓含水層的滲透系數(shù)通常受到含水層結(jié)構(gòu)、土體粒度、圍壓大小的影響。初步選取抽水試驗(yàn)鉆孔所揭示的承壓含水層厚度、泥層砂層比、最厚砂層占比、有效應(yīng)力與底礫層厚比作為研究對(duì)象的影響指標(biāo),從中篩選關(guān)鍵影響指標(biāo),并探討其對(duì)滲透系數(shù)的影響,最后建立相關(guān)計(jì)算公式。為便于計(jì)算,在有效應(yīng)力計(jì)算中,容重統(tǒng)一取15 kN/m3。
此次模型建立選取祁東煤礦部分四含抽水鉆孔影響指標(biāo)數(shù)據(jù),見(jiàn)表1。
表1 祁東煤礦部分四含抽水鉆孔影響指標(biāo)數(shù)據(jù)
為進(jìn)一步明確表1中各指標(biāo)對(duì)滲透系數(shù)的影響程度,對(duì)表1中各抽水鉆孔指標(biāo)數(shù)據(jù)進(jìn)行相關(guān)性分析,分析不同特征指標(biāo)與滲透系數(shù)之間的線性關(guān)系顯著水平,從而可通過(guò)抽水鉆孔指標(biāo)數(shù)據(jù)建立簡(jiǎn)單實(shí)用的預(yù)測(cè)滲透系數(shù)的表達(dá)式。
對(duì)表1中數(shù)據(jù)進(jìn)行整理,底礫層厚比為0.036~ 0.550,承壓含水層厚度為21.31~73.00 m,泥層砂層比為0.042~2.400,最厚砂層占比為0.067~0.548,有效應(yīng)力為1 527.70~2 428.30 kPa。將上述指標(biāo)與滲透系數(shù)進(jìn)行Pearson相關(guān)性分析,結(jié)果見(jiàn)表2,由此可以看出,除底礫層厚比和最厚砂層占比外,其余指標(biāo)與滲透系數(shù)相關(guān)性均不高,且僅底礫層厚比、最厚砂層占比、有效應(yīng)力與滲透系數(shù)顯著性水平小于0.05,呈顯性相關(guān)。
表2 各自變量與因變量K相關(guān)性
因此,為進(jìn)一步研究各指標(biāo)與滲透系數(shù)的相關(guān)性,對(duì)各指標(biāo)進(jìn)行對(duì)數(shù)化處理。選取lg、lg、lg、lg與lg作為自變量,lg作為因變量進(jìn)行相關(guān)性分析,結(jié)果見(jiàn)表3。結(jié)果顯示各自變量與因變量lg的相關(guān)性從大到小排序?yàn)閘g、lg、lg、lg、lg,其中l(wèi)g與lg間的相關(guān)系數(shù)過(guò)小,且顯著性水平大于0.05,線性相關(guān)不顯著。
表3 對(duì)數(shù)化后自變量與因變量lgK的相關(guān)性
當(dāng)一個(gè)因變量被多個(gè)自變量同時(shí)控制時(shí),簡(jiǎn)單的相關(guān)系數(shù)通常不能真實(shí)地反映因變量與各自變量的關(guān)系。因此,為選取適當(dāng)指標(biāo)進(jìn)行回歸分析,還需計(jì)算各自變量與因變量的偏相關(guān)系數(shù)[18]。偏相關(guān)系數(shù)指的是排除其他自變量對(duì)某個(gè)自變量與因變量的影響后,因變量與該自變量的相關(guān)程度,反映自變量與因變量的凈相關(guān)程度[10]。偏相關(guān)系數(shù)絕對(duì)值越大,說(shuō)明該自變量與因變量的凈相關(guān)程度越大。因此,在決定引入哪個(gè)自變量進(jìn)入回歸方程時(shí),應(yīng)以偏相關(guān)系數(shù)的大小作為判斷依據(jù)。選定lg作為因變量,、、、、、lg、lg、lg、lg與lg作為自變量,得到不同自變量與因變量的偏相關(guān)系數(shù)(表4)。
表4 因變量lgK與各自變量偏相關(guān)系數(shù)統(tǒng)計(jì)
結(jié)果表明,以lg作為因變量,lg、lg、lg、lg與lg作為自變量的雙對(duì)數(shù)形式的偏相關(guān)系數(shù)明顯高于、、、與作為自變量的半對(duì)數(shù)形式的偏相關(guān)系數(shù)。因此,將、、、與剔除出線性回歸方程。在對(duì)數(shù)形式的自變量中,凈相關(guān)程度從高到低排列為lg、lg、lg、lg、lg。其中,lg與lg的凈相關(guān)程度最高,lg、lg與lg的凈相關(guān)程度遠(yuǎn)低于其他影響指標(biāo),且回歸系數(shù)檢驗(yàn)得到的相伴概率值Sig.分別為0.249、0.189,均大于0.05,說(shuō)明lg、lg與lg之間不僅凈相關(guān)程度低且線性關(guān)系的顯著性水平也差,應(yīng)剔除出回歸方程。
綜上分析結(jié)果,松散承壓含水層滲透系數(shù)的關(guān)鍵影響指標(biāo)為有效應(yīng)力、底礫層厚比和泥層砂層比,且各自變量與因變量之間采取雙對(duì)數(shù)形式所呈現(xiàn)的線性關(guān)系最為顯著。
淮北煤田四含底部常見(jiàn)含大塊礫石的砂土層(底礫層),受沉積環(huán)境影響,底礫層分布無(wú)序,其中礫石大小懸殊,對(duì)含水層透水性具有顯著影響。王禎偉[19]統(tǒng)計(jì)了淮北煤田四含碎屑粒度與滲透系數(shù)的關(guān)系,得出含水層滲透性由粒度結(jié)構(gòu)決定。李江華等[20]對(duì)多倫煤礦松散砂礫含水層的底礫層分布情況進(jìn)行統(tǒng)計(jì),并采用砂土滲潰性試驗(yàn)裝置對(duì)底礫層滲潰性進(jìn)行研究。
通過(guò)計(jì)算底礫層厚度與松散承壓含水層厚度的比值(底礫層厚比,計(jì)算結(jié)果見(jiàn)表1),可得到底礫層厚比與滲透系數(shù)的關(guān)系(圖3)。
圖3 滲透系數(shù)K與底礫層厚比T的關(guān)系
由圖3可以看出,滲透系數(shù)隨底礫層厚比的增加而增大。
從理論上分析,飽和土體中的滲流場(chǎng)與應(yīng)力場(chǎng)相互作用,相互制約。滲流產(chǎn)生的靜水壓力和動(dòng)水壓力改變滲透介質(zhì)的應(yīng)力狀態(tài),滲透介質(zhì)的透水性也將隨應(yīng)力場(chǎng)的變化而改變。羅曉輝[21]認(rèn)為,土體滲透系數(shù)與有效應(yīng)力和壓縮系數(shù)有關(guān);楊志錫等[22]給出了土體滲透系數(shù)與有效應(yīng)力的分段耦合關(guān)系式。
整理表1數(shù)據(jù),得到松散承壓含水層滲透系數(shù)隨有效應(yīng)力的變化規(guī)律,如圖4所示??梢?jiàn),隨著有效應(yīng)力的增加,滲透系數(shù)總體呈下降趨勢(shì),這是由于有效應(yīng)力越大,一些大孔隙越容易受壓閉合,顆粒間連通性變差,必然會(huì)引起滲透系數(shù)的減小[23-27]。
圖4 滲透系數(shù)K與有效應(yīng)力σ的關(guān)系
松散承壓含水層的組成成分較為復(fù)雜,礫石、黏土、砂質(zhì)亞黏土、含黏土質(zhì)粉砂、細(xì)砂、中砂等交替出現(xiàn)[18],因此,同一含水層各區(qū)域泥層砂層比不盡相同。根據(jù)表1中抽水鉆孔數(shù)據(jù)得到松散承壓含水層各泥層砂層比與滲透系數(shù)的關(guān)系(圖5),總體上滲透系數(shù)隨著泥層砂層比的增加而減小。
圖5 滲透系數(shù)K與泥層砂層比I的關(guān)系
為進(jìn)一步確定松散承壓含水層滲透系數(shù)的各影響指標(biāo)與滲透系數(shù)間的定量關(guān)系,采用多元線性回歸方法,得到各關(guān)鍵影響指標(biāo)與滲透系數(shù)的估算模型。根據(jù)關(guān)鍵影響指標(biāo)分析結(jié)果,將與滲透系數(shù)相關(guān)性最高的lg作為主要自變量,分別與lg和lg進(jìn)行不同組合的多元線性回歸分析,以取得最優(yōu)的估算模型,分析結(jié)果見(jiàn)表5。
由表5可知,當(dāng)模型中l(wèi)g不作為主要自變量,僅以lg、lg作為自變量的回歸方程1相關(guān)系數(shù)最低。僅以lg作為自變量的多元線性回歸方程5,相關(guān)系數(shù)稍低。分別以lg、lg、lg作為自變量的多元線性回歸方程2、方程3與方程4相關(guān)系數(shù)均在0.79以上。此外,同時(shí)考慮lg、lg、lg的多元線性回歸方程4相關(guān)系數(shù)與調(diào)整2均高于其他方程,即其線性擬合程度最高。
利用方程4對(duì)表1中的滲透系數(shù)進(jìn)行估算,將其結(jié)果與抽水試驗(yàn)得到的滲透系數(shù)進(jìn)行對(duì)比,如圖6所示。圖中顯示,方程4估算結(jié)果與抽水試驗(yàn)結(jié)果吻合較好,滲透系數(shù)估算值的上下限分別為試驗(yàn)值的3倍和1/3倍,遠(yuǎn)小于一個(gè)數(shù)量級(jí),這樣的誤差范圍在滲透系數(shù)的估算模型中是可以接受的。因此,松散承壓含水層滲透系數(shù)估算模型為:
表5 多元線性回歸方程、線性系數(shù)及顯著性特征
注:為相關(guān)系數(shù);調(diào)整2為可決系數(shù);為方差檢驗(yàn)量;Sig.為顯著性水平(<0.05);、、、為數(shù)值。
圖6 回歸模型估算值與抽水試驗(yàn)值對(duì)比
lg=0.040+1.186lg–0.964lg–0.468lg(1)
該估算模型說(shuō)明,當(dāng)松散層底礫層厚比和有效應(yīng)力一定時(shí),滲透系數(shù)隨土體泥層砂層比呈指數(shù)遞減關(guān)系;當(dāng)?shù)椎[層厚比和泥層砂層比一定時(shí),滲透系數(shù)隨有效應(yīng)力呈指數(shù)遞減關(guān)系;當(dāng)有效應(yīng)力和泥層砂層比一定時(shí),滲透系數(shù)隨底礫層厚比呈指數(shù)遞增關(guān)系。僅需底礫層厚比、有效應(yīng)力與泥層砂層比,利用式(1)即可較為準(zhǔn)確地估算含水層不同區(qū)域的滲透系數(shù),且這些基本擬合參數(shù)可通過(guò)地質(zhì)勘探鉆孔直接獲得,在實(shí)際工程中具有重要的應(yīng)用價(jià)值。
為驗(yàn)證該模型的正確性與實(shí)用性,整理淮北煤田祁南煤礦、朱仙莊煤礦和青東煤礦部分抽水鉆孔數(shù)據(jù),進(jìn)行滲透系數(shù)估算,結(jié)果見(jiàn)表6。
圖7是滲透系數(shù)估算值與抽水試驗(yàn)值的對(duì)比。結(jié)果顯示,大部分估算值集中于3倍和1/3倍試驗(yàn)值之間,進(jìn)一步論證了該估算模型的正確性與實(shí)用性。
表6 祁南、朱仙莊和青東煤礦部分四含抽水鉆孔影響指標(biāo)數(shù)據(jù)
續(xù)表
圖7 祁南、朱仙莊、青東煤礦滲透系數(shù)估算值與抽水試驗(yàn)值對(duì)比
a.基于祁東煤礦松散承壓含水層抽水鉆孔資料,通過(guò)多元線性回歸分析,明確滲透系數(shù)的關(guān)鍵影響指標(biāo)為底礫層厚比、有效應(yīng)力和泥層砂層比,提出了基于關(guān)鍵影響指標(biāo)的滲透系數(shù)估算模型。
b.滲透系數(shù)隨底礫層厚比的增加而增大,隨有效應(yīng)力和泥層砂層比的增加而減小,且滲透系數(shù)與各影響指標(biāo)之間所呈現(xiàn)的線性關(guān)系以雙對(duì)數(shù)形式最為顯著。
c.將所建模型應(yīng)用于祁南、朱仙莊、青東煤礦,估算其松散承壓含水層的滲透系數(shù),結(jié)果顯示模型估算值與抽水試驗(yàn)值接近,說(shuō)明模型可應(yīng)用于含水層大范圍滲透系數(shù)的確定。
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Variation law and estimation model of permeability coefficient in unconsolidated confined aquifer
CHEN Luwang, PENG Zhihong, WANG Yingxin, GE Rutao, LI Ruirui
(School of Resources and Environmental Engineering,Hefei University of Technology, Hefei 230009,China)
The coal measure strata in the concealed coalfields in North China are generally covered by the Quaternary loose soils. Many hydrogeological hazards, such as mine water inrush, surface subsidence and wellbore deformation failure, have occurred in mining under unconsolidated confined aquifer, which has caused huge economic losses and casualties. The permeability coefficient is an important parameter that reflects the permeability of soil medium in the unconsolidated confined aquifer. A reasonable estimation of its values has important guiding significance for the prevention and control of such hydrogeological hazards. At present, the permeability coefficient of the unconsolidated confined aquifer in the concealed coalfield in North China is often only determined by the pumping test, and there are few models to estimate the permeability coefficient of unconsolidated confined aquifer based on geological exploration borehole information and data. In the paper, the data of the existing pumping test boreholes in the unconsolidated confined aquifer in the Qidong coalmine of the Huaibei Coalfield was collected and the thickness of confined aquifer, the mud-sand ratio, the thickest sand ratio, the effective stress and the thickness ratio of bottom gravel were selected as influencing indices. The thickness ratio of bottom gravel, the effective stress and the mud-sand ratio were determined as the key influencing indices after analyzing the correlation with the permeability coefficient. Therefore, its influence laws on permeability coefficient are analyzed, and the results show that the permeability coefficient of unconsolidated confined aquifer increases with the thickness ratio of bottom gravel, and decreases with the effective stress and the mud-sand ratio. Then, using multiple linear regression analysis, a permeability coefficient estimation model was proposed based on the thickness ratio of bottom gravel, the effective stress and the mud-sand ratio. The estimation model has been successfully estimated the permeability coefficients of the unconsolidated confined aquifer in Qinan, Zhuxianzhuang and Qingdong coalmines of the Huaibei Coalfield, and the estimated results are consistent with the values of pumping test.
unconsolidated confined aquifer; permeability coefficient; thickness ratio of bottom gravel; effective stress; mud-sand ratio; multiple linear regression
移動(dòng)閱讀
語(yǔ)音講解
P641;TD741
A
1001-1986(2021)01-0189-09
2020-10-09;
2020-11-28
國(guó)家自然科學(xué)基金項(xiàng)目(41972256)
陳陸望,1973年生,男,湖北蘄春人,博士,教授,博士生導(dǎo)師,從事煤礦防治水方面的研究. E-mail:luwangchen8888@163.com
陳陸望,彭智宏,王迎新,等. 松散承壓含水層滲透系數(shù)變化規(guī)律與估算模型研究[J]. 煤田地質(zhì)與勘探,2021,49(1):189–197.doi: 10.3969/j.issn.1001-1986.2021.01.020
CHEN Luwang,PENG Zhihong,WANG Yingxin,et al. Variation law and estimation model of permeability coefficient in unconsolidated confined aquifer[J]. Coal Geology & Exploration,2021,49(1):189–197.doi: 10.3969/j.issn.1001- 1986.2021.01.020
(責(zé)任編輯 周建軍)