金瀏 李平 杜修力
摘 要:已有箍筋約束混凝土軸壓本構(gòu)關(guān)系模型大多未考慮尺寸效應(yīng)的影響,或通過(guò)采用強(qiáng)度折減系數(shù)法來(lái)粗糙反映尺寸的影響。為研究大尺寸箍筋約束混凝土柱軸心受壓性能及尺寸效應(yīng)規(guī)律,根據(jù)已有箍筋約束混凝土圓柱和方柱軸壓破壞試驗(yàn)結(jié)果,分析了體積配箍率、箍筋形式(方箍及圓箍)及試件尺寸對(duì)箍筋約束混凝土應(yīng)力應(yīng)變曲線的影響。考慮體積配箍率及箍筋形式的影響,建立了箍筋約束混凝土峰值應(yīng)變尺寸效應(yīng)公式,并結(jié)合前期箍筋約束混凝土名義軸壓強(qiáng)度(峰值應(yīng)力)尺寸效應(yīng)公式,提出了可考慮尺寸影響的箍筋約束混凝土軸向壓縮全應(yīng)力應(yīng)變關(guān)系模型。與試驗(yàn)及模擬結(jié)果進(jìn)行對(duì)比發(fā)現(xiàn),建立的可考慮強(qiáng)度和峰值應(yīng)變尺寸效應(yīng)的本構(gòu)關(guān)系與已有試驗(yàn)結(jié)果吻合較好,模型計(jì)算曲線與試驗(yàn)曲線接近。
關(guān)鍵詞:約束混凝土;箍筋;尺寸效應(yīng);壓縮強(qiáng)度;應(yīng)力應(yīng)變關(guān)系
中圖分類號(hào):TU375.3 文獻(xiàn)標(biāo)志碼:A 文章編號(hào):2096-6717(2020)01-0081-09
Abstract:Most of the existing constitute models of stirrup-confined concrete do not consider the size effect. A few consider the size effect using a strength reduction coefficient. In order to investigate the mechanical properties and size effect behaviors of the large-sized stirrup-confined RC columns under axial compressive load, the influence of volume stirrup ratio, the arrangement of stirrups as well as the specimen size on stress-strain curves of confined RC columns were analyzed based on the experimental results of the circular and squared concrete columns. The size effect formula of peak strain for stirrup-confined RC columns was established considering the influence of volumetric stirrup ratio and stirrup type. Moreover, combined with the size effect formula of peak stress in the previous study, the stress-strain model considering the size effect for stirrup-confined RC columns was proposed. Through comparison with the experimental and simulation data, it is demonstrated that the size effect formula of peak stress and peak strain showed good consistency with the experimental results, and the stress-strain model provided satisfactory predictions in large-sized stirrup-confined RC columns.
Keywords:confined concrete; stirrup; size effect; compressive strength; stress-strain
約束混凝土力學(xué)性能的研究表明,箍筋的約束作用能夠顯著改善混凝土的強(qiáng)度和延性。學(xué)者們對(duì)箍筋約束混凝土柱軸心受壓性能開(kāi)展了大量研究,并提出了考慮箍筋間距、箍筋形式及混凝土強(qiáng)度等多種參數(shù)影響的本構(gòu)模型。Kent等[1]提出的應(yīng)力應(yīng)變曲線的上升段采用分?jǐn)?shù)方程,下降部分采用線性函數(shù)表示。Saatcioglu等[2]提出的應(yīng)力應(yīng)變模型包括拋物線形式的上升段,線性下降段和等于20%峰值強(qiáng)度的殘余強(qiáng)度。Mander等[3]、Razvi等[4]、Chung等[5]、趙作周等[6]、史慶軒等[7]也分別提出了不同的約束混凝土本構(gòu)模型。然而,上述箍筋約束混凝土應(yīng)力應(yīng)變關(guān)系模型多針對(duì)試件尺寸小于工程中實(shí)際應(yīng)用的構(gòu)件,難以考慮試件尺寸對(duì)混凝土力學(xué)性能的影響。
在證實(shí)混凝土材料存在尺寸效應(yīng)的基礎(chǔ)上[8-12],研究者也對(duì)箍筋約束混凝土構(gòu)件的軸心受壓性能進(jìn)行了試驗(yàn)研究[13-17],結(jié)果表明:箍筋約束混凝土的軸壓強(qiáng)度存在明顯的尺寸效應(yīng),且隨約束作用的增強(qiáng)而減弱。另外,Kim等[13]基于試驗(yàn)提出了箍筋約束混凝土尺寸效應(yīng)公式,并且得出尺寸效應(yīng)的強(qiáng)弱受體積配箍率的影響,即隨著體積配箍率的增加而逐漸減弱,當(dāng)體積配箍率達(dá)到某一臨界值時(shí),混凝土尺寸效應(yīng)將消失。Du等[17]也得出了相同的研究結(jié)論,他們還研究了不同箍筋形式下約束混凝土抗壓強(qiáng)度的尺寸效應(yīng),結(jié)果表明:由于圓形箍筋約束作用較方形箍筋強(qiáng),圓形箍筋約束混凝土柱的尺寸效應(yīng)較弱。實(shí)際上,一些傳統(tǒng)的本構(gòu)模型對(duì)尺寸效應(yīng)已有考慮,如Park等[18]和Legeron等[19]的工作,采用強(qiáng)度折減系數(shù)(如取值為0.85)的方式來(lái)考慮試件尺寸的影響。這是一種粗糙的處理方法,不能科學(xué)地體現(xiàn)構(gòu)件的承載力、變形能力隨尺寸變化而產(chǎn)生的非線性變化特性。宋佳等[20]在Kim等[21]提出的峰值應(yīng)力(強(qiáng)度)尺寸效應(yīng)公式基礎(chǔ)上,建立了可考慮尺寸影響的箍筋約束混凝土軸壓本構(gòu)關(guān)系模型。盡管如此,Kim等[20]的強(qiáng)度模型不能描述箍筋約束作用對(duì)約束混凝土柱軸壓強(qiáng)度尺寸效應(yīng)的定量影響。
近年來(lái),Jin等[22]結(jié)合材料層次經(jīng)典的尺寸效應(yīng)律及箍筋約束作用機(jī)制,建立了約束混凝土柱軸壓強(qiáng)度(峰值應(yīng)力)的半經(jīng)驗(yàn)半理論公式。筆者在該研究工作的基礎(chǔ)上,進(jìn)一步考慮試件尺寸、體積配箍率、箍筋形式對(duì)箍筋約束混凝土峰值壓縮應(yīng)變的定量影響,并建立考慮尺寸影響的箍筋約束混凝土峰值應(yīng)變的計(jì)算公式。進(jìn)而,結(jié)合峰值應(yīng)力(強(qiáng)度)和峰值應(yīng)變計(jì)算公式,建立能考慮尺寸影響的箍筋約束混凝土軸壓應(yīng)力應(yīng)變關(guān)系模型。與現(xiàn)有的考慮尺寸效應(yīng)的箍筋約束混凝土本構(gòu)模型相比,模型中峰值應(yīng)力公式的力學(xué)機(jī)理清晰,能夠定量地描述箍筋率以及結(jié)構(gòu)尺寸對(duì)峰值應(yīng)力及峰值應(yīng)變的影響。
1 箍筋約束混凝土的受壓性能及尺寸效應(yīng)分析
1.1 箍筋約束混凝土軸壓力學(xué)性能
文獻(xiàn)[22-23]在箍筋約束混凝土軸壓破壞試驗(yàn)[17,24]的基礎(chǔ)上,深入開(kāi)展了三維細(xì)觀數(shù)值模擬與研究,考慮了試件尺寸、體積配箍率及箍筋約束形式的影響,分析了箍筋約束混凝土柱軸壓破壞力學(xué)性能及尺寸效應(yīng)規(guī)律,最終建立了能反映箍筋率定量影響的約束混凝土軸壓強(qiáng)度尺寸效應(yīng)半理論半經(jīng)驗(yàn)公式。表1為箍筋約束混凝土圓柱[22]及方柱[23]的試件幾何參數(shù)及部分模擬結(jié)果。試件編號(hào)如Y-0-S、F-0-S中,首字母為箍筋約束形式,“Y”代表圓形,“F”代表方形;0為體積配箍率;“S”、“M”、“L”、“U”分別表示小、中、大、特大4種尺寸,圓柱及方柱的模型尺寸見(jiàn)表1。試件詳細(xì)設(shè)計(jì)參數(shù)見(jiàn)文獻(xiàn)[22-23]。其中,混凝土試件的峰值應(yīng)力σcc定義為
1.2 應(yīng)力應(yīng)變曲線影響因素
1.2.1 試件尺寸 圖1為文獻(xiàn)[22-23]模擬獲得的具有相同體積配箍率、不同試件尺寸的圓形及方形箍筋約束混凝土柱應(yīng)力應(yīng)變曲線。圖1中,方形截面柱所采用的材料參數(shù)(骨料、砂漿及界面過(guò)渡區(qū)等細(xì)觀組分的本構(gòu)模型力學(xué)參數(shù),詳見(jiàn)文獻(xiàn)[22-23])比圓柱大,所以,方柱的峰值強(qiáng)度比圓柱高。由圖1可知,不同尺寸試件的曲線上升段幾乎重合,初始切線模量基本一致,然而峰值應(yīng)力、峰值應(yīng)變以及峰值后軟化曲線有較大差別。隨著試件尺寸增大,約束混凝土柱的峰值應(yīng)力顯著降低,峰值應(yīng)變也有所減小,但變化不明顯。同時(shí),隨著試件尺寸增大,箍筋對(duì)混凝土的約束作用減弱,混凝土試件破壞脆性增強(qiáng),應(yīng)力應(yīng)變曲線下降段越來(lái)越陡。
1.2.2 體積配箍率 圖2為文獻(xiàn)[22-23]模擬獲得的圓形及方形箍筋約束混凝土柱在相同尺寸不同配箍率下的應(yīng)力應(yīng)變曲線。從圖2中可以看出,隨體積配箍率的增大,約束混凝土的峰值應(yīng)力增大,下降段的坡度變緩,試件破壞時(shí)延性有所提高。這是因?yàn)轶w積配箍率的增大,箍筋對(duì)混凝土的約束作用增強(qiáng),混凝土的脆性程度降低。
1.2.3 箍筋約束形式 由圖2中的曲線可知,箍筋約束形式對(duì)約束混凝土的應(yīng)力應(yīng)變曲線有顯著影響。兩種曲線的區(qū)別主要體現(xiàn)在峰值點(diǎn)附近以及曲線的下降段。圓形箍筋約束混凝土柱的峰值點(diǎn)附近曲線比方形箍筋約束試件更加圓滑,沒(méi)有明顯的尖峰。另外,圓形箍筋約束混凝土柱的應(yīng)力應(yīng)變曲線下降段較平緩。這是因?yàn)榉叫喂拷钤谒膫€(gè)角部處的約束力較大,截面邊長(zhǎng)中部的箍筋約束力小,對(duì)混凝土的約束不均勻,而圓形箍筋對(duì)混凝土的約束力分布均勻,約束作用較強(qiáng)。
2 考慮尺寸影響的峰值應(yīng)力和峰值應(yīng)變
2.1 峰值應(yīng)力
文獻(xiàn)[22-23]分別基于圓形和方形箍筋約束混凝土柱軸心受壓試驗(yàn),結(jié)合三維細(xì)觀數(shù)值模擬分析,探討了箍筋的約束作用對(duì)混凝土柱軸壓破壞及尺寸效應(yīng)的影響機(jī)制。歸納總結(jié)出箍筋的約束作用一方面可以提高混凝土的強(qiáng)度,另一方面可以削弱混凝土的尺寸效應(yīng),這兩方面的作用分別由強(qiáng)度提高系數(shù)φ和尺寸效應(yīng)削弱系數(shù)β來(lái)表征。
2.1.3 峰值應(yīng)力公式的驗(yàn)證 為了驗(yàn)證所提出的箍筋約束混凝土峰值應(yīng)力尺寸效應(yīng)計(jì)算公式的準(zhǔn)確性,選取了文獻(xiàn)[16,28-30]中15根圓形箍筋約束混凝土柱試件和36根方形箍筋約束混凝土柱試件,對(duì)試驗(yàn)數(shù)據(jù)進(jìn)行了整理,如表2所示。統(tǒng)計(jì)試件的截面尺寸范圍為200~600 mm,抗壓強(qiáng)度范圍為25~51 MPa,配箍率范圍為0.6%~4.5%。圖5分析了搜集的Mander等[28]、Li等[16]、錢(qián)稼茹等[29]、胡海濤等[30]的試驗(yàn)峰值應(yīng)力值與本文公式計(jì)算值的對(duì)比情況,可以看出,峰值應(yīng)力公式能較好地預(yù)測(cè)約束混凝土的峰值應(yīng)力。此外,關(guān)于圓形箍筋約束混凝土柱的軸壓試驗(yàn)較少,已有的試驗(yàn)數(shù)據(jù)顯示峰值應(yīng)力的計(jì)算值略顯保守??傮w來(lái)說(shuō),所提出的峰值應(yīng)力計(jì)算公式具有較高的精確度。
3.4 模型驗(yàn)證
采用本文模型計(jì)算箍筋約束混凝土的應(yīng)力應(yīng)變曲線,并與文獻(xiàn)[17,22-23]中部分試驗(yàn)及模擬曲線進(jìn)行了比較,如圖8、圖9所示。從圖8、圖9可以看出,不論是箍筋約束混凝土圓柱還是方柱,建議的應(yīng)力應(yīng)變模型與試驗(yàn)及模擬曲線吻合較好,能夠反映不同設(shè)計(jì)參數(shù)的箍筋約束混凝土柱的應(yīng)力應(yīng)變規(guī)律。另外,從圖8(c)、(d)及圖9(c)、(d)可以看出,本文理論模型曲線的軟化下降段與試驗(yàn)曲線還存在差異,這是由于未考慮約束混凝土極限應(yīng)變及破壞應(yīng)變的影響所造成的。
圖10中同時(shí)給出了本文模型對(duì)文獻(xiàn)[22]中試件的預(yù)測(cè)曲線與Mander模型預(yù)測(cè)曲線(未考慮尺寸的影響),可知:本文模型考慮了尺寸的影響,不同尺寸試件的峰值應(yīng)力和峰值應(yīng)變有較大差別。試件尺寸較小時(shí),本文模型與Mander模型相差較小,但隨著試件尺寸的增大,考慮尺寸影響的模型與傳統(tǒng)本構(gòu)模型差別愈發(fā)顯著??傮w來(lái)說(shuō),考慮尺寸影響的軸壓本構(gòu)模型能夠更加準(zhǔn)確地預(yù)測(cè)大尺寸約束混凝土試件的軸壓性能,而未考慮尺寸影響的應(yīng)力應(yīng)變模型高估了大尺寸試件的峰值應(yīng)力和峰值應(yīng)變,這大大降低了工程設(shè)計(jì)的可靠度。
4 結(jié)論
在前期研究的基礎(chǔ)上,分析箍筋約束混凝土柱軸心受壓應(yīng)力應(yīng)變曲線的影響因素,提出了考慮尺寸影響的箍筋約束混凝土本構(gòu)關(guān)系模型,主要結(jié)論如下:
1)試件尺寸是箍筋約束混凝土柱軸壓力學(xué)性能的重要影響因素,隨著試件尺寸的增大,峰值應(yīng)力和峰值應(yīng)變均有減小的趨勢(shì),在建立箍筋約束混凝土本構(gòu)關(guān)系時(shí)應(yīng)考慮試件尺寸的影響。
2)對(duì)箍筋約束混凝土軸壓試驗(yàn)中峰值應(yīng)變數(shù)據(jù)進(jìn)行回歸分析,提出了約束混凝土的峰值應(yīng)變計(jì)算公式,該公式能夠較好地描述試件尺寸及約束比對(duì)峰值應(yīng)變的影響。
3)建立了考慮尺寸影響的箍筋約束混凝土本構(gòu)關(guān)系模型,該模型與試驗(yàn)及模擬曲線吻合較好,能夠較準(zhǔn)確地反映大尺寸試件的應(yīng)力應(yīng)變關(guān)系。
本文僅探討了箍筋率、箍筋形式(方形箍筋及圓形箍筋)和試件尺寸對(duì)約束混凝土軸壓力學(xué)性能的影響,尚未考慮箍筋間距、混凝土強(qiáng)度及長(zhǎng)細(xì)比等因素的影響,后續(xù)仍需對(duì)此進(jìn)行深入的分析。若要提出具有更廣泛適用性的計(jì)算方法,尚需根據(jù)更多參數(shù)的試驗(yàn)數(shù)據(jù)調(diào)整已有模型。
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(編輯 胡玲)