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圆钢管自应力钢渣增强混凝土柱的受力机制及承载力计算

方圆, 于峰, 张扬, 徐琳, 王旭良

方圆, 于峰, 张扬, 等. 圆钢管自应力钢渣增强混凝土柱的受力机制及承载力计算[J]. 复合材料学报, 2020, 37(5): 1211-1220. DOI: 10.13801/j.cnki.fhclxb.20190916.001
引用本文: 方圆, 于峰, 张扬, 等. 圆钢管自应力钢渣增强混凝土柱的受力机制及承载力计算[J]. 复合材料学报, 2020, 37(5): 1211-1220. DOI: 10.13801/j.cnki.fhclxb.20190916.001
FANG Yuan, YU Feng, ZHANG Yang, et al. Mechanical behavior and bearing capacity calculation of self-stressing steel slag aggregate reinforced concrete filled circular steel tube columns[J]. Acta Materiae Compositae Sinica, 2020, 37(5): 1211-1220. DOI: 10.13801/j.cnki.fhclxb.20190916.001
Citation: FANG Yuan, YU Feng, ZHANG Yang, et al. Mechanical behavior and bearing capacity calculation of self-stressing steel slag aggregate reinforced concrete filled circular steel tube columns[J]. Acta Materiae Compositae Sinica, 2020, 37(5): 1211-1220. DOI: 10.13801/j.cnki.fhclxb.20190916.001

圆钢管自应力钢渣增强混凝土柱的受力机制及承载力计算

基金项目: 国家自然科学基金(51608003;51578001;51878002);安徽省教育厅自然科学基金重大项目(KJ2015ZD10);安徽省重点研究与开发计划(1704a0802131);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016072);住房和城乡建设部科学技术项目(2012-K2-7);安徽省自然科学基金(1208085QE88)
详细信息
    通讯作者:

    于峰,博士,教授,博士生导师,研究方向为新型组合结构、绿色建筑材料、固体废弃物资源化利用、纤维增强复合材料在土木工程中的应用 E-mail:yufeng2007@126.com

  • 中图分类号: TU398.9

Mechanical behavior and bearing capacity calculation of self-stressing steel slag aggregate reinforced concrete filled circular steel tube columns

  • 摘要: 为研究圆钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)柱的受力机制,设计了8根钢渣/混凝土@圆钢管柱进行轴心受压加载试验,其中短柱试件6个,中长柱试件2个。试验考虑钢渣/混凝土膨胀率、径厚比和长径比共3个变化参数。观察试件的受力破坏全过程,获取应力-应变曲线、峰值应力等重要参数,分析各变化参数对钢渣/混凝土@圆钢管轴压柱受力性能的影响。结果表明:钢渣/混凝土@圆钢管轴压短柱的破坏形态表现为中部鼓曲状剪压破坏,而钢渣/混凝土@圆钢管轴压中长柱则呈弯曲屈曲破坏;各试件受力破坏全过程曲线均经历峰值点、下降段、缓慢上升段等历程,与普通钢渣/混凝土相比,各试件的峰值应变和峰值应力明显提高,且钢渣/混凝土@圆钢管轴压短柱试件较钢渣/混凝土@圆钢管轴压中长柱试件提高更为显著。根据极限平衡条件和全过程分析,提出钢渣/混凝土@圆钢管柱承载力计算公式。在试验研究基础上,建立钢渣/混凝土@圆钢管柱的应力-应变关系模型,理论计算结果与试验实测数据吻合较好。研究成果可为钢渣/混凝土@圆钢管柱的进一步研究和工程应用提供参考。
    Abstract: To study the mechanical mechanism of self-stressing steel slag aggregate reinforced concrete filled circular steel tube (steel slag aggregate/concrete@circular steel tube) columns, eight specimens including six short columns and two intermediate length columns were designed for axial compression test, the variable parameters, such as the diameter-thickness ratio, expansion rate of steel slag aggregate concrete and length-diameter ratio were considered. The whole failure process of specimens was observed, and then the strain-stress curves as well as the peak stress was obtained. The influence of variable parameters on the mechanical behavior of self-stressing steel slag aggregate/concrete@circular steel tube columns was analyzed. Test results indicate that the short columns under axial load exhibit shear failure while the intermediate length columns experience global flexural buckling failure mode. The stress-strain curves of all specimens are basically similar, which undergo the peak point, descending section, slow rise section and so on. The peak strain and peak stress of all specimens are significantly increased compared with those of common steel slag aggregate concrete, and the improvement effects are more obvious in short columns than those in intermediate length columns. According to the limit equilibrium condition and entire process analysis, the calculation formula of bearing capacity of self-stressing steel slag aggregate/concrete@circular steel tube columns was proposed, and then the stress-strain model of self-stressing steel slag aggregate/concrete@circular steel tube columns was established depending on the experimental data. The theoretical calculation results are in good agreement with test data. The research results can provide reference for further research and engineering application of self-stressing steel slag aggregate/concrete@circular steel tube columns.
  • 钢渣是炼钢过程中产生的主要废渣,在我国每年有近2 000亿千克的排放量。目前,钢渣的利用率低,大多处于堆积废弃状态,仅有少部分用于矿坑回填和筑路,造成环境污染、资源浪费及土地占用等问题[1-2]。近年来,将钢渣作为掺合料配制钢渣/混凝土,在建筑材料领域得到一定范围的应用。由于钢渣中f-CaO和MgO在水化反应过程中产生膨胀,很大程度上制约钢渣/混凝土在土木工程中的应用。因此,国内外学者围绕如何抑制钢渣膨胀性能(控制体积安定性),对钢渣/混凝土开展大量理论和试验研究,提出钢渣陈化、硅质材料、添加粉煤灰等抑制钢渣膨胀的相关措施[3-8]

    国内外学者对普通钢管混凝土、钢管再生混凝土等进行大量的试验及理论研究[9-14],取得较多成果,并在实际工程中得到较为广泛应用。与普通钢管混凝土和钢管再生混凝土相似,钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)是将钢渣/混凝土灌入钢管内,通过钢管对核心钢渣/混凝土的约束作用,可显著改善钢渣/混凝土@圆钢管的承载力和延性。

    目前,国内学者对钢渣/混凝土@圆钢管研究较少,Beggas等[15]对钢渣/混凝土@钢管试件与普通混凝土@钢管试件的导热情况进行对比分析,结果表明,钢渣/混凝土@钢管试件能有效减少热量损失,导热系数比普通混凝土@钢管试件降低了48%。Ferhoune[16]对结晶碎钢渣/混凝土填充的矩形钢管短柱进行试验研究,主要考虑短柱的高度、核心混凝土组成和偏心情况三个影响因素,结果表明,试件的高度和偏心率对矩形短柱承载力的影响比较明显,结晶碎钢渣/混凝土填充的矩形钢管短柱可在实际工程中得到应用。

    综上所述,国内外对钢渣/混凝土和混凝土@钢管开展了大量研究,取得了丰硕的成果。但对钢渣/混凝土@圆钢管柱受力性能研究较少,无法形成相关计算理论,目前也无规范指导工程实践,严重影响钢渣/混凝土@圆钢管的工程应用。

    本文利用钢渣膨胀性能,合理设计钢渣与混凝土的配比,使钢渣/混凝土产生微膨胀,弥补普通混凝土@钢管紧箍力出现滞后缺陷,确保核心混凝土提前进入三向受压状态,改善混凝土@钢管的工作性能。

    本文开展8根钢渣/混凝土@圆钢管柱的试验研究,分析钢渣膨胀率、径厚比和长径比等因素对钢渣/混凝土@圆钢管柱的破坏形态和受力机制的影响,根据极限平衡条件和全过程分析,提出钢渣/混凝土@圆钢管柱的极限承载力计算公式,并建立钢渣/混凝土@圆钢管柱的应力-应变关系模型。研究成果扩大了钢渣/混凝土的应用范围,实现废弃钢渣再生利用,具有较好的推广应用价值。

    设计8根圆钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)柱试件进行轴心受压试验,考虑钢渣/混凝土膨胀率、径厚比、长径比3个变化参数。其中短柱试件6根,试件高度均为500 mm,分为两个不同的系列,各自的钢渣/混凝土膨胀率分别为2.8×10−4和−3.5×10−4;长柱试件2根,试件高度分别为1 000 mm和1 500 mm。钢管的壁厚分为2.08 mm、3.63 mm、4.22 mm。所有的钢渣/混凝土均采用相同的配比,水泥∶水∶天然粗骨料∶细骨料=1∶0.55∶2.63∶1.70,细骨料采用不同粒径组成的钢渣,保持水泥、天然粗骨料、自来水完全相同,在细骨料质量不变的前提下改变钢渣的粒径组成情况以获得不同膨胀率的钢渣/混凝土。文献[17-18]给出上述两种可控膨胀率的钢渣/混凝土的具体配置情况。表1为钢渣/混凝土组分含量及实测强度。各试件的设计参数和材料性能如表2所示。不同钢渣粒径情况下钢渣/混凝土的膨胀率为一正一负,这主要是由于细粒径钢渣的比表面积大,其晶体结构及钢渣表面的物理化学性质与粗粒径钢渣不同,晶格更容易发生重结晶,水分子更容易进入钢渣内部,且f-CaO分为单一相CaO和固溶体相,单一相CaO在常温下24 h可以完全水化成Ca(OH)2,而固溶体相需要100℃煮沸3 h才可以部分水化成Ca(OH)2,细粒径钢渣中单一相CaO含量高,固溶体相含量低,生成Ca(OH)2和Mg(OH)2的摩尔体积大于水化反应时失水的摩尔体积[19-20]

    表  1  钢渣/混凝土组分含量及实测强度
    Table  1.  Proportion and measured strength of steel slag/concrete
    Particle size of
    steel slag/mm
    Sand
    ratio/%
    Material usage/(kg.m−3)Cube compressive strength/MPaExpansion rate/10−4
    Tap
    water
    CementCoarse aggregate
    (gravel)
    Fine aggregate
    (sand)
    Fine aggregate
    (steel slag)
    1.18–2.360201365961062134.29−3.5
    0.15–0.3(75%)+
    0.3–0.6(25%)
    0201365961062121.85 2.8
    下载: 导出CSV 
    | 显示表格
    表  2  圆钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)柱试件相关参数及实测强度
    Table  2.  Parameters and test strength of steel slag aggregate reinforced concrete filled circular steel tube columns (steel slag aggregate/ concrete@ circular steel tube) column samples
    SamplePct/10−4L/mmD/mmts/mmL/Dfsy/MPafsu/MPafco/MPaθNae/kNσmax/MPaεamaxεcmax
    12.85001402.083.5717631217.500.5862540.6−0.01250.0082
    2−3.55001402.083.5717631227.440.4873747.9−0.01190.0069
    32.85001403.633.5723329617.501.231 01666.0−0.01470.0091
    4−3.55001403.633.5723329627.441.141 14774.5−0.01340.0079
    52.85001404.223.5723630117.501.421 12372.9−0.01580.0103
    6−3.55001404.223.5723630127.441.361 22379.4−0.01510.0095
    72.81 0001403.637.1423329617.501.2385855.7−0.01230.0082
    82.81 5001403.6310.7123329617.501.2379951.9−0.01010.0070
    Notes: Pct—Expansion rate of steel slag aggregate concrete; D,ts—Outer diameter and thickness of steel tube, respectively; L—Height of specimen; fsy, fsu—Yield and ultimate strength of steel tube, respectively; fco—Compressive strength of steel slag aggregate concrete; Nae—Measured ultimate strength of column; θ—Confinement coefficient, θ=AsfsyμfcoAc; σmax—Ultimate stress of column; εamax—Ultimate axial strain of column; εcmax—Ultimate circumferential strain of column.
    下载: 导出CSV 
    | 显示表格

    试验在安徽工业大学结构与抗震实验室进行,采用500 t液压式长柱试验机进行单调静力加载,采用荷载和位移混合控制的加载制度,先进行荷载控制加载,然后转为位移控制加载。

    图1为钢渣/混凝土@圆钢管柱的破坏形态。可知,钢渣/混凝土@圆钢管柱的破坏过程大致经历弹性、弹塑性和塑性3个阶段。当荷载加载至0.5 N之前,试件基本处于弹性工作阶段,此阶段荷载和位移呈线性关系,加载试件的外观保持完好,试件采用荷载控制加载;随着荷载继续增加,钢管表面浮锈逐渐脱落,直至极限荷载的70%~80%时,钢管局部出现屈服,试件进入塑性阶段,此时转为位移控制加载;试件达到峰值荷载后,继续位移加载,当荷载下降至极限荷载的90%左右时,发现钢管局部屈曲,继续加载直至试件破坏过程中,钢渣/混凝土@圆钢管柱试件基本没有新的鼓曲环出现,相比而言,加载后期膨胀率高的试件出现的鼓曲环较多,大部分出现2~3个鼓曲环(如试件1、试件3、试件8),个别试件出现4个鼓曲环(如试件5和试件7),短柱试件鼓曲环基本上出现在端部或中部位置处,而中长柱则出现在顶端附近及中上部位置处(如试件7);最终短柱试件因轴向压缩变形过大而发生中部鼓曲状剪压破坏,而中长柱则呈弯曲屈曲破坏。

    图  1  钢渣/混凝土@圆钢管柱的破坏形态
    Figure  1.  Failure modes of steel slag aggregate/concrete@circular steel tube columns

    结合长柱试验机自动采集的各试件受力全过程荷载-位移曲线数据和静态数据采集仪TDS - 530采集到的应变和位移数据,绘出各试件的应力-应变(轴向和环向应变)曲线,如图2所示,其中εaaεal分别为钢渣/混凝土@圆钢管柱轴向和环向应变。

    图  2  钢渣/混凝土@圆钢管柱的应力-应变曲线
    Figure  2.  Stress-strain curves of self-stressing steel slag aggregate/concrete@circular steel tube columns

    可以看出,钢渣/混凝土@圆钢管柱各试件的轴向和环向应力-应变曲线的变化趋势基本相似,曲线经历弹性阶段、弹塑性阶段和塑性阶段。加载初期,膨胀率对钢渣/混凝土@圆钢管柱试件的应力-应变曲线上升段影响不明显,不同膨胀率试件的应力-应变曲线几乎重合,但相比而言,膨胀率大的试件弹性工作阶段较长,这主要是由于在自应力作用下,核心钢渣/混凝土提前进入三向应力状态,抑制钢渣/混凝土微裂缝的过早开展,增强钢渣/混凝土的早期刚度。随着径厚比的增大,钢渣/混凝土@圆钢管柱轴压试件弹性工作阶段变短,这主要是由于径厚比越大,钢管壁厚相对越小,钢管对核心钢渣/混凝土的约束作用越弱,核心钢渣/混凝土越容易产生裂缝。钢渣/混凝土@圆钢管柱试件屈服之后,试件应力缓慢增长,径厚比和长径比越大,试件应变增长速度越快,但极限荷载点对应的应变值随径厚比的影响不明显。与钢渣/混凝土@圆钢管短柱相比,钢渣/混凝土@圆钢管中长柱的弹性工作阶段较短,屈服应变和极限应变值也较小。

    表2为钢渣/混凝土@圆钢管柱各试件的峰值应力和峰值应变。可知,径厚比分别为67.3、38.6、33.2的钢渣/混凝土@圆钢管柱试件的峰值应力均值分别为44.3 MPa、70.3 MPa、76.2 MPa,所对应的轴向峰值应变均值分别为−0.0122、−0.0141、−0.0155,环向峰值应变均值分别为0.0076、0.0085、0.0099;长径比分别为3.57、7.14、10.71的钢渣/混凝土@圆钢管柱试件的峰值应力值分别为66.0 MPa、55.7 MPa、51.9 MPa,所对应的轴向峰值应变值分别为−0.0147、−0.0123、−0.0101,环向峰值应变分别为0.0091、0.0082、0.0070。钢渣/混凝土@圆钢管柱试件的峰值应力和峰值应变均远大于同强度等级的钢渣/混凝土试件[17-18],且钢渣/混凝土@圆钢管轴压短柱试件较中长柱试件的的峰值应力和峰值应变提高更为显著,可见钢管对钢渣/混凝土的约束效应明显。在膨胀率和长径比相同的情况下,随着径厚比的减小,钢渣/混凝土@圆钢管柱试件的峰值应力和峰值应变(轴向和环向)均有所提高;对于膨胀率和径厚比相同的钢渣/混凝土@圆钢管柱试件,随着长径比的增大,试件的峰值应力和峰值应变(轴向和环向)均呈减小趋势;膨胀率对钢渣/混凝土@圆钢管柱的破坏机制有影响但不明显,随着膨胀率的增大,试件的峰值应力和峰值应变略有减小。

    钢管内核心钢渣/混凝土处于三向受压状态,考虑其自应力对钢渣/混凝土@圆钢管柱承载力的影响,将自应力对试件承载力的提高等效为核心钢渣/混凝土轴压强度的提高,引入钢渣/混凝土强度增强系数μ,核心钢渣/混凝土的等效轴心抗压强度计算如下:

    fck=fco+Kσ0=(1+Kσ0fco)fco=μfco (1)
    σ0=Ec(PctPcr) (2)

    式中:fck为三向受压钢渣混凝土等效抗压强度;K为试验实测确定的侧压系数;σ0为钢渣混凝土与钢管之间产生的自应力;Pcr为钢渣混凝土限制膨胀率。

    由于不受变形过程的影响,因此可采用极限平衡法对钢渣/混凝土@圆钢管柱的极限承载力进行分析计算。同时,考虑圆钢管内的核心钢渣/混凝土不服从正交流动法则,属假塑性元件,可采用静力法求解。图3为钢渣/混凝土@圆钢管柱的圆钢管和核心钢渣/混凝土受力简图,根据极限平衡静力条件可得:

    图  3  钢渣/混凝土@圆钢管柱受力简图
    Figure  3.  Force diagram of steel slag aggregate/concrete@circular steel tube column
    Na=Acσc+Asσs (3)
    σl=prc/ts=2pAc/As (4)
    σc=μfco+4.0p (5)

    式中:Na为轴压钢渣/混凝土@圆钢管短柱承载力;σs为钢管纵向应力;σc为钢管约束作用下钢渣/混凝土抗压强度;σ1为环向应力;AcAs分别为核心混凝土和钢管的截面积。假定钢管是理想弹塑性材料,服从Von Mises屈服准则,可得:

    σs2+σsσl+σl2=fsy2 (6)

    将式(4)及式(6)联合求解得:

    σs=[13θ2(pμfco)21θpμfco]fsy (7)

    钢渣/混凝土@圆钢管柱的极限承载力由钢管的承载力和核心钢渣/混凝土的承载力共同组成,将式(5)和式(7)代入式(3),可得:

    Na=μfcoAc[1+3pμfco+θ23(pμfco)2] (8)

    为求钢渣/混凝土@圆钢管短柱的极限承载力,对式(8)求导,并取dNa/dp=0,可得:

    pμfco=12θ (9)

    将式(9)代入式(8),可得:

    Na=μfcoAc(1+2θ) (10)

    表3为钢渣/混凝土@圆钢管短柱极限承载力的计算值与试验值的对比。可以看出,钢渣/混凝土@圆钢管短柱极限承载力计算值与试验值的比值均在10%范围内变化,均值为0.953,标准差为0.054,变异系数为0.0567。结果表明,基于极限平衡条件分析提出的钢渣/混凝土@圆钢管柱极限承载力计算公式的计算理论值与试验值吻合较好。

    表  3  钢渣/混凝土@圆钢管轴压短柱承载力试验值与计算值比较
    Table  3.  Comparison of calculated values and test data of self-stressing steel slag aggregate/concrete@circular steel tube short columns under axial load
    SpecimenD/tsL/DPct/10–4Na/kNNae/kNNa/NaeNa/Nae
    AveragevalueStandard deviationVariation coefficient
    167.303.57 2.8 590.56250.94480.9530.0540.0567
    267.303.57−3.5 650.47370.8825
    338.563.57 2.81 018.41 0161.0024
    438.563.57−3.51 042.81 1470.9092
    533.173.57 2.81 151.31 1231.0252
    633.173.57−3.51 164.81 2230.9524
    下载: 导出CSV 
    | 显示表格

    基于文献[21]基础,依据组合切线模量理论,采用修正的欧拉公式,考虑钢渣/混凝土与钢管之间自应力的影响,钢渣/混凝土@圆钢管轴压中长柱承载力计算如下:

    Nal=π2EtI/L2 (11)
    Et=(A1fyB1σ0)σ0E(fyfp)fp (12)

    式中:Nal为试件欧拉临界力;I为试件截面惯性矩(I=πD4/64);Et为试件组合切线模量;E为试件弹性模量(E=fp/ξp);σ0为试件欧拉临界应力(σ0=Nal/AscAsc为试件截面面积);εp为试件组合比例极限应变(εp=0.67fsy/Es);fy为试件组合屈服强度;fp为试件轴压组合比例极限;A1B1分别为通过回归分析得到的参数,其表达式分别为

    A1=1(fp/fy)2E/E (13)
    B1=1(fp/fy)E/E (14)

    式中,E为钢渣/混凝土@圆钢管柱的强化模量,为考虑钢管与钢渣/混凝土之间自应力的影响,引入钢渣/混凝土强度增强系数μfy进行修正,其表达式为

    E={5000θ+550θ (15)
    {f_{\rm{y}}} = (1.212 + {C_1}\theta + {D_1}{\theta ^2})\mu {f_{{\rm{co}}}} (16)
    {f_{\rm{p}}} = (0.192{{{f_{{\rm{sy}}}}} / {235}} + 0.488){f_{\rm{y}}} (17)

    式中:\alpha 为含钢率,取\alpha {\rm{ = }}{{{A_{\rm{s}}}} / {{A_{\rm{c}}}}}{C_1}{D_1}分别为试验回归分析得到的参数,表达式为

    {{\rm{C}}_1}{\rm{ = }}0.175 \, 9{{{f_{{\rm{sy}}}}} / {235}} + 0.974 (18)
    {D_1} = - 0.103 \; 8{{\mu {f_{{\rm{co}}}}} / {20}} + 0.030 \; 9 (19)

    将式(12)代入式(11),可得:

    {N_{{\rm{al}}}} = \frac{{{A_1}{f_{\rm{y}}}{A_{{\rm{sc}}}}}}{{{B_1}}} - \frac{{{L^2}\left( {{f_{\rm{y}}} - {f_{\rm{p}}}} \right)A_{{\rm{sc}}}^{\rm{2}}{f_{\rm{p}}}}}{{{{\text{π}}^2}EI{B_1}}} (20)

    试验结果表明,长径比对钢渣/混凝土@圆钢管柱轴压试件承载力的影响比较明显,随着长径比的增大,轴压试件承载力逐渐降低。从式(20)可以看出,钢渣/混凝土@圆钢管轴压中长柱计算公式相当繁琐,而钢渣/混凝土@圆钢管轴压短柱试件极限承载力的计算公式相对比较简单,因此,结合工程实际需要,对轴压中长柱承载力计算公式进行相应简化。在轴压短柱承载力计算公式基础上,引进试件承载力稳定系数{\varphi _{\rm{l}}},提出钢渣/混凝土@圆钢管轴压中长柱承载力的计算可简化为

    {N'_{{\rm{al}}}} = {\varphi _{\rm{l}}}{N_{\rm{a}}} (21)
    {\varphi _{\rm{l}}}{\rm{ = }}0.003 \; 923{\left( {{L / D}} \right)^2} - 0.086 \; 83{L / D} + 1.26 (22)

    式中,{N'_{{\rm{al}}}}为轴压中长柱稳定承载力,经试验数据回归分析得出承载力稳定系数{\varphi _{\rm{l}}}与轴压试件长径比L/D之间的相关关系如图4所示。

    图  4  钢渣/混凝土@圆钢管柱承载力稳定系数{\varphi _{\rm{l}}}与长径比{L / D}的关系
    Figure  4.  Relationship between load capacity stability {\varphi _{\rm{l}}} and length-diameter ratio {L / D} of self-stressing steel slag aggregate/concrete@circular steel tube column

    表4为钢渣/混凝土@圆钢管轴压中长柱极限承载力计算结果与试验结果对比。可知,钢渣/混凝土@圆钢管中长柱极限承载力理论公式计算值和简化公式计算值与试验值的比值均在10%范围内变化,均值分别为0.961和0.995,均方差分别为0.0304和0.0019。结果表明,基于上述分析方法提出的钢渣/混凝土@圆钢管中长柱承载力计算公式计算的理论值与试验值吻合较好。

    表  4  钢渣/混凝土@圆钢管轴压中长柱承载力试验值与计算值比较
    Table  4.  Comparison of calculated values and test data of self-stressing steel slag aggregate/concrete@circular steel tube intermediate length columns under axial load
    SpecimenD/tsD/LPct/10−4Nal/kNNae/kNNal/kN{{{N_{{\rm{al}}}}}}/{{{N_{{\rm{ae}}}}}}{{{{N'}_{{\rm{al}}}}}}/{{{N_{{\rm{ae}}}}}}
    738.56 7.142.88068588550.9400.997
    838.5610.712.87857997940.9820.994
    下载: 导出CSV 
    | 显示表格

    钢渣/混凝土@圆钢管柱达到极限承载力时对应的轴向应变为极限压应变,是衡量钢渣/混凝土@圆钢管柱变形能力的重要指标。为得到钢渣/混凝土@圆钢管轴压短柱的极限压应变,对试验数据进行回归整理分析,如图5所示,钢渣/混凝土@圆钢管短柱轴向极限压应变计算如下:

    图  5  钢渣/混凝土@圆钢管短柱极限压应变{\varepsilon _{{\rm{au}}}}与套箍系数\theta 的关系
    Figure  5.  Relationship between ultimate compressive strain {\varepsilon _{{\rm{au}}}} and confinement coefficient \theta of self-stressing steel slag aggregate/concrete@circular steel tube short column
    {\varepsilon _{{\rm{au}}}} = {k_{\rm{a}}}\left( {0.002 \; 7{\theta ^2}{\rm{ - }}0.005 \; 7\theta + 0.015 \; 4} \right) (23)

    式中:{\varepsilon _{{\rm{au}}}}为钢渣/混凝土@圆钢管短柱极限压应变;{k_{\rm{a}}}为极限压应变折减系数,当试件核心钢渣/混凝土膨胀率为−3.5×10−4时,取{k_{\rm{a}}}{\rm{ = }}0.95,当试件核心钢渣/混凝土膨胀率为2.8×10−4时,取{k_{\rm{a}}}{\rm{ = }}1

    试验结果表明,与承载力类似,长径比对钢渣/混凝土@圆钢管柱轴压试件极限压应变的影响也比较明显,随着长径比的增大,轴压试件极限压应变减小。在轴压短柱极限压应变计算公式基础上,引进试件应变稳定系数{\varphi _{\rm{s}}},提出钢渣/混凝土@圆钢管轴压中长柱极限压应变简化计算公式如下:

    {\varepsilon _{{\rm{al}}}}={\varphi _{\rm{s}}} {\varepsilon _{\rm{a}}} (24)
    {\varphi _{\rm{s}}}{\rm{ = 0}}{\rm{.004 \; 3}}{\left( {{L / D}} \right)^2}{\rm{ - }}0.105\left( {{L / D}} \right){\rm{ + }}1.32 (25)

    式中,{\varepsilon _{{\rm{al}}}}为中长柱极限压应变,经试验数据回归分析得出的应变稳定系数{\varphi _{\rm{s}}}与轴压试件长径比L/D之间的相关关系如图6所示。

    图  6  钢渣/混凝土@圆钢管柱应变稳定系数{\varphi _{\rm{s}}}与长径比{L / D}的关系
    Figure  6.  Relationship between strain stability factor {\varphi _{\rm{s}}} and length-diameter ratio {L / D} of self-stressing steel slag aggregate/concrete@circular steel tube column

    表5为钢渣/混凝土@圆钢管轴压柱极限压应变理论计算结果与试验结果对比。可知,钢渣/混凝土@圆钢管轴压短柱和轴压中长柱极限压应变理论计算值与试验实测极限压应变值偏差均较小,对于钢渣/混凝土@圆钢管轴压短柱,极限压应变理论计算值与试验实测极限压应变值比值的均值为0.9113,均方差为0.1098;对钢渣/混凝土@圆钢管轴压中长柱,极限压应变理论计算值与试验实测极限压应变值比值的均值为0.9134,均方差为0.0385。结果表明,钢渣/混凝土@圆钢管轴压柱的极限压应变计算公式的计算理论值与试验值吻合良好。

    表  5  钢渣/混凝土@圆钢管轴压柱极限压应变计算结果与试验结果比较
    Table  5.  Comparison of calculated values and test data of ultimate compressive strain of self-stressing steel slag aggregate/concrete@circular steel tube columns under axial load
    SpecimenL/DPct/10−4\varepsilon _{\rm ae}\varepsilon _{{\rm{au}}}^{\rm{c}}\varepsilon _{{\rm{al}}}^{\rm{c}}{{\varepsilon _{{\rm{au}}}^{\rm{c}}}}/{{{\varepsilon _{{\rm{ae}}}}}}{{\varepsilon _{{\rm{al}}}^{\rm{c}}}}/{{{\varepsilon _{{\rm{ae}}}}}}
    1 3.57 2.80.01250.01301.0402
    2 3.57−3.50.01190.01261.0588
    3 3.57 2.80.01470.01250.8503
    4 3.57−3.50.01340.01180.8806
    5 3.57 2.80.01580.01280.810 1
    6 3.57−3.50.01450.01200.8276
    7 7.14 2.80.01230.01090.8862
    810.71 2.80.01010.00950.9406
    Notes: \varepsilon _{{\rm{au}}}^{\rm{c}}—Calculated value of ultimate compressive strain of short columns; \varepsilon _{{\rm{al}}}^{\rm{c}}—Calculated value of ultimate compressive strain of intermediate length columns; {\varepsilon _{{\rm{ae}}}}—Test data of ultimate compressive strain of columns.
    下载: 导出CSV 
    | 显示表格

    试验中涉及影响轴压钢渣/混凝土@圆钢管柱承载力的因素较多,为便于轴压构件的理论分析和工程应用,确定其应力-应变关系模型非常必要。本文通过对试验数据的回归分析,得出应力-应变关系数学表达式为

    {\sigma _{\rm{a}}}{\rm{ = }}{a_2}{\varepsilon _{\rm{a}}}^3{\rm{ + }}{b_2}{\varepsilon _{\rm{a}}}^2 + {c_2}{\varepsilon _{\rm{a}}} + {d_2} (26)

    式中:{\sigma _{\rm{a}}}为轴压钢渣/混凝土@圆钢管柱压应力;{a_2}{b_2}{c_2}{d_2}分别为回归分析得到的参数,表达式分别为

    {a_2} = - 6.33{\psi ^3}{\rm{ + }}2.51{\psi ^2} - 2.34\psi {\rm{ + 8}}{\rm{.01}} (27)
    {b_2} = 4.62{\psi ^3} - 1.53{\psi ^2} + 1.62\psi {\rm{ + 7}}{\rm{.10}} (28)
    {c_2} = 829.25{\psi ^3} - 325.34{\psi ^2} + 475.12\psi {\rm{ + 163}}{\rm{.43}} (29)
    {d_2} = - 102.35{\psi ^3} + 319.73{\psi ^2} - 324.13\psi {\rm{ + 110}}{\rm{.44}} (30)

    式中,\psi 为考虑长径比和约束效应影响的系数,取\psi {\rm{ = }}{\varphi _{\rm{l}}} \theta ,其中试验数据回归分析得出的稳定系数{\varphi _{\rm{l}}}根据式(22)计算。

    图7为钢渣/混凝土@圆钢管柱实测应力-应变曲线与计算应力-应变曲线的比较。可见,由拟合公式计算出的钢渣/混凝土@圆钢管柱试件轴压应力-应变本构关系能较好地反映出试验实测结果。

    图  7  钢渣/混凝土@圆钢管柱实测应力-应变曲线与计算应力-应变曲线的比较
    Figure  7.  Comparisons between measured stress-strain curves and calculated stress-strain curves of self-stressing steel slag aggregate/concrete@circular steel tube column

    通过对8根圆钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)柱的试验与理论分析,主要得到以下结论。

    (1) 钢渣/混凝土@圆钢管轴压柱的受力全过程与普通混凝土@钢管柱相类似,钢渣/混凝土@圆钢管轴心受压短柱的破坏形态表现为中部鼓曲状剪压破坏,而钢渣/混凝土@圆钢管轴心受压中长柱则呈弯曲屈曲破坏。

    (2) 8根钢渣/混凝土@圆钢管柱轴压试件的应力-应变曲线呈相似的变化趋势,均经历峰值点、下降段、缓慢上升段等历程,各试件的峰值应力和峰值应变均远大于同强度等级的钢渣/混凝土,且轴压短柱试件较中长柱试件提高更为显著,表明钢管约束钢渣/混凝土的效应明显。

    (3) 在膨胀率和长径比相同的情况下,随着径厚比的减小,钢渣/混凝土@圆钢管柱试件的峰值应力(峰值应变)增大;在膨胀率和径厚比相同的情况下,随着长径比的增大,钢渣/混凝土@圆钢管柱试件的峰值应力(峰值应变)呈减小趋势;膨胀率对钢渣/混凝土@圆钢管柱的破坏机制有影响,但不明显。

    (4) 根据极限平衡条件分别对钢渣/混凝土@圆钢管轴压短柱和钢渣/混凝土@圆钢管轴压中长柱在极限状态下的受力情况进行理论分析,推导钢渣/混凝土@圆钢管轴压短柱及轴压中长柱的极限承载力计算公式,理论计算结果与试验实测结果吻合较好。

    (5) 采用全过程分析法,拟合出钢渣/混凝土@圆钢管轴压柱应力-应变关系数学表达式,拟合的应力-应变关系表达式能较好地反映出试验实测结果。

  • 图  1   钢渣/混凝土@圆钢管柱的破坏形态

    Figure  1.   Failure modes of steel slag aggregate/concrete@circular steel tube columns

    图  2   钢渣/混凝土@圆钢管柱的应力-应变曲线

    Figure  2.   Stress-strain curves of self-stressing steel slag aggregate/concrete@circular steel tube columns

    图  3   钢渣/混凝土@圆钢管柱受力简图

    Figure  3.   Force diagram of steel slag aggregate/concrete@circular steel tube column

    图  4   钢渣/混凝土@圆钢管柱承载力稳定系数{\varphi _{\rm{l}}}与长径比{L / D}的关系

    Figure  4.   Relationship between load capacity stability {\varphi _{\rm{l}}} and length-diameter ratio {L / D} of self-stressing steel slag aggregate/concrete@circular steel tube column

    图  5   钢渣/混凝土@圆钢管短柱极限压应变{\varepsilon _{{\rm{au}}}}与套箍系数\theta 的关系

    Figure  5.   Relationship between ultimate compressive strain {\varepsilon _{{\rm{au}}}} and confinement coefficient \theta of self-stressing steel slag aggregate/concrete@circular steel tube short column

    图  6   钢渣/混凝土@圆钢管柱应变稳定系数{\varphi _{\rm{s}}}与长径比{L / D}的关系

    Figure  6.   Relationship between strain stability factor {\varphi _{\rm{s}}} and length-diameter ratio {L / D} of self-stressing steel slag aggregate/concrete@circular steel tube column

    图  7   钢渣/混凝土@圆钢管柱实测应力-应变曲线与计算应力-应变曲线的比较

    Figure  7.   Comparisons between measured stress-strain curves and calculated stress-strain curves of self-stressing steel slag aggregate/concrete@circular steel tube column

    表  1   钢渣/混凝土组分含量及实测强度

    Table  1   Proportion and measured strength of steel slag/concrete

    Particle size of
    steel slag/mm
    Sand
    ratio/%
    Material usage/(kg.m−3)Cube compressive strength/MPaExpansion rate/10−4
    Tap
    water
    CementCoarse aggregate
    (gravel)
    Fine aggregate
    (sand)
    Fine aggregate
    (steel slag)
    1.18–2.360201365961062134.29−3.5
    0.15–0.3(75%)+
    0.3–0.6(25%)
    0201365961062121.85 2.8
    下载: 导出CSV

    表  2   圆钢管自应力钢渣增强混凝土(钢渣/混凝土@圆钢管)柱试件相关参数及实测强度

    Table  2   Parameters and test strength of steel slag aggregate reinforced concrete filled circular steel tube columns (steel slag aggregate/ concrete@ circular steel tube) column samples

    SamplePct/10−4L/mmD/mmts/mmL/Dfsy/MPafsu/MPafco/MPaθNae/kNσmax/MPaεamaxεcmax
    12.85001402.083.5717631217.500.5862540.6−0.01250.0082
    2−3.55001402.083.5717631227.440.4873747.9−0.01190.0069
    32.85001403.633.5723329617.501.231 01666.0−0.01470.0091
    4−3.55001403.633.5723329627.441.141 14774.5−0.01340.0079
    52.85001404.223.5723630117.501.421 12372.9−0.01580.0103
    6−3.55001404.223.5723630127.441.361 22379.4−0.01510.0095
    72.81 0001403.637.1423329617.501.2385855.7−0.01230.0082
    82.81 5001403.6310.7123329617.501.2379951.9−0.01010.0070
    Notes: Pct—Expansion rate of steel slag aggregate concrete; D,ts—Outer diameter and thickness of steel tube, respectively; L—Height of specimen; fsy, fsu—Yield and ultimate strength of steel tube, respectively; fco—Compressive strength of steel slag aggregate concrete; Nae—Measured ultimate strength of column; θ—Confinement coefficient, \theta {\rm{ = }}\displaystyle\frac{{{A_{\rm{s}}}{f_{{\rm{sy}}}}}}{{\mu {f_{{\rm{co}}}}{A_{\rm{c}}}}}; σmax—Ultimate stress of column; εamax—Ultimate axial strain of column; εcmax—Ultimate circumferential strain of column.
    下载: 导出CSV

    表  3   钢渣/混凝土@圆钢管轴压短柱承载力试验值与计算值比较

    Table  3   Comparison of calculated values and test data of self-stressing steel slag aggregate/concrete@circular steel tube short columns under axial load

    SpecimenD/tsL/DPct/10–4Na/kNNae/kNNa/NaeNa/Nae
    AveragevalueStandard deviationVariation coefficient
    167.303.57 2.8 590.56250.94480.9530.0540.0567
    267.303.57−3.5 650.47370.8825
    338.563.57 2.81 018.41 0161.0024
    438.563.57−3.51 042.81 1470.9092
    533.173.57 2.81 151.31 1231.0252
    633.173.57−3.51 164.81 2230.9524
    下载: 导出CSV

    表  4   钢渣/混凝土@圆钢管轴压中长柱承载力试验值与计算值比较

    Table  4   Comparison of calculated values and test data of self-stressing steel slag aggregate/concrete@circular steel tube intermediate length columns under axial load

    SpecimenD/tsD/LPct/10−4Nal/kNNae/kNNal/kN{{{N_{{\rm{al}}}}}}/{{{N_{{\rm{ae}}}}}}{{{{N'}_{{\rm{al}}}}}}/{{{N_{{\rm{ae}}}}}}
    738.56 7.142.88068588550.9400.997
    838.5610.712.87857997940.9820.994
    下载: 导出CSV

    表  5   钢渣/混凝土@圆钢管轴压柱极限压应变计算结果与试验结果比较

    Table  5   Comparison of calculated values and test data of ultimate compressive strain of self-stressing steel slag aggregate/concrete@circular steel tube columns under axial load

    SpecimenL/DPct/10−4\varepsilon _{\rm ae}\varepsilon _{{\rm{au}}}^{\rm{c}}\varepsilon _{{\rm{al}}}^{\rm{c}}{{\varepsilon _{{\rm{au}}}^{\rm{c}}}}/{{{\varepsilon _{{\rm{ae}}}}}}{{\varepsilon _{{\rm{al}}}^{\rm{c}}}}/{{{\varepsilon _{{\rm{ae}}}}}}
    1 3.57 2.80.01250.01301.0402
    2 3.57−3.50.01190.01261.0588
    3 3.57 2.80.01470.01250.8503
    4 3.57−3.50.01340.01180.8806
    5 3.57 2.80.01580.01280.810 1
    6 3.57−3.50.01450.01200.8276
    7 7.14 2.80.01230.01090.8862
    810.71 2.80.01010.00950.9406
    Notes: \varepsilon _{{\rm{au}}}^{\rm{c}}—Calculated value of ultimate compressive strain of short columns; \varepsilon _{{\rm{al}}}^{\rm{c}}—Calculated value of ultimate compressive strain of intermediate length columns; {\varepsilon _{{\rm{ae}}}}—Test data of ultimate compressive strain of columns.
    下载: 导出CSV
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    其他类型引用(9)

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  • 收稿日期:  2019-06-05
  • 录用日期:  2019-08-24
  • 网络出版日期:  2019-09-16
  • 刊出日期:  2020-05-14

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