大体积混凝土计算

大体积混凝土浇筑裂缝控制的施工计算KF001,,,,,,

,,,,,,,

裂缝控制原理,在大体积混凝土浇筑前，根据施工拟采取的防裂措施和现有的施工条件，先,,,,,

,计算混凝土的水泥水化热的绝热最高温升值、各龄期收缩变形值、收缩当量,,,,,

,温差和弹性模量，然后通过计算，估量可能产生的最大温度收缩应力，如不,,,,,

,超过混凝土的抗拉强度，则表示所采取的防裂措施能有效控制、预防裂缝的,,,,,

,出现；如超过混凝土的抗拉强度，则可采取措施调整混凝土的入模温度、降,,,,,

,低水化热温升值、降低混凝土内外温差、改善施工操作工艺和混凝土拌合物,,,,,

,性能、提高抗拉强度或改善约束等技术措施重新计算，直至计算的应力在允,,,,,

,许的范围。,,,,,

,,,,,,,

1、计算参数,,,,,,

钢筋混凝土底板尺寸,,长度l(m),宽度b(m),厚度h(m),,

,,40,20,1.30,,

混凝土标号,C30、S6,,,,,

混凝土配合比,水泥,水,砂,石,粉煤灰,外加剂

,425#普通,,中砂,碎石5-31,,

,1,0.46,1.8,2.86,0.17,0.016

kg/m3,380,175,684,1087,65,6.08

混凝土浇筑温度Tj(℃),,25,,,,

混凝土入模温度T0(℃),,28,,,,

,,,,,,,

2、混凝土的最终绝热温升Tmax(℃),,,,,,

Tmax=W×Q/(c×ρ)=,,61.5,,,,

其中,W--每立方米混凝土中水泥用量(kg/m3),,,,380,

,Q--每公斤水泥水化热量(kJ/kg),,,,377,

,c--混凝土的比热(J/kg∙K),,,,0.97,

,ρ--混凝土的密度(kg/m3),,,,2400,

,,,,,,,

3、各龄期混凝土的绝热温升T(t)(℃),,,,,,

T(t)=Tmax×(1－e-mt),,,,,,

其中,m----经验系数(随水泥品种、比表面及浇筑温度而异),,,,,0.384

,e----常数,,,,,2.718

,t(d)----混凝土的龄期,,,,,

计算结果,混凝土龄期t(d),,T(t)(℃),,,

,3,,42.1,,,

,6,,55.4,,,

,9,,59.6,,,

,12,,60.9,,,

,15,,61.3,,,

,18,,61.5,,,

,21,,61.5,,,

,24,,61.5,,,

,27,,61.5,,,

,30,,61.5,,,

,,,,,,,

4、各龄期混凝土内部最高温度Tn(t)(℃),,,,,,

Tn(t)=Tj+T(t)×ξ,,,,,,

其中,ξ----不同龄期和浇筑厚度的降温系数,,,查表,,

,混凝土龄期t(d),,ξ,,,

,3,,0.65,,,

,6,,0.62,,,

,9,,0.59,,,

,12,,0.48,,,

,15,,0.38,,,

,18,,0.29,,,

,21,,0.23,,,

,24,,0.19,,,

,27,,0.16,,,

,30,,0.15,,,

计算结果,混凝土龄期t(d),,Tn(t)(℃),△Tn(t)(℃),,

,3,,52.4,,,

,6,,59.3,-7.0,,

,9,,60.2,-0.8,,

,12,,54.2,5.9,,

,15,,48.3,5.9,,

,18,,42.8,5.5,,

,21,,39.1,3.7,,

,24,,36.7,2.5,,

,27,,34.8,1.8,,

,30,,34.2,0.6,,

,,,,,,,

,混凝土龄期t(d),,与外界气温之差△T1(t)(℃),,,

,,,△T1(t)＝Tn(t)-Tj,,,

,3,,27.4,,,

,6,,34.3,,,

,9,,35.2,,,

,12,,29.2,,,

,15,,23.3,,,

,18,,17.8,,,

,21,,14.1,,,

,24,,11.7,,,

,27,,9.8,,,

,30,,9.2,,,

,,,,,,,

5、各龄期混凝土表面温度Tb(t)(℃),,,,,,

Tb(t)=Tq+4×h'×(H-h')×△T1(t)/H2,,,,,,

其中,Tq----不同龄期的大气平均温度(℃),,,25,,

,H----混凝土的计算厚度(m),,,H=h+2h'=,2.32,

,h'----混凝土的虚厚度(m),,,h'=K×λ/β=,,0.51

,K----计算折减系数,,,0.666,,

,λ----混凝土的导热系数(W/m∙K),,,2.33,,

,β----模板及保温层的传热系数(W/m2∙K),,,,,

,,β=1/∑(δi/λi+1/βq)=,,3.04,,

,δi----各种保温材料的厚度(m),,,草袋,,0.04

,λi----各种保温材料的导热系数(W/m2∙K),,,,,0.14

,βq----空气层传热系数(W/m2∙K),,,,23,

计算结果,混凝土龄期t(d),,Tb(t)(℃),,,

,3,,43.8,,,

,6,,48.6,,,

,9,,49.1,,,

,12,,45.1,,,

,15,,41.0,,,

,18,,76.5,,,

,21,,60.7,,,

,24,,50.2,,,

,27,,42.2,,,

,30,,39.6,,,

,龄期t(d),内部温度与表面温度之差,,表面温度与大气温度之差,,

,,△T2(t)＝Tn(t)-Tb(t)(℃),,△T3(t)=Tb(t)-Tq(℃),,

,3,8.6,,18.8,,

,6,10.8,,23.6,,

,9,11.0,,24.1,,

,12,9.2,,20.1,,

,15,7.3,,16.0,,

,18,-33.7,,51.5,,

,21,-21.6,,35.7,,

,24,-13.5,,25.2,,

,27,-7.4,,17.2,,

,30,-5.4,,14.6,,

,,,,,,,

6、各龄期混凝土收缩相对变形值εy(t),,,,,,

εy(t)＝εy0×（1－e-0.01t)×M1×M2×M3…M10,,,,,,

其中,混凝土在标准状态下的最终(极限)收缩值εy0,,,,,0.000324

,混凝土收缩变形不同条件影响修正系数M,,,,,

,M1,普通水泥,,,1.00,

,M2,水泥细度为5000孔,,,1.35,

,M3,骨料为花岗岩,,,1.00,

,M4,水灰比为0.46,,,1.05,

,M5,水泥浆量为0.27,,,1.32,

,M6,自然养护28天,,,0.93,

,M7,环境相对湿度为70%,,,0.77,

,M8,水力半径的倒数为0.016,,,0.56,

,M9,机械振捣,,,1.00,

,M10,配筋率0.005,,,0.90,

,,,M1×M2×….×M10=,,0.68,

计算结果,混凝土龄期t(d),,εy(t),,,

,3,,6.51926E-06,,,

,6,,1.28459E-05,,,

,9,,1.89855E-05,,,

,12,,2.49437E-05,,,

,15,,3.07259E-05,,,

,18,,3.63371E-05,,,

,21,,4.17826E-05,,,

,24,,4.70671E-05,,,

,27,,5.21955E-05,,,

,30,,5.71723E-05,,,

,,,,,,,

7、各龄期混凝土的当量温差Ty(t)(℃),,,,,,

Ty(t)＝εy(t)/α,,,,,,

其中,α--混凝土的线膨胀系数,,,0.00001,,

计算结果,混凝土龄期t(d),,Ty(t)(℃),△Ty(t)(℃),,

,3,,0.65,,,

,6,,1.28,0.63,,

,9,,1.90,0.61,,

,12,,2.49,0.60,,

,15,,3.07,0.58,,

,18,,3.63,0.56,,

,21,,4.18,0.54,,

,24,,4.71,0.53,,

,27,,5.22,0.51,,

,30,,5.72,0.50,,

,,,,,,,

8、各龄期混凝土的弹性模量E(t)(N/mm2),,,,,,

E(t)＝E0(1－e-0.09t),,,,,,

其中,E0--混凝土的最终(28d)弹性模量(N/mm2),,,,30000,

计算结果,混凝土龄期t(d),,E(t)(N/mm2),,,

,3,,7098,,,

,6,,12517,,,

,9,,16653,,,

,12,,19811,,,

,15,,22222,,,

,18,,24062,,,

,21,,25467,,,

,24,,26539,,,

,27,,27358,,,

,30,,27983,,,

,,,,,,,

9、混凝土的综合温度差△Tt(℃),,,,,,

△T(t)=△T1(t)-Th,,,,,,

其中,Th--混凝土浇筑后达到稳定时的温度(℃),,,,20.0,

计算结果,混凝土龄期t(d),,△T(t)(℃),,,

,6,,14.34,,,

,9,,15.16,,,

,12,,9.24,,,

,15,,3.31,,,

,18,,-2.17,,,

,21,,-5.85,,,

,24,,-8.31,,,

,27,,-10.15,,,

,30,,-10.77,,,

,,,,,,,

10、各龄期混凝土的温度(包括收缩)应力σ(t)(N/mm2),,,,,,

σ(t)=-E(t)×α×△T(t)×S(t)×R/(1-μ),,,,,,

其中,S(t)--考虑混凝土徐变影响的松弛系数,,,,查表,

,混凝土龄期t(d),,S(t),,,

,6,,0.519,,,

,9,,0.475,,,

,12,,0.442,,,

,15,,0.411,,,

,18,,0.389,,,

,21,,0.369,,,

,24,,0.355,,,

,27,,0.341,,,

,30,,0.331,,,

,R--混凝土的外约束系数,,,,0.25,

,μ--混凝土的泊松比,,,,0.15,

计算结果,混凝土龄期t(d),,σ(t)(N/mm2),,,

,6,,-0.2740,,,

,9,,-0.3527,,,

,12,,-0.2381,,,

,15,,-0.0889,,,

,18,,0.0598,,,

,21,,0.1617,,,

,24,,0.2302,,,

,27,,0.2786,,,

,30,,0.2934,,,

,,,,,,,

11、计算结论,,,,,,

28d混凝土抗拉强度ft,,,2.01,N/mm2,,

,,,,,,,

通过计算，说明由于降温和收缩产生的温度应力小于混凝土的抗拉强度，可采取一次连续,,,,,,

浇筑混凝土底板，不会产生贯穿的有害裂缝。,,,,,,

,,,,,,,

大体积混凝土浇筑后裂缝控制的施工计算KF001,,,,,,

裂缝控制原理,在大体积混凝土浇筑后，应根据实测温度值和绘制的温度升降曲线，分别计,,,,,

,算各降温阶段的混凝土温度收缩应力。如累计的总拉应力不超过同龄期的混,,,,,

,凝土抗拉强度，则说明采取的防裂措施能够有效控制和预防有害裂缝的出现，,,,,,

,如超过该阶段的混凝土抗拉强度，则应采取措施加强养护，减缓其降温的速,,,,,

,度，提高该龄期的混凝土抗拉强度，以达到控制裂缝的出现。,,,,,

,,,,,,,

12、各龄期混凝土实际水化热最高温升值Td(℃),,,,,,

Td=Tn－T0,,,,,,

其中,Tn----各龄期混凝土温度值,,,,,

计算结果,混凝土龄期t(d),,Td(℃),,,

,3,,24.4,,,

,6,,31.3,,,

,9,,32.2,,,

,12,,26.2,,,

,15,,20.3,,,

,18,,14.8,,,

,21,,11.1,,,

,24,,8.7,,,

,27,,6.8,,,

,30,,6.2,,,

,,,,,,,

13、混凝土水化热平均温度Tx(t)(℃),,,,,,

Tx(t)=Tb+2×(Tn-Tb)/3,,,,,,

计算结果,混凝土龄期t(d),,Tx(t)(℃),△Tx(t)(℃),,

,3,,49.5,,,

,6,,55.8,-6.3,,

,9,,56.5,-0.7,,

,12,,51.2,5.3,,

,15,,45.9,5.3,,

,18,,54.0,-8.2,,

,21,,46.3,7.7,,

,24,,41.2,5.2,,

,27,,37.3,3.9,,

,30,,36.0,1.3,,

,,,,,,,

14、各龄期混凝土综合温差T(t)(℃),,,,,,

△T(t)=△Tx(t)+△Ty(t),,,,,,

计算结果,混凝土龄期t(d),,△T(t)(℃),,,

,6,,-5.6,,,

,9,,-0.1,,,

,12,,5.9,,,

,15,,5.9,,,

,18,,-7.6,,,

,21,,8.3,,,

,24,,5.7,,,

,27,,4.4,,,

,30,,1.8,,,

,,,,,,,

15、各龄期混凝土总温差T0(t)(℃),,,,,,

T0(t)=∑T(t)=,18.5,,,,,

,,,,,,,

16、最大温度应力值σ(t)(N/mm2),,,,,,

σ(t)=α/(1-μ)×(1-1/(cosh×β×l/2))∑(E(t)×△T(t)×S(t)),,,,,,

其中,β----约束状态影响系数,,,,,

,β=(Cx/(h×E(t)))1/2,,,,,

,Cx----地基水平阻力系数(N/mm3),,,0.06,,

,l----混凝土结构物长度(mm),,,40000,,

,S(t)--考虑混凝土徐变影响的松弛系数,,,,查表,

,混凝土龄期t(d),,S(t),,,

,6,,0.208,,,

,9,,0.212,,,

,12,,0.215,,,

,15,,0.23,,,

,18,,0.252,,,

,21,,0.301,,,

,24,,0.367,,,

,27,,0.473,,,

,30,,1,,,

计算结果,,,,,,

龄期t(d),Cx/(h×E(t),β,cosh(β·l/2),E(t)×△Tt×S(t),,σ(t)

6,3.68742E-09,0.00006072,1.83270680,-14636,,-0.0782

9,2.77148E-09,0.00005264,1.60743367,(420),,-0.0019

12,2.32971E-09,0.00004827,1.50326825,25109,,0.0989

15,2.07697E-09,0.00004557,1.44496139,30109,,0.1091

18,1.91812E-09,0.00004380,1.40878751,(46164),,-0.1576

21,1.8123E-09,0.00004257,1.38489291,63306,,0.2070

24,1.73906E-09,0.00004170,1.36844851,55351,,0.1753

27,1.68702E-09,0.00004107,1.35680926,56705,,0.1754

30,1.64934E-09,0.00004061,1.3