Restrained Length Calculation Procedure

管道规格
1.1 DN = 700
nominal size
管道外径
DE = 738 mm
external diameter
2
管道截面积 = π×DE /4
1.1.2 cross-sectional area A = 3.14×738×738/4
of pipe = 427762.4 mm
2

壁厚等级
1.2 K = 9
thickness class
管道壁厚
1.2.1 e = 10.8 mm
thickness of pipe
管道长度
1.3 Standardized lengths Lu = 5.9 m
of restrained pipe
弯头角度
1.4 θ = 22.50 °
angle of bend
安全系数
1.5 SF = 2.0
safety factor
管道压力
1.6 P = 1.00 MPa
degsin pressure
1、计算条件design conditions

土壤内摩擦角
1.7 internal friction ϕ = 29 °
angle of the soil
内摩擦角系数
ratio of pipe fϕ
1.7.1 = 0.75
friction angle to
soil friction angle
土壤粘聚力 Cs 2
1.8 = 0.00 kN/m
soil cohesion
粘聚力系数
ratio of pipe fc
1.8.1 = 0.00
cohesion to soil
cohesion
沟槽系数
1.9 trench condition Kn = 0.80
modifer
土壤重度 3
1.10 γ = 14.14 kN/m
backfll soil density
管顶覆土深度
1.11 depth of cover to top H = 2.00 m
of pipe
管中心线覆土深度
1.12 depth of cover to Hc = 2.369 m
pipe centerline
水密度 3
1.13 ρ水 = 1000 kg/m
water density

球墨铸铁密度 3
1.14 ρ铸铁 = 7050 kg/m
ductile iron density
thrust force
2、水流推力

= P×A×sin(θ/2)/1000
水流推力 = 1×427762.4×sin(22.5/2)/1000
2.1 T
thrust force
= 83.45 kN
2 2
= {π×(DE/2000) ‐π×[(DE‐e)/2000] }×ρ铸铁
[3.14×738/2000×738/2000‐3.14×(738‐10.8)/2000×(738‐
管道重量 Wp =
3.1 10.8)/2000]×7050
unit weight of pipe
= 173.9 kg/m
= 1.70 kN/m
= π×[(DE‐e)/2000]2×ρ水
3、摩擦力unit frictional resistance

水重 Ww = 3.14×(738‐10.8)/2000×(738‐10.8)/2000×1000
3.2
unit weight of water = 415.3 kg/m
= 4.07 kN/m
= γ×H×DE/1000
管顶土重 We
3.3 = 14.14×2×738/1000
earth prism load
= 20.87 kN/m
管道表面积 = π×DE/2000
3.4 surface area of pipe Ap = 3.14×738/2000
exterior = 1.159 2
m /m
= ϕ×fϕ
摩擦角
3.5 δ = 29×0.75
pipe friction angle
= 21.75 °
= Cs×fc
粘聚力
3.6 C = 0×0
pipe cohesion
2
= 0.00 kN/m
= (ApC+(2We+Wp+Ww)tanδ)×cos(θ/2)
摩擦力
3.7 unit frictional Ff = [1.159×0+(2×20.87+1.7+4.07)×tan21.75]×cos(22.5/2)
resistance
= 18.59 kN/m
= tan2(45+ϕ/2)
朗肯被动土压力系数 Nϕ
4.1 = [tan(45+29/2)]^2
tan2 (45° + φ/2)
= 2.88
unit bearing resistance

= γ×Hc×Nϕ+2×Cs×Nϕ^0.5
朗肯被动土压力 Pp
4、被动土压力

4.2 = 14.14×2.369×2.88+2×0×2.88^0.5
passive soil pressure
= 98.54 kN/m
= Kn×Pp×DE/1000×0.5×cos(θ/2)

= 0.8×98.54×738/1000×0.5×cos(22.5/2)
被动土压力
4.3 unit bearing Rs
resistance
= 28.53 kN/m
restrained pipe on each side of

= SF×T/(Ff+Rs)
5、自锚管长度number of the

弯头一侧自锚管长度
length of the
5.1 L = 2×83.45/(18.59+28.53)
restrained pipe on
each side of the bend
the bend

= 3.54 m

弯头一侧自锚管支数
number of the
5.2 n = 1
restrained pipe on
each side of the bend