Anchor Block Design
Anchor Block Design
Anchor Block Design
Uncategorised software
All users are responsible for
checking their own calculations.
Version
Date
This spreadsheet carries out a design for WSD Type 2 Thrust Blocks.
The details of the calculations here should be read in conjunction with
Technical Note Nr I.1 (Appendix I) of the WSD Technical Manual TM/03
on Pipes and Pipelines.
Data is entered into the blue boxed cells (unprotected) in the worksheet THRUST2
General Design Parameters, such as soils data etc, are entered in cells E16:E25
Case parameters such as Pipe diameter, test pressure, bend angle, pipe cover are
entered into the design table K37:N61
Notes
1
The formula for pipe OD applies to ductile iron pipes. This will be good enough
for pipes with OD up to 5% greater than the nominal diameter.
For other pipes, eg AC Class 18,24 etc and PCP pipes, the formula in cell P38
should be amended. For AC pipes copy the formula from the cells below P38.
Dimension A is now defined as the chord length across the outside of the bend.
Previously it was the chord length on the bend centre line plus a bit.
This in fact makes little difference to the block design overal.
Dimension A may be changed by adjusting the formulae in cells E52: E53
Derivation added for formula used for solution , See Columns M-T of this sheet
In the EXCEL version, the formulae in column G are merely labels and have been typed in longhand.
In the LOTUS version, the formulae are the ones actually used to calculate the values.
REVISION RECORD
130976479.xls.ms_office
Thrust2*.xls
2/24/2013
Derivation of Formulae
Ground Level
Lf2=200 min
Block
cover
Pipe cover
45
2H/3
d
OD
d
H/3
SECTION X-X
PLAN
VOLUME of BLOCK
Centre middle - rectangular
Centre- top & bottom
Ends - middle
Ends -top & bottom
Face
Bit around Pipe
Total Volume
=A.(B-A)/2.Z
+A.(B-A)/2/2.(H-Z).
+(B-A).Z/2.(B-A)/2
+(B-A).(H-Z)/3.(B-A)/2
+B.H.Lf2
+Vol3
VolT= A.B.Z/2-A^2.Z/2+A.B.H/4-A^2.H/4-A.B.Z/4+A^2.Z/4+B^2.Z/4-A.B.Z/2+A^2.Z/4
+B^2.H/6-B^2.Z/6-A.B.H/3+A.B.Z/3+A^2.H/6-A^2.Z/6+B.H.Lf2+Vol3
= B^2.[Z/4+H/6-Z/6]
+B.[A.Z/2+A.H/4-A.Z/4-A.Z/2-A.H/3+A.Z/3+H.Lf2]
+[-A^2.Z/2-A^2.H/4+A^2.Z/4+A^2.Z/4+A^2.H/6-A^2.Z/6+Vol3]
= B^2.[H+Z/2]/6
+B.[(Z-H).A/12+H.Lf2]
+[-(Z+H/2).A^2/6+Vol3]
B^2.[ (H+Z/2)..Yc/6]
+B.[ (Kp-Ka).Ys/2.((CovB+H)^2-CovB^2)
-.Yc.(H-Z).A/12
+.Yc.H.Lf2]
+[ Yc..Vol3
-Yc..(Z+H/2).A^2/6
-Fs.T]
=YYB2
=YYB1.2.YYB2
=YYB0.YYB2
B= -YYB1+SQRT(YYB1^2-YYB0)
+ve root applies
In Block Volume Calculation, (B-A)/2 is always >=0 as clearance between pipe and trench wall
is assumed to be never greater than Lf2.
130976479.xls.ms_office
Thrust2*.xls
2/24/2013
Project Name:
Description :
Designed by:
Checked by:
Date:
DegS
FS
Sf
Ysd
Yss
Ycd
CovB
d2
Lf2
30
1.5
0
17.5
9
23
deg
dry
kN/m3
kN/m3
kN/m3
0.3 m
0.2 m
0.2 m
ref
DNmm
DN
DegB
AngB
Pt
Cover
100
0.1
22.5
0.3927
9
1
Suggested Values
for Standard design
30
1.5
0=dry 1=submerged
17.5
9
23
CASE PARAMETERS
Diameter
Bend angle
Test pressure
Cover to pipe
mm
m
deg
rad
bar
m
=INDEX(DATA,REF+1,1)
=DNMM/1000
=INDEX(DATA,REF+1,2)
=DEGB*PI()/180
=INDEX(DATA,REF+1,3)
=INDEX(DATA,REF+1,4)/1000
CALCULATIONS
Angle of soil friction
AngS 0.5236 rad
Active
Ka
0.333
Passive
Kp
3.000
Net
Kn
2.667
Base friction
Kb
0.577
Pipe outside diameter
OD 0.11879 m
Copy relevant formula up into OD box
0.11879 DI/GRP
0.1131 AC-12
0.1155 AC-18
0.12 AC-24
Cross sectional area
XAP 0.01108
Design thrust
Td 3.89187 kN
Dimension A
Term 1
$E$52
0.07804 m
(Empirical)
Term 2
$E$53
0.14712 m
Sum
As 0.22515 m
Round off to nearest 50
A
0.250 m
Effective Soil Density
Ys
17.50 kN/m3
Effective concrete Density
Yc
23.00 kN/m3
Depth to pipe centre
Ds
1.059 m
Block height at face
Y1H 1.13909 m
Block height at block
Y2H 0.51879 m
Block face base depth
Z1H 1.43909 m
130976479.xls.ms_office
$E$65
0.1263 m
THRUST2
=DEGS*PI()/180
=TAN(PI()/4-ANGS/2)^2
=TAN(PI()/4+ANGS/2)^2
=KP-KA
=TAN(ANGS)
=$DN*1.0329+0.0155
=$DN*1.0329+0.0155
=$DN*1.084+0.0047
=$DN*1.131+0.0024
=$DN*1.2
=PI()*OD^2/4
=XAP*PT*100*2*SIN(ANGB/2)
=2*2*DN*SIN(ANGB/2)
=0.15*COS(ANGB/2)
=E52+E53
=ROUND(E54*2,1)/2
=IF(SF=0,YSD,YSS)
=IF(SF=0,YCD,YCD-9.8)
=COVER+OD/2
=(DS-COVB)*1.5
=OD+2*D2_
=COVB+Y1H
=TD*FS/(KN*YS*(Z1H^2-COVB^2)/2)
2/24/2013
rounded up to nearest 50
Design with base friction
Area of conc at block
Volume of concrete at pipe
Thrust term
Soil cover at block face
Soil cover at pipe
Quadratic coefficients
YA1
$E$70
$E$71
$E$72
Vol2A
WW
0.250 m
0.01389
0.00588
0.01226
0.00264
0.00852
0.01748
m2
m3
m2
m3
m3
kN
YYB11
46.223 kN/m
YYB12
3.02521 kN/m
YYB01
0.11317 kN
YYB02
0.0101 kN
YYB21
2.40868 kN/m2
YYB13
-0.3432 kN/m
YYB03
-0.1934 kN
YYB04
-5.8378 kN
C1
0.300 m
C2
0.800 m
YYB2 2.40868 kN/m2
YYB1 10.1518 kN/m
YYB0 -2.4528 kN
$E$91
B
Taper length
top slope
Volume
130976479.xls.ms_office
Y1B
0.250 m
0.250 m
TL
0 m
1 in
0
$E$96
0.05695 m3
$E$97
0 m3
Vol22
0.06548 m2
THRUST2
=MAX(ROUND(2*E65+0.049,1)/2,A)
=(A-OD/2*SIN(ANGB))*OD/2*COS(ANGB/2)
=YA1*Y2H-PI()*OD^2/8*(A-OD/2*SIN(ANGB/2))
=D2_*OD/2+(OD/2)^2*(1-PI()/4)/2
=E71*(A-3/2*OD*SIN(ANGB/2))
=E70+E72
=DN^2*PI()/4*(A-OD*SIN(ANGB/2))*9.81
=YS*KN*(Z1H^2-COVB^2)/2
=KB*YC*LF2*Y1H
=KB*YC*VOL2A
=IF(SF=0,KB*WW,0)
=KB*YC*(Y2H+Y1H/2)/6
=-KB*YC*A*(Y1H-Y2H)/12
=-KB*YC*A^2*(Y2H+Y1H/2)/6
=-TD*FS
=COVB
=COVER-D2_
=YYB21
=(YYB11+YYB12+YYB13)/2/YYB2
=(YYB01+YYB02+YYB03+YYB04)/YYB2
=MAX(-E88+SQRT(E88^2-E89),A)
=ROUND(2*E91+0.049,1)/2
=(B-A)/2
=TL/(COVER-COVB-D2_)
=B*Y1H*LF2
=TL/3*(B*Y2H+A*Y1H+(B*Y1H+A*Y2H)/2)
=E97+E96+VOL2A
2/24/2013
Project Name:
Description :
Ground Level
Lf2=200 min
Block
cover
Pipe cover
45
A
J
OD
2H/3
H/3
SECTION X-X
PLAN
Applicability and principal design parameters
Pipes with OD not greater than DN + 5%, eg DI, GRP
Granular soils,
(Passive-Active) pressure integrated over height of block
130976479.xls.ms_office
30
1.5
300
dry
17.5
9
23
degrees
mm
kN/m3
kN/m3
kN/m3
RESULTS
Test
Press
bar
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
Pipe
Cover
mm
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Row
Ref
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
OD
mm
119
119
119
170
170
170
222
222
222
274
274
274
274
325
325
325
325
429
429
429
429
480
480
480
480
Thrust
kN
3.9
7.6
14.1
8.0
15.7
29.0
13.6
26.7
49.3
10.4
20.7
40.5
74.9
14.7
29.2
57.3
105.8
25.5
50.7
99.4
183.7
32.0
63.6
124.8
230.6
THRUST2
H
mm
1139
1139
1139
1178
1178
1178
1217
1217
1217
1255
1255
1255
1255
1294
1294
1294
1294
1371
1371
1371
1371
1410
1410
1410
1410
Block Dimensions
A
B
mm
mm
250
250
300
300
400
450
250
250
350
500
550
850
300
400
450
750
650
1350
250
300
350
550
500
1050
800
1850
250
400
400
750
600
1350
950
2450
300
600
450
1100
750
2100
1250
3650
350
700
500
1300
850
2450
1400
4250
2/24/2013
130976479.xls.ms_office
THRUST2
2/24/2013