Anchor Block Design

THRUST BLOCK DESIGN-WSD THRUST BLOCK TYPE 2 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.

2

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

3

Derivation added for formula used for solution , See Columns M-T of this sheet

4

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

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Thrust2*.xls

2/24/2013

Derivation of Formulae

B

Face cast against excavation

X

Ground Level Lf2=200 min

Block cover

Pipe cover 45

A

2H/3

d OD d

Z

H/3

X

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]

RESOLVING THRUSTS HORIZONTALLYFs.T=Ys/2.(Kp-Ka).[(CovB+H)^2-CovB^2].B+Yc.µ.VolT Substituting VolT and grouping in terms of coefficients of B^n gives 0=

B^2.[ (H+Z/2).µ.Yc/6] +B.[ (Kp-Ka).Ys/2.((CovB+H)^2-CovB^2) -µ.Yc.(H-Z).A/12 +µ.Yc.H.Lf2] +[ Yc.µ.Vol3 -Yc.µ.(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.

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THRUST BLOCK DESIGN - STANDARD WSD THRUST BLOCK TYPE 2

Version & Date

All Users are responsible for checking their own calculation

Project Name: Description : Designed by: Checked by: Date:

Standard Thrust Block Anchor Block Type 2 for Bends

SOIL & GENERAL DATA Angle of soil friction Factor of Safety (Sliding) Submerged conditions Soil density(non submerged) Soil sensity (submerged) Concrete density Type 2 block parameters Block Cover Dim d at block Depth of face before taper Row ref in table

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

0

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

Ht of block above/below pipe 0.2

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

Soil pressure only Face Length

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$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

Weight of water at pipe Passive soil force Block wt face bit at pipe water at pipe taper

Thrust term Soil cover at block face Soil cover at pipe Quadratic coefficients

Final Block Details Dimension B Round up

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

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Project Name: Description :

B

Standard Thrust Block Anchor Block Type 2 for Bends

Face cast against excavation

X

Ground Level Lf2=200 min

Block cover

Pipe cover 45

A J

OD

d

2H/3

d

H/3

X

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

Angle of soil friction Factor of safety Cover to block Submerged conditions Soil density(non submerged) Soil sensity (submerged) Concrete density DESIGN TABLE Nom Bend Dia Angle mm deg 100 22.5 100 45 100 90 150 22.5 150 45 150 90 200 22.5 200 45 200 90 250 11.25 250 22.5 250 45 250 90 300 11.25 300 22.5 300 45 300 90 400 11.25 400 22.5 400 45 400 90 450 11.25 450 22.5 450 45 450 90

130976479.xls.ms_office

30 1.5 300 dry 17.5 9 23

OD = OD adopted for calculations Hb = Height of thrust block overall A = width of thrust block at pipe B = width of thrust block at face

degrees

If top slope > 1in3 then consider Type 1 Block If Dim B > 5 m then consider increase in pipe cover or a special design

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

Volume top slope m3 1 in 0.065 0.0 0.078 0.0 0.120 0.1 0.071 0.0 0.160 0.2 0.308 0.3 0.132 0.1 0.289 0.3 0.665 0.7 0.103 0.1 0.208 0.2 0.497 0.6 1.149 1.1 0.153 0.2 0.331 0.4 0.756 0.8 1.924 1.5 0.277 0.3 0.626 0.7 1.678 1.4 4.202 2.4 0.354 0.4 0.837 0.8 2.257 1.6 5.751 2.9

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THRUST2

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