Load Calculation for Cut & Cover Tunnel

Project: Project:

DMRC CC30: CC30: Design Design and construct construction ion of of undergrou underground nd metro metro corrido corridorr between ch. 3440.493m to 5641.450m

Part Part:: Subject: Subject:

Cut Cut & Cover Cover Tunn Tunnel el Sec Secti tion on bet betwe ween en cha chain inag age e ____ ______ __m m to ____ ______ ___m _m Calculati Calculation on of Backfill Backfill over over tunnel tunnel roof along along align alignment ment

Calculation of Backfill Depth along Tunnel Alignment: Sl. No. 1 2 3 4 5 6 7 8 9 10 11 12 13

Ground Level (GL) 215.844 215.762 215.895 215.947 219.163 216.411 216.228 216.388 216.008 215.926 216.019 215.983 215.908

Rail Level (RL) 207.62 207.485 207.285 207.085 206.959 207.052 207.322 207.607 207.893 208.463 208.749 208.034 209.319

Height from the Rail Level to Soffit of Roof Slab Thickness of Roof Slab The chainage of design section  Average ground level at design chainage Rail level at design chainage

Average GL GL 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 216.268 = = = = =

Avg.GL-RL 8.648 8.783 8.983 9.183 9.309 9.216 8.946 8.661 8.375 7.805 7.519 8.234 6.949

Earth Filling Depth 2.698 2.833 3.033 3.233 3.359 3.266 2.996 2.711 2.425 1.855 1.569 2.284 0.999

5.35 m 0.6 m

216.008 207.893

m m m

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Calculation of Support Spring Constants for STAAD Analysis

Calculations for Support Spring Constants at different Nodes 3

5100 kN/m

Subgrade modulus of soil below the foundation, k = (from sub-soil investigation data)

The tunnel structure is modeled in STAAD as 2D frame for per meter length of the tunnel. S.N. 1

Nodes Nos.

Dist. B/W Nodes (m)

Dist. Effective (in m)

Spring Constant (k*Dist. Effective)

55

0 -0.275

0.138

701

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Calculation of Support Spring Constants for STAAD Analysis

Calculations for Support Spring Constants at different Nodes 3

5100 kN/m

Subgrade modulus of soil below the foundation, k = (from sub-soil investigation data)

The tunnel structure is modeled in STAAD as 2D frame for per meter length of the tunnel. S.N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Nodes Nos.

Dist. B/W Nodes (m)

Dist. Effective (in m)

Spring Constant (k*Dist. Effective)

55 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 57

0 -0.275 0.000 0.275 0.575 1.075 1.575 2.075 2.575 3.175 3.675 4.175 4.675 5.100 5.400 5.550 5.700 6.000 6.500 7.000 7.500 7.925 8.425 8.925 9.425 9.925 10.525 10.825 11.100 11.375

0.138 0.275 0.288 0.400 0.500 0.500 0.500 0.550 0.550 0.500 0.500 0.463 0.363 0.225 0.150 0.225 0.400 0.500 0.500 0.463 0.463 0.500 0.500 0.500 0.550 0.450 0.288 0.275 0.138

701 1403 1466 2040 2550 2550 2550 2805 2805 2550 2550 2359 1849 1148 765 1148 2040 2550 2550 2359 2359 2550 2550 2550 2805 2295 1466 1403 701

0

X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Y 0 0.275 0.575 1.075 1.575 2.075 2.575 3.175 3.675 4.175 4.675 5.1 5.4 5.55 5.7 6 6.5 7 7.5 7.925 8.425 8.925 9.425 9.925 10.525 10.825 11.1 0 0 0 0 0 5.55 5.55 5.55 5.55 5.55 11.1 11.1 11.1 11.1 11.1 0 0.275 0.775 2.775 4.9 5.4 5.55 5.7 6.2 10.325 10.825

Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3 0.6 5.6 6.1 6.4 0.3 0.6 5.6 6.1 6.4 0.3 0.6 5.6 6.1 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4

X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

diff 0 0.275 0.575 1.075 1.575 2.075 2.575 3.175 3.675 4.175 4.675 5.1 5.4 5.55 5.7 6 6.5 7 7.5 7.925 8.425 8.925 9.425 9.925 10.525 10.825 11.1 0 0 0 0 0 5.55 5.55 5.55 5.55 5.55 11.1 11.1 11.1 11.1 11.1 0 0.275 0.775 2.775 4.9 5.4 5.55 5.7 6.2 10.325 10.825

Y 0.275 0.3 0.5 0.5 0.5 0.5 0.6 0.5 0.5 0.5 0.425 0.3 0.15 0.15 0.3 0.5 0.5 0.5 0.425 0.5 0.5 0.5 0.5 0.6 0.3 0.275

0 0.275 0.5 2 2.125 0.5 0.15 0.15 0.5 4.125 0.5

d5ff 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3 0.6 5.6 6.1 6.4 0.3 0.6 5.6 6.1 6.4 0.3 0.6 5.6 6.1 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4

 

0.3 0.3 5 0.5 0.3 0.3 0.3 5 0.5 0.3 0.3 0.3 5 0.5 0.3

54

11.1

6.4

0

54

11.1

0.275

6.4

Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Load Calculation for STAAD Analysis

Design Data:  Average Ground Level at Design Section, GL Ground Water Table below the ground level Ground Water Table at RL, GWT Total Height of Cut & Cover Tunnel Rail Level at the Design Section, RL Height of Rail above the Base Slab Roof Slab Thickness Base Slab Thickness External Wall Thickness Internal Wall Thickness Clear Height of the tunnel (internal clearance) Founding Level / Bottom of Base Slab Level Top of Roof Slab Level Thickness of Earthfill over Roof Slab

= = = = = = = = = = = = = =

Density of Reinforced Concrete Density of Plain Cement Concrete

= =

Dry Density of Soil, gdry

=

20.000

kN/m

Saturated Bulk Density of Soil, gsat

=

20.000

kN/m

Submerged Density of Soil, gsub

=

10.190

kN/m

Unit weight of Water, gwater 

=

9.810

kN/m

 Angle of internal friction of soil, f  Angle of wall friction, d Cohesion, C  At rest earth pressure co-efficient, K 0

= = = =

30.000 20.000

 Active earth pressure co-efficient, K a

=

0.279

216.008 0.000 216.008 7.000 207.893 0.450 0.600 0.600 0.550 0.300 5.800 206.843 213.843 2.165

m m m m m m m m m m m m m m 3

24 kN/m 3 22 kN/m

0.500

° ° 0 kN/m2

L/C - 1

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Load Calculation for STAAD Analysis

Self Welght: 3

Density of reinforced concrete is considered as 24 kN/m The Self Weight is applied in the STAAD software by the "Self Weight" command.

L/C - 2

Statically Imposed Dead Load (SIDL): Dead load due to rail track on base slab (Second Stage concrete) 450 mm thick second stage concrete is considered for dead load calculation purpose which includes 370 mm thick Secondary stage concrete and equivalent weight of 80mm thick concrete as weight of  rail and its fixtures. Load intensity

L/C - 3

=

0.45 x 22

= = =

2.165 m 3 20 kN/m 43.3 KN/m

Live Load on Concourse and Platform: There is no concourse and platform inside the cut & cover tunnel section. The live load is considered as =

L/C - 5

2

Soil Backfill Load: Thickness of backfill over the roof slab Density of Backfill Considered Backfill load at top of slab

L/C - 4

9.9 kN/m

=

0 kN/m

2

Train Live Load on Base Slab: 2

The live load due to train is considered as 15 kN/m over top of base slab.  As the tunnel section is modeled for 1m width only, the UDL on base slab =

15 kN/m

Lateral Earth Pressure: Lateral earth pressures on structural wall are calculated corresponding to following values of coefficient of lateral earth pressure. i) Coefficient of lateral earth pressure at rest = 0.5 ii) Coefficient of lateral earth pressure during active stage = 0.279 Lateral earth pressures shown below are at top of roof slab and at bottom of base slab.

L/C - 6

Dry Density of Soil, gdry

=

Saturated Bulk Density of Soil, gsat

=

20 kN/m 20 kN/m

Submerged Density of Soil, gsub

=

10.19 kN/m

Lateral Earth Pressure at Submerged Condition (Water Table at GL), K0 = 0.05  At rest earth pressure condition.

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Load Calculation for STAAD Analysis

Earth Pressure at top of tunnel roof = K0 x gsub x (GL - Top of Roof level) =

0.5 x 10.19 x (216.008 - 213.843)

=

11.031 kN/m

Earth Pressure at bottom of tunnel base slab = K0 x gsub x (GL - Bottom of Base Slab) =

L/C - 7

0.5 x 10.19 x (216.008 - 206.843)

=

46.696 kN/m

Lateral Earth Pressure at Submerged Condition (Water Table at GL), Ka = 0.279  Active earth pressure condition. Earth Pressure at top of tunnel roof = Ka x gsub x (GL - Top of Roof level) =

0.279 x 10.19 x (216.008 - 213.843)

=

6.155 kN/m

Earth Pressure at bottom of tunnel base slab = Ka x gsub x (GL - Bottom of Base Slab) =

L/C - 8

0.279 x 10.19 x (216.008 - 206.843)

=

26.056 kN/m

=

21.650 kN/m

Lateral Earth Pressure at Saturated Condition, K0 = 0.05  At rest earth pressure condition. Earth Pressure at top of tunnel roof = K0 x gsat x (GL - Top of Roof level) =

0.5 x 20 x (216.008 - 213.843)

Earth Pressure at bottom of tunnel base slab = K0 x gsat x (GL - Bottom of Base Slab) =

L/C - 9

0.5 x 20 x (216.008 - 206.843)

=

91.650 kN/m

=

12.081 kN/m

Lateral Earth Pressure at Saturated Condition , Ka = 0.279  Active earth pressure condition. Earth Pressure at top of tunnel roof = Ka x gsat x (GL - Top of Roof level) =

0.279 x 20 x (216.008 - 213.843)

Earth Pressure at bottom of tunnel base slab = Ka x gsat x (GL - Bottom of Base Slab) =

L/C - 10

0.279 x 20 x (216.008 - 206.843)

=

51.141 kN/m

Vertical Surcharge Load (on Roof Slab) 2

Vertical Surcharge load of 20 kN/m on normal ground level (vertical only) for roof slab only.

L/C - 11

Lateral Surcharge Load on Wall (Towards Right), K0 = 0.5 Vertical Surcharge Load at Ground Level is considered a = Earth pressure co-efficient =

24 kN/m 0.5

2

(infinite extent considered)

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Load Calculation for STAAD Analysis

Lateral earth pressure on Wall

L/C - 12

=

0.5 x 24

Lateral earth pressure on Wall

24 kN/m 0.5

=

0.5 x 24

2

(infinite extent considered)

12 kN/m

=

2

Lateral Surcharge Load on Wall (Both Sides), K0 = 0.5 24 kN/m 0.5

Vertical Surcharge Load at Ground Level is considered a = Earth pressure co-efficient =

2

(infinite extent considered)

12 kN/m

2

=

21.239 kN/m

2

9.81 x (216.008 - 206.843)

=

89.909 kN/m

2

9.81 x (216.008 - 206.843)

=

89.909 kN/m

2

Lateral earth pressure on Wall

L/C - 14

2

Lateral Surcharge Load on Wall (Towards Left), K0 = 0.5 Vertical Surcharge Load at Ground Level is considered a = Earth pressure co-efficient =

L/C - 13

12 kN/m

=

=

0.5 x 24

=

Water Pressure on Walls (Hydrostatic Pressure) Water Table at Level, GWT Top of Roof Slab Bottom of Base Slab Unit weight of Water, gwater 

= = = =

216.008 m 213.843 m 206.843 m 9.81 kN/m

Water Pressure at top of tunnel roof = gwater  x (GWT - Top of Roof level) =

9.81 x (216.008 - 213.843)

Water Pressure at bottom of base slab = gwater  x (GWT - Bottom of Base slab) =

L/C - 15

Uplift Water Pressure on the Base Slab Uplift Pressure

L/C - 16

=

Racking Force (Towards Right) The racking force is applied on the structure by applying a racking displacement calculated by Free Field Deformation of the soil. The detail calculation for the racking displacement is attached. The racking displacement is calculated as

L/C - 17

Racking Force (Towards Left)

=

3.6624 mm (towards right)

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Load Calculation for STAAD Analysis

The racking force is applied on the structure by applying a racking displacement calculated by Free Field Deformation of the soil. The detail calculation for the racking displacement is attached. The racking displacement is calculated as

=

3.6624 mm (towards left)

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Calculation of Free Field Raking Displacement

Introduction: Evaluation of Free Field Raking effect on under ground structures due to earth quake. For Raking only the f ree field deformation is considered ignoring the soil structure interaction. This assumption is on conservative side. The effect of soil structure interaction is to decrease the raking effect but even for  very soft soil, this reduction is of the order of 15% only.

Main References: 1. Hashash, Y.M.A., Hook, J.A., Schmidt, B., Yao, J., "Seismic Design and analysis of Underground Structures". 2. Wang, J., "Seismic Design of Tunnels". 3. Kuesel, R.K., "Earthquake design criteria for subways". 4. Macormick.

Data: Overall height of tunnel, H = Height of earth fill over roof = Gravitational Acceleration, g =

7 m= 2.165 m 2 9.807 m/sec =

7000 mm 2

980.7 m/sec

2.0 SEISMIC PARAMETRS 2.1 Peak Ground Acceleration (amax): MDE (Max Design Earthquake) or MCE (Max Considered Earthquake) = 0.24 x g =

From IS:1893-2002: Z 0.1 0.16 0.24 0.36

Zone 

II III IV V

= Z 0.24 =

(From DMRC) Intensity MSK64 VI or less low moderate VII VIII severe IX or more very severe

ODE (Operating Design Earthqake) or DBE (Design Basis Earthquke) = 0.12 x g =

x

Seismic Zone =

980.7 2 235.368 cm/sec

IV

= Z/2 0.12 =

x

980.7 117.684 cm/sec2

2.2 Peak Ground Acceleration at Depth (as): Overall height of tunnel, H = 7 Height of earth fill over roof = 2.165 Therefore, Depth of Tunnel (C.G. from the GL) =

m m 2.165 + 7 / 2 =

5.665 m

Depth factor considered as 1 from the table below as =

1 x amax =

1.0

x

0.24 =

0.24

Table 4 of Ref 1

Tunnel Depth(m)

Ratio of ground motion at tunnel depth to motion at

IS :1893-1984 for info only

Depth, d =

Project:

DMRC CC30: Design and construction of underground metro corridor between ch. 3440.493m to 5641.450m

Part: Subject:

Cut & Cover Tunnel Section between chainage ______m to _______m Calculation of Free Field Raking Displacement

5.665 m

ground surface

30

1 0.9 0.8 0.7

depth

ratio

0

1

30

0.5

2.3 Peak Ground Velocity(Vs): Ratio Vs (cm/sec) / amax (g) =

Table 2 of Ref 1

Moment Magnitude Mw (Ref 4) Rock 6.5 7.5 8.5

Ratio Vs(cm/sec)/amax(g) Source - to - Site Distance (Km) 0-20 20-50 2 3

109

Derived from Vs

Range of Share Velocity (m/sec) 50-100 4 >750

66 97 127

76 109 140

86 97 152

Stiff Soil 6.5 7.5 8.5

200-750 94 140 180

102 127 188

109 155 193

Soft Soil 6.5 7.5 8.5

140 208 269

132 165 244

142 201 251