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GEOGRID DESIGN FOR RAILWAY BASE ON SOFT SOIL

by Petrucio Santos

INTRODUCTION

Geogrid reinforcement of roads/railways and parking decks on soft soil needs to be

designed on the base of sound engineering principles.

Geogrids provide the following reinforcing mechanisms:

- base course lateral restrain mechanism for horizontal stresses generated by deck soil

self weight;

- base course lateral restrain mechanism for horizontal stresses generated by wheels

loading;

- membrane mechanism at the deck – subgrade interface.

Each of these three mechanisms produce tensile forces in geogrid reinforcement layers.

The general scheme of a road or a parking deck may include the following layers:

- asphalt course AC (the wearing course and the binder layer are considered as one only

layer whose thickness is the total thickness of the two ones);

- base course BC;

- subbase course SB;

- subgrade SG.

Therefore a 4 layers model has been developed for geogrid design: the general scheme of

the model and all symbols, that will be used for subsequent calculations, are shown in

the following Figure.

WHEEL LOAD

Design axle load [kN] W 100:=

Wheel load [kN] PW

250=:=

Tyre inflation pressure [kPa] p 700:=

Radius of equivalent contact area [m] roP

p π⋅0.151=:=

Equivalent Standard Axle Load (ESAL) [kN] Pa 80:=

TRUCK LOAD FOR FIRST

radius of wheel (circular contact area) [m ] rw 0.15:=

Tire pressure [kPa] pw 600:=

Thickness [m] hw 0.30:=

ASPHALT BASE

Unit weight [kN/m³] g1 24:=

Thickness [m] h1 0.1:=

Load spreading angle [deg] a1 55:=

BASE COURSE

Unit weight [kN/m³] g2 20:=

Friction angle phi2 35:=

Cohesion [kPa] c2 0:=

Base course thickness [m] h2 0.60:=

Load spreading angle [deg] a2 45:=

Number of layers Nr2 2:=

Average geogrid spacing [m] Sv2 Sv2 0← Nr2 0=if

Sv2h2

Nr2← Nr2 0≠if

Sv2 Sv2←

Sv2

0.3=:=

Active pressure coefficient K2 tan 45phi2

2−

deg⋅

2

0.271=:=

SUBBASE COURSE

Unit weight [kN/m³] g3 18:=

Friction angle [deg] phi3 35:=

Cohesion [kPa] c3 0:=

Subbase course thickness [m] h3 0.3:=

Load spreading angle [deg] a3 40:=

Number of layers Nr3 1:=

Average geogrid spacing [m] Sv3 Sv3 0← Nr3 0=if

Sv3h3

Nr3← Nr3 0≠if

Sv3 Sv3←

Sv3

0.3=:=

Active pressure coefficient K3 tan 45phi3

2−

deg⋅

2

0.271=:=

SUBGRADE

CBR CBRsg 1:=

FS BEARING CAPACITY FSbc 3:=

MEMBRANE THEORY COEFFICIENT

omg e( ) om 2.07← e 1=if

om 1.47← e 2=if

om 1.23← e 3=if

om 1.08← e 4=if

om 0.97← e 5=if

om

:=

VALUES AT LAYERS INTERFACES

Asphalt layer bottom

z1 h1 0.1=:=

r1 ro z1 tan a1 deg⋅( )⋅+ 0.294=:=

sv1 pro

2

r12

⋅ 184.631=:=

Base course bottom

z2 h1 h2+ 0.7=:=

r2 r1 z2 z1−( ) tan a2 deg⋅( )⋅+ 0.894=:=

sv2 sv1r1

2

r22

⋅ 19.931=:=

Subbase bottom

z3 h1 h2+ h3+ 1=:=

r3 r2 z3 z2−( ) tan a3 deg⋅( )⋅+ 1.145=:=

sv3 sv2r2

2

r32

⋅ 12.133=:=

GEOGRID DESIGN FOR BASE COURSE

LAYER NUMBER (until 5 layers)

Position of reinforcement from

base course bottomPosition of reinforcement from top of layer

Hbc

0

0.30

0

0

0

0

:= Zbc i 0←

Zi

z1← i Nr2( )≥if

Zi

z2 Hbci

−← i Nr2<if

i 0 5..∈for

Zbc Z←

Zbc

0.7

0.4

0.1

0.1

0.1

0.1

=:=

Horizontal forces acting:

Soil_Thrust

Wheel_Loading

j 0←

Tzj

0←

rj

r1←

svj

0←

j Nr2 1+≥if

Tzj

0.5 K2⋅ 2 g1⋅ h1⋅ g2 Zbcj

Zbcj 1+

+ 2 h1⋅−( )⋅+ ⋅ Zbc

jZbc

j 1+−( )⋅←

rj

r1 Zbcj

z1−( ) tan a2 deg⋅( )⋅+←

svj

sv1r1

2

rj( )

2

⋅←

j Nr2 1+<if

j 0 5..∈for

Tpk

0.5 K2⋅ svk

svk 1+

+( )⋅ Zbck

Zbck 1+

−( )⋅← k Nr2 1+<if

Tpk

0← k Nr2 1+≥if

k 0 5..∈for

Tz Tz←

Tp Tp←

Tz

Tp

:=

Soil_Thrust

0.927

0.439

0

0

0

0

= Wheel_Loading

2.646

9.341

0

0

0

0

=

First_lift_ro rw 0.15=:=

First_lift_hw hw 0.3=:=

First_lift_rf First_lift_ro First_lift_hw tan a2 deg⋅( )⋅+ 0.45=:=

First_lift_tp pw 600=:=

First_lift_Afπ

4

First_lift_rf2

⋅ 0.159=:=

Wtc2 Wtc2 0← h3 0>if

W11

3g2⋅

First_lift_rf3

First_lift_ro3

−( )

First_lift_rf2

tan a2 deg⋅( )⋅( )⋅←

W2 First_lift_tpFirst_lift_ro

2

First_lift_rf2

⋅ 60 π⋅CBRsg

FSbc

⋅−←

Wtc2 W1 W2+←

h3 0≤if

Wtc2 Wtc2←

Wtc2

0=:=

εr2 3:=

omega omg εr2( ) 1.23=:=

Tm2 Tm2 0← h3 0>if

Tm2 0← Wtc2 0≤if

Tm2 Wtc2 First_lift_rf⋅ omega⋅← Wtc2 0>if

h3 0≤if

Tm2 Tm2←

Tm2

0=:=

Tot Soil_Thrust Wheel_Loading+

3.573

9.78

0

0

0

0

=:=

Tot0

Soil_Thrust0

Wheel_Loading0

+ Tm2+:=Tot

3.573

9.78

0

0

0

0

=

GEOGRID DESIGN FOR SUBBASE COURSE

LAYER NUMBER (until 5 layers)

Position of reinforcement from

base course bottomPosition of reinforcement from top of layer

Hsbc

0

0

0

0

0

0

:= Zsbc i 0←

Zi

z2← i Nr3( )≥if

Zi

z3( ) Hsbci

−← i Nr3<if

i 0 5..∈for

Zsbc Z←

Zsbc

1

0.7

0.7

0.7

0.7

0.7

=:=

Horizontal forces acting:

Soil_Thrust_sb

Wheel_Loading_sb

j 0←

Tzj

0←

rj

r1←

svj

0←

j Nr3 1+≥if

CTE1 g3 Zsbcj

Zsbcj 1+

+ 2 h2⋅−( )⋅←

CTE2 Zsbcj

Zsbcj 1+

−( )←

Tzj

0.5 K3⋅ 2 g1 h1⋅ g2 h2⋅+ 2 h2⋅−( )⋅ CTE1+[ ]⋅ CTE2⋅←

rj

r2 Zsbcj

z2−( ) tan a3 deg⋅( )⋅+←

svj

sv2r2

2

rj( )

2

⋅←

j Nr3 1+<if

j 0 5..∈for

Tpk

0.5 K3⋅ svk

svk 1+

+( )⋅ Zsbck

Zsbck 1+

−( )⋅← k Nr3 1+<if

Tpk

0← k Nr3 1+≥if

k 0 5..∈for

Tz Tz←

Tp Tp←

Tz

Tp

:=

Soil_Thrust_sb

1.439

0

0

0

0

0

= Wheel_Loading_sb

1.303

0

0

0

0

0

=

First_lift_ros rw 0.15=:=

First_lift_hws hw 0.3=:=

First_lift_rfs First_lift_ro First_lift_hw tan a3 deg⋅( )⋅+ 0.402=:=

First_lift_tps pw 600=:=

First_lift_Afsπ

4

First_lift_rfs2

⋅ 0.127=:=

Wtc3 Wtc3 0← h3 0=if

W11

3g3⋅

First_lift_rfs3

First_lift_ros3

−( )

First_lift_rfs2

tan a3 deg⋅( )⋅( )⋅←

W2 First_lift_tpFirst_lift_ros

2

First_lift_rfs2

⋅ 60 π⋅CBRsg

FSbc

⋅−←

Wtc3 W1 W2+←

h3 0≠if

Wtc3 Wtc3←

Wtc3

23.541=:=

εr3 3:=

omega2 omg εr3( ) 1.23=:=

Tm3 Tm3 0← h3 0=if

Tm3 0← Wtc3 0≤if

Tm3 Wtc3 First_lift_rfs⋅ omega2⋅← Wtc3 0>if

h3 0≠if

Tm3 Tm3←

Tm3

11.632=:=

Tot_sb Soil_Thrust_sb Wheel_Loading_sb+

2.742

0

0

0

0

0

=:=

Tot_sb0

Soil_Thrust_sb0

Wheel_Loading_sb0

+ Tm3+:=

Tot_sb

14.375

0

0

0

0

0

=