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Design of Unpaved RoadsDesign of Unpaved RoadsDesign of Unpaved RoadsDesign of Unpaved Roads

A Geotechnical PerspectiveA Geotechnical PerspectiveA Geotechnical PerspectiveA Geotechnical Perspective

� CGTR 2017CGTR 2017CGTR 2017CGTR 2017

� NERISTNERISTNERISTNERIST

Arindam DeyAssistant ProfessorDepartment of Civil Engineering

Geotechnical Engineering DivisionIIT Guwahati

Introduction

• Road Network in India

� Over 42 lakh kms (CIA, 2012)

� 48% Unpaved Roads (MoRTH, 2008)

• Unpaved roads (Includes haul roads and access roads)

� Sand or stone aggregate placed directly over the local soil subgrade

� No permanent surfacing before immediate application

• Constant passage of traffic over time

� Settlement

� Rutting

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Layout of the Presentation

• Unpaved Roads

� Quasi-Static Analysis and Formulations : Design Charts

� Influence of Traffic

� Numerical FE Modeling: PLAXIS 2D v2012 : Safe Designing Methodology

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Axle Load on an Unpaved Road: Load Distribution

• Total load

� Replaced by Equivalent single axle load(P)

• Evenly distributed (4 wheels)

• Axle load expressed in terms of

� Contact areas of tires (Ac)

� Tire inflation pressures (Pc)

• Contact area

� Equivalent rectangular contact area(LxB).

� Assumption: Equivalent uniformlydistributed contact pressure (Pec)

• Dual tire printsEquivalent Contact Dimensions: Present Study

� On-Highway trucks

� Off-Highway trucks

2c

L B B P P= =

2 2c

L B B P P= =

Geometry of unpaved road, vehicle axle loads and contact

areas [Adopted from Giroud and Noiray(1981)]

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(Giroud and Noiray, 1981)

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Load Distribution by Aggregate Layer on Subgrade

• Load-Distribution Shape

� Pyramidal

� Load-dispersion angle (α0)

• Stresses generated on the aggregate-subgrade interface

� With geotextile �p , Without geotextile � p0

• Aggregate thickness

� With geotextile � h, Without geotextile � h0

0 4 2aggα α π φ= = −

( )( )

( )( )

0 0

0 0 0 02 2 tan 2 tan

2 2 tan 2 tan

Pp h

B h L h

Pp h

B h L h

γα α

γα α

= ++ +

= ++ +

Load distribution by aggregate layer on the subgrade soil (a) Without

geotextile (b) With geotextile [Giroud and Noiray(1981)]

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( )0

2

u

u

p c

p c

π

π

=

= +

Idea from Past Research

• Proposed design charts

� Uses only undrained cohesion

• c-φ soil: Strength Parameters

� Cohesion

� Angle of internal friction

• Conventional Design Charts

� Over estimation of aggregate layer thickness

� Only a degenerated condition

• Improvisation over the Giroud & Noiray’s Model (1981)

� Accounts internal friction angle of soil subgrade

� Reveals substantial reduction in aggregate thickness (Compared after inclusion of φ)

� Accounts moving load as static

• Maximum axle load

• “Quasi-Static Analysis”

� Detailed parametric study

• Influence & Sensitivity of various contributory parameters.

� Design Charts (with & without Geotextiles) for several combination of various parameters

Present Study6

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Quasi-static Analysis of Unpaved Roads

• Unpaved roads: Aggregate cover

� Acts as load-dispersing mechanism � Reduce subgrade stresses

� Minimizes hindrance for passage of vehicles

• Shear strength of the soil (Mohr-Coulomb expression)

• Allowable bearing capacity (qall) (Terzaghi, 1943)

� Bearing capacity factors

tancτ σ φ= +

00.5 '

c q

all

cN h N B Nq

FOS

γγ γ+ +=

32( )

4 2 2cos( )4 2

2( 1) tan

( 1)cot

q

q

c q

N e

N N

N N

π φ

γ

π φ

φ

φ

−

= +

= +

= −

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Design of Unpaved Road without Geotextile

• Net pressure on the subgrade soil

• Net Pressure ≤ Allowable Bearing Capacity (FOS=1)

• Solution � Required thickness of aggregate layer on c-φ subgrade without geotextile

Load distribution by aggregate layer on the

subgrade soil without geotextile [Giroud and

Noiray(1981)]

( )( )0 0

0 0 0 02 2 tan 2 tan

Pp h

B h L hγ

α α= +

+ +

0 0 0 0

0 0 0 0

0.5 ( 2 tan )2( 2 tan )( 2 tan )

c q

Ph cN h N B h N

B h L hγγ γ γ α

α α+ = + + +

+ +

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Design of Unpaved Road with Geotextile

• Subgrade soil

� Undrained and Incompressible

• Geotextile

� Stretched wavy shape due to settlement under tires and heave in between them

• Generation of tension membrane effect

� Reduction of pressure by geotextile : pg

• Pressure transferred to subgrade soil, p*(portion AB)

*

gp p p= −

Kinematics of unpaved roads with geotextile [Giroud and Noiray(1981)]

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Design of Unpaved Road with Geotextile

• Pressure (p*) ≤ Allowable bearing capacity of the subgrade soil

K� Tension-elongation modulus

ε� Elongation of Geotextile

s� Function of rut depth(r)

FOS =1

• Solution � Required thickness of aggregate layer on c-φ subgrade with single layer of geotextile

* 0.5 ( 2 tan )2( 2 tan )( 2 tan )

g c q

Pp h p cN hN B h N

B h L hγγ γ γ α

α α= + − = + + +

+ +

( )2

1 2 tan 22

g

ap K a a B h

sε α

= + = +

'1

'

b b

a aε

+= −

+

Shape of deformed geotextile [Giroud and Noiray (1981)]

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Parameters…

• MATLAB codes

� Compute required aggregate thickness (with and without geotextile layer)

• Sensitivity plotted

� For various important parameters

Range of various parameters chosen (Indian traffic conditions)

Axle Load (P) 30 kN–360 kN (MoRTH, GoI, 2005; IRC-37-2001)

Tire inflation pressure (Pc) 150 kPa–750 kPa (AFJM, 1994; Khanna and Justo,

2001)

Angle of internal friction of

aggregate (φagg)

25°– 35°

Angle of internal friction of soil

(φ)

0-50°[Covers the broad domain of soil- purely

cohesive soil to rocky subgrade]

Soil cohesion (c): 0–500 kPa [Covers purely cohesionless soil to hard

clay in the subgrade]

Unit weight of soil and

aggregate (γ):

19 kN/m3 [Kept same- No significant variation in γ ]

Track widths of Indian Cargo

vehicles (e)

1.7 – 2.6 m

Tension-elongation modulus of

geotextiles (K)

1-5000 kN/m (Giroud and Noiray, 1981)

Factor of safety (FOS): 1 – 2 [FOS =1 (ultimate bearing capacity) other FoS

(allowable bearing strength)]

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Design Charts: Effect of Cohesion of subgrade soil

• Soft soil: Very low c and φ values

� Immensely thick aggregate layer

• Optimum cohesion of 30 kPa to substantially reduce

the aggregate layer thickness

� Adopt some subgrade modification techniques for

soils with natural cohesion less than 30 kPa

• Application of geotextiles can be a solution

• Stiffer clays

� Theoretically no necessity of aggregate layer

• With Geotextile

• Without Geotextile12

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Design Charts: Effect of Angle of Internal Friction of subgrade soil

• Subgrade containing coarser soil particles

� Enhanced angle of internal friction

• Increase in bearing strength � Substantialreduction in the required aggregate thickness

• Analysis by Giroud and Noiray (1981)

� Based on purely cohesive soils

• Results in overestimated results for naturalsubgrade soils having cohesionless particles aswell

• With Geotextile

• Without Geotextile13

Design Charts: Effect of Axle Load and Tire Pressure

• Increment in Axle Load

� Required aggregate thickness is higher

• Obvious observation

• Increment in tire inflation pressure

� Does not significantly affect the requiredaggregate thickness for lower axle loads

• Lower tire inflation pressure �Higher equivalent contact area

• With Geotextile • With Geotextile

c=5 kPa, aggϕ = 35°, soilϕ = 5°, K=100 kN/m, r=0.3 m, e=1.7 m c=5 kPa, aggϕ = 35°, soil

ϕ = 5°, K=100 kN/m, r=0.3 m, e=1.7 m

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Benefit from Geotextile: Tensile Strength• Depicts benefit of geotextiles :

� Enhanced tensile strength of geotextile

• Reduction in required aggregate thickness

� Zero tensile strength

• Absence of geotextile

• Efficacy of geotextiles

� Degree of improvement (If)

• 100% improvement theoretically signifies that aggregate cover is not necessary

• With Geotextile

• With Geotextile

0

0

100i

f

K KI

K

−= ×

0Ki

K = Thickness at initial K value = Thickness at final K value

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Effect of Rut Depth• Lower rut depths

� Negligible or Nil efficacy of geotextiles

• Reconfirms the finding of Holtz and Sivakugan (2005)

• Larger rut depth

� Large deformation

• Enhanced mobilization of membranetension � Increased efficiency of thegeotextile� Substantial reduction in h

• With Geotextile

• With Geotextile

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Benefit from Geotextile: Comparison

• The reduction in thickness increases with increase in tensile strength- Economy

• Comparison shows a reduction of ~200 mm Aggregate layer thickness

• With Geotextile: (K= 100 kN/m)

• With Geotextile: (K= 400 kN/m)

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Typical Quick Design Charts: Unreinforced and Reinforced Case

Without Geotextile With Geotextile

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Influence of Traffic

N=10

N=100

N=1000

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Influence of traffic

• Webster and Alford’s Expression

� For rut depth= 0.075 m

� Standard Axle load= 80 kN

• Need to extend the applicability

� Rut depth

� Other Axle Loads

� Bearing capacity of subgrade

Black’s Expression (Field test data)

• Equation: Multiple passage

� Solution Technique : MATLAB

� Yields cumulative aggregate thickness (hm)

( )0.63

0.19 logs

m

Nh

CBR=

3.95

s i

i s

N P

N P

=

( )log log 2.34 0.075s s

N N r⇔ − −

s iP P⇔

10uq CBR=

( )0.63

0.81log 3.19 log 1.89 5.95i i

m

u

N P rh

q

+ − −=

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Design Charts without Geotextile: Multiple Passage

Multiple Passage: Without Geotextile Multiple Passage: Without Geotextile

P = 80 kN P = 190 kN

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Design Charts with Geotextile: Multiple Passage

Multiple Passage: With Geotextile

K = 500 kN/m, e = 1.7

Multiple Passage: With Geotextile

K = 1000 kN/m, e = 1.7

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Summary…

• Accounting both subgrade strength parameters (c & φ) in present study

� Realistic estimation of h- Economical design

� Influential contributory parameters

• Axle load (P)

• Subgrade strength parameters (c and φ)

• Angle of internal friction of aggregate (φagg)

� Parameters having minimal effects on required aggregate thickness

• Tire inflation pressure (for lower axle loads)

• Location of vehicles

� Tensile strength of geotextile

• Significantly affects degree of improvement (in terms of reduction in h)

� Beneficial effect of geotextile is highlighted for higher rut depths (elevated ‘tensioned membrane’ effect)

� Cumulative Aggregate Thickness � Based on Empirical formulas � not for N > 10,000

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Need for Continuum Modeling

• Lack of practical applicability� Very low value of subgrade strength�High aggregate thickness (Vice-Versa)

• Construction Failure

� Unbound Aggregate �Mechanically unstable

• Punching Failure

• Fine content required � 4-8% (IRC:SP:77-2008)

• To bring Precision � Limit Equilibrium - Finite Element Approach

� LE: Simplification for complex numerical problem – Resort to FE approach

� Propagation of failure

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Modeling tool

• PLAXIS 2D v2012

� Performs deformation & stability analysis – Geotechnical applications

� Convenient GUI : allows automatic generation of 2D FE mesh (Global and Local refinement)

� Realistic construction simulation : allows activating, de-activating element clusters, loads

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Present Study: Model Description

• Model Type

� Plain Strain Geometry

• Uniform cross-section

• Same stress state perpendicular to cross-section

• Model Geometry� 2 Layered System

• Subgrade & Aggregate

� Side Slopes

• 3H: 1V (stable side slope)

� Model Boundaries

Properties Subgrade Aggregate

Constitutive Model Mohr-Coulomb Mohr-Coulomb

Unit Weight (γ) 19 kN/m² 19 kN/m²

Elastic Modulus (E) 6 MPa 20 MPa

Poisson’s Ratio (ν) 0.4 0.3

Initial Void Ratio (eint) 0.5 0.1

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Model Geometry: Unreinforced Model

Unreinforced Model Geometry Finite Element Mesh: Triangular- 15 nodded

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Failure under Aggregate Load

• Checking Stability

� csoil , φsoil , φagg: Analytical results

� cagg= 0.001 (to avoid numerical instability)

• Result: Failure in Subgrade

� During lay of aggregate

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Critical/Limiting Failure Conditions

• Subgrade Failure� Aggregate Load ≤ Allowable Bearing Capacity of Subgrade

,min

0

0.5s c s

s

c N BNh

FOS

γγγ

+=

Failure Zone Cmin chart

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Failure under Vehicular Loading

• Checking Stability

� cs,min , φsoil , φagg: Analytical results

� cagg= 0.001 (to avoid numerical instability)

• Result: Failure in Aggregate

� Due to punching

• Mechanical Instability

• Absence of Fine soil

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Critical/Limiting Failure Conditions

• Aggregate Failure

� Stress intensity under tire ≤ Allowable Bearing Capacity of Aggregate

• Result

� With each φagg : Different FOS

� Variation in axle load: Varying stress distribution angle � different stress intensities

• Stability Check : Excessively strong Subgrade

,min 0.5

2

a c ac N tNP

tL FOS

γγ+=

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Combined Configuration

• Subgrade

� cs,min , φsoil : Determined from failure

only due to aggregate load

• Aggregate

� ca,min , φagg : Determined only from

punching failure of aggregate under vehicle load

• Loading� Subgrade fails: enhancement of

parameters required (cs,min� csa,min )

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Estimation of enhanced Subgrade cohesion (csa,min)

• Parametric Trial-and-Error determination• Determination of the property enhancement zone

� Total Deviatoric Strain plot

� Total Displacement plot

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Design Methodology: Unreinforced Case

Geometry and Cluster Parameters: Design ChartsGeometry and Cluster

Parameters: Design Charts

If subgrade fails :Aggregate loadIf subgrade fails :Aggregate load

Find cs,minand test model with this valueFind cs,minand test

model with this value

Passes: Test Aggregate under load

Passes: Test Aggregate under load

Passes: OKPasses: OKFails: Find ca,min and test model

Fails: Find ca,min and test model

Passes: Find csa,minand test model

Passes: Find csa,minand test model

Passes : OKPasses : OK

Fails : Fine TuneFails : Fine Tune

Fails: Fine Tune

Fails: Fine Tune

Fails: Fine TuneFails: Fine Tune

If subgradepasses : OKIf subgradepasses : OK

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Thickness Reduction using GeotextileModel Number 3674 8000 1900 2400 63352

Model Load P = 30 kN P = 80 kN P =190 kN P = 240 kN P = 360 kN

Initial model height 1.14 m 0.72 m 1.1 m 1.24 m 1.46 m

Reduced height without

geotextile0.5 m 0.70 m 1.05 m 1.15 m 1.46 m

Reduced height with

geotextile0.4 m 0.55 m 0.65 m 0.75 m 1.20 m

Reduction due to

geotextile0.10 m 0.15 m 0.4 m 0.4 m 0.2 m

Percentage Reduction 20 % 21.42 % 38.09 % 34.78 % 14.28 %

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Conclusions…

• To impart mechanical stability to Stacked Unbound Aggregate

� Mixture of aggregate, sand, fine-sized particles

• Stress distribution angle

� Presence of fine material in cluster voids � Varies with varying axle load even for same φ value

• Modification of Strength Parameters: Subgrade

� Based on strain concentration pattern under operational conditions

• Advantage of Numerical MOdelin

� Coupled stress-deformation based analysis (c-φ soil)

� Different from conventional stress based stability of only cohesive soil

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