GEOSYNTHETICS ASIA 2012

5th Asian Regional Conference on Geosynthetics

13 to 15 December 2012 | Bangkok, Thailand

DESIGN METHOD FOR GEOGRID REINFORCEMENT OF

ROAD BASES

P. Rimoldi 1, M. Scotto2, and D. Ghosal3

1
Officine Maccaferri SpA, Italy; Tel: +39-051-6436000; Fax: +39-051-6436201;
Email: pietro.rimoldi@gmail.com
2
Officine Maccaferri SpA, Italy; Tel: +39-051-6436000; Fax: +39-051-6436201;
Email: moreno.scotto@gmail.com
3
Maccaferri Malaysia Sdn Bhd, Tel: +60-3-79557800; Fax: +60-3-79557801;
Email: ghoshal@maccaferri-asia.com

ABSTRACT

Geogrids are extensively used for reinforcing paved and unpaved road bases on soft soils. Anyway the
present design methods provide no indication for the number of required layers and the mechanical
characteristics of reinforcing geogrids. Hence a new design method has been developed which affords the design
of geogrids for road base reinforcement, based on a 4 layers model: asphalt (binder and wearing course), in case
of paved roads; base, subbase, subgrade. Once the base and/or subbase thickness has been defined with one of
the available methods (as an example: Giroud – Han method, Leng- Gabr method, etc.), the proposed design
method affords to calculate the tensile forces in reinforcing geogrids generated by: self weight of the different
layers; wheel load of heavy vehicles; membrane effect at the base (or subbase) – subgrade interface. It is then
possible to set the number and the mechanical characteristics of geogrid layers required for absorbing the
horizontal forces generated by the above listed mechanisms. Hence the proposed design method affords the
design of geogrids in the safe construction of paved and unpaved roads on soft soil.

Keywords: Geogrids, road bases, design method

INTRODUCTION roads, the limit state criterion cannot be the failure

but rather the operating condition criterion, that is
The design methods for paved and unpaved the deformations shall be limited.
roads (as an example: Giroud – Han method, Leng- To achieve this goal we must put a limit on
Gabr method, etc.) usually assume that the road geogrid strain: both theory and practical experience
base is reinforced with just one geogrid layer, but suggest that geogrid strain shall be limited to 5 %.
the actual required geogrid reinforcement needs to Obviously, more important is the road structure
be designed on the base of sound engineering we are designing and lower the design geogrid strain
principles. shall be. Hence for important structures the geogrid
Geogrids provide the following reinforcing strain shall be limited to 2 %, while for less
mechanisms: important structures (or when the design conditions
- base course lateral restrain mechanism for afford slightly larger deformations) 3 %, 4 % or 5 %
horizontal stresses generated by the soil geogrid strain can be acceptable. We must take into
self weight; account the fact that roads are never subject to long
- base course lateral restrain mechanism for lasting applied load, rather they are subject to instant
horizontal stresses generated by wheels loads when there is wheels passage. Hence the
loading; geogrid strain limit shall be applied to short term
- tensioned membrane mechanism at the base tensile strength, as measured in a wide width tensile
or subbase – subgrade interface. test according to EN ISO 10319 standard.
Each of these three mechanisms produce tensile The scope of the present paper is to present a
forces in geogrid reinforcement layers. method for defining the tensile forces produced on
Sound engineering principles dictate to calculate geogrid layers by the three active mechanism above
these tensile forces, and the overall tensile forces identified, then for designing the number and
generated in each layer of geogrids, and then to vertical position of the required geogrid layers, once
select the appropriate geogrid for each layer based the required base and/or subbase thickness has been
on a limit state criterion. defined with the available design methods for paved
When we are dealing with paved or unpaved and unpaved roads.

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GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

MULTI-LAYER MODEL above it, can be easily calculated based on classic

geotechnical theory.
The general scheme of a road or a parking deck The vertical stress at depth Z1, due to asphalt self
may include the following layers: weight, is:
- asphalt course AC (wearing course and binder
layer are considered as one only layer whose σvi = γ1 Z1 (1)
thickness is the total thickness of the two ones);
- base course BC; where:
- subbase course SB; γ1 = unit weight of the asphalt layer (kN/m3)
- subgrade SG.
Therefore a 4 layers model has been developed For Z1 < Z < Z2:
for geogrid design: the general scheme of the model
and all symbols, that will be used for subsequent σv = γ1 Z1 + γ2 (Z – Z1) (2)
calculations, are shown in Fig. 1.
The related horizontal stress is:

Fig. 1 - General scheme of the 3 layers model

The model assumes that the wheel load is applied σh = K2 σv (3)

as a uniform vertical pressure σv0 = p (tyre inflation
pressure) on a circular area with equivalent radius where:
r0; this load spreads in the 3 layers of the road K2 = tan2(45° - φ2 / 2) = active soil thrust
structure (AC, BC and SB) according to their load parameter for BC (4)
spreading angles α1, α2, α3. φ2 = friction angle of BC
At least the base course shall be present and shall
be reinforced with geogrids; the asphalt course may Then we assume that the tensile force T zi
not be present (in case of an unpaved road) and, if generated in the i-th geogrid in the base course is the
present, it is not reinforced; the subbase course may integral of the horizontal soil stresses between the i-
be present or not; when it is present, it may be either th geogrid layer and the (i-1)th geogrid layer:
reinforced with geogrids or unreinforced.
Tzi = 0,5 K2 [ γ2 (Zi2 – Zi2-1) + γ1 Z1 ] (5)

FORCE DUE TO HORIZONTAL SOIL For Z2 < Z < Z3:

THRUST
σv = γ1 Z1 + γ2 (Z2 – Z1) + γ3 (Z – Z2) (6)
The tensile force Tzi , generated in the i-th
geogrid layer by the horizontal thrust of the soil The related horizontal stress is:

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 GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

σh = K3 σv (7) TPi = 0,5 (σhi + σhi-1) (Zi – Zi-1) (19)

where:
K3 = tan2(45° - φ3 / 2) = active soil thrust FORCE DUE TO MEMBRANE MECHANISM
parameter for SB (8) AT THE INTERFACE WITH SUBGRADE
φ3 = friction angle of SB
The first geogrid layer, at the interface with the
The tensile force Tzi generated in the i-th geogrid subgrade, is subject to the highest vertical
in the subbase course is: deformations, when the first soil layer is spread and
compacted, due to the settlement of the soft
Tzi = 0,5 K3 [ γ3 (Zi2 – Zi2-1) + γ1 Z1 + subgrade; the next geogrid layers, instead, are far
+ γ2 (Z2 – Z1) ] (9) less subject to vertical displacements.
Hence we can reasonably assume that the first
geogrid layer is subject to the tensioned membrane
FORCE DUE TO HORIZONTAL STRESSES mechanism, that is the first geogrid can be
GENERATED BY WHEELS LOADING considered as a catenary layer, while for the next
layers such mechanism is negligible.
If we assume that the wheel load is applied on a We will refer to the scheme shown in Fig. 2.
circular area of equivalent radius r0 and that the
load spreads in the layers below as a cone whose First Case: When the Subbase is not Present.
generatrix is inclined of the load spreading angle αi,
then the radius r at depth Z below the top surface is: According to tensioned membrane theory
(Giroud et Al, 1990), the uniform vertical load WTC
For 0 < Z < Z1: on the catenary layer of reinforcement is:

r = r0 + Z tan α1 (10) WTC = [(volume V of load cone below the wheel) ·

(fill density γ) + wheel load P – subgrade reaction
Since it must be: π r02 σv0 = π ri2 σvi R] / (area A at reinforcement catenary layer)
then the vertical stress produced by the wheel load
at depth Z is: For the geogrid layer at base course bottom V
and A become:
σv = σv0 r02 / ri2 (11)
V = 1/3 π rf2 hf – 1/3 π r02 (hf – Zf) (20)
For Z1 < Z < Z2:
A = π rf2 (21)
r = r1 + (Z – Z1) tan α2 (12)
where: Zf = depth of first base course lift (m)
σv = σv1 r12 / ri2 (13) hf = height of the load cone (m)

σh = K2 σv (14) The wheel load P and the tyre pressure p in this

case are referred to a truck or dumper used at the job
Then we assume that the tensile force TPi site for carrying the soil.
generated in the i-th geogrid in the base course by Since we are dealing with the first lift of
the wheel load is the integral of the horizontal soil aggregate placed on a soft soil, very heavy vehicles
stresses between the i-th geogrid layer and the shall not be used.
(i-1)th geogrid layer, which can be exprees as: Hence we can reasonably assume the same wheel
load P and tyre pressure p used for road design.
TPi = 0,5 (σhi + σhi-1) (Zi – Zi-1) (15) We can reasonably assume that the subgrade
reaction R is equal to the allowable bearing capacity
For Z2 < Z < Z3: of a cohesive soil layer with geogrid reinforcement
(Rodin, 1965), that is:
r = r2 + (Z – Z2) tan α3 (16)
R = 2 π cu A / FS = 2 π (30 CBRSG) A / FS =
σv = σv2 r22 / ri2 (17) = 60 π CBRSG A / FS (22)

σh = K3 σv (18) where:
FS = Factor of Safety for subgrade bearing capacity
The tensile force TPi generated in the i-th geogrid cu = undrained cohesion of subgrade
in the subbase course is: CBRSG = California Bearing Ratio of subgrade

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GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

Fig. 2 - Scheme of the first geogrid layer

Second Case: When the Subbase is Present.

Since it is:
In such case the geogrid at base course bottom is
rf = r0 + Zf tan α2 (23) not subject to the tensioned membrane mechanism,
hence:
hf = rf / tan α2 (24)
Tm2 = 0 (30)
(hf – Zf) = r0 / tan α2 (25)
The geogrid layer at subbase bottom instead is
P = π r02 p (26) subject to the tensioned membrane mechanism;
hence, considering the first lift of subbase course,
We finally get, for the first lift of the base we get:
course:
WTC2 = [(γ2 / 3) (rf3 – r03) / (rf2 tan α2)] + rf = r0 + Zf tan α3 (31)
+ p (r02 / rf2 ) + 60 π CBRSG A / FS (27)
hf = rf / tan α3 (32)
The tensile load in the catenary reinforcement at
base course bottom is determined based on tensioned (hf – Z1) = r0 / tan α3 (33)
membrane theory and is a function of the amount of
strain in the reinforcement. The tension in the WTC3 = [(γ3 / 3) (rf3 – r03) / (rf2 tan α3)] +
reinforcement is determined from the following p (r02 / rf2 ) + 60 π CBRSG A / FS (34)
equation:
Tm3 = WTC3 Ω rf (35)
Tm2 = WTC2 Ω rf (28)
Also in this case, if the bearing capacity of the
where: subgrade is enough to support the first lift of the
Ω = dimensionless factor from tensioned subbase course and the wheel load, WTC3 becomes
membrane theory, as a function of reinforcement negative; in such case no tensioned membrane
strain εr (Table 1) mechanism occur, hence:

Table 1 – Values of dimensionless factor Ω Tm3 = 0 (36)

εr (%) Ω
1 2,07
TOTAL HORIZONTAL FORCE
2 1,47
3 1,23 The total horizontal force that the i-th geogrid
4 1,08 layer has to withstand is then:
5 0,97
Ttot-i = Tzi + TPi + Tm (37)
If the bearing capacity of the subgrade is enough
to support the first lift of the base course and the Where Tm, as said, applies only to the first
wheel load, WTC2 becomes negative; in such case geogrid layer at the interface with the subgrade,
no tensioned membrane mechanism occur, hence: either of the base course or of the subbase course.
Tm2 = 0 (29)

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 GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

GEOGRIDS DESIGN Table 3 – Road data for Example 1

The i-th geogrid layer shall be able to provide a

tensile force equal to or larger than T tot-i at a
maximum strain of 5 %.
More important is the road structure we are
designing and lower the design geogrid strain shall
be. Hence for important structures the geogrid strain
shall be limited to 1 – 2 %, while for less important
structures (or when the design conditions afford
slightly larger deformations) 3 %, 4 % or 5 %
geogrid strain can be acceptable.
The above mentioned limit strain criterion shall
be applied to the short term tensile strength of
geogrids, as measured in a wide width tensile test
according to EN ISO 10319 standard.
Hence for designing the geogrids for a reinforced
base and / or subbase, the Engineer shall have at
hand the tensile strengths at 1%, 2 %, 3 %, 4 % and
5 % for a whole range of bidirectional geogrids,
with ultimate tensile strengths in the indicative range
of 20 – 50 kN/m.
Table 4 – Traffic data for the Example 1

EXAMPLE 1

Let’s design the paved road structure shown in

Table 3 with the traffic data shown in Table 4; let’s
design with reinforced base and reinforced subbase.
Design of the road structure is carried out with
AASHTO 1993 method for unreinforced road, and
with modified AASHTO 1993 method for reinforced
road.
For reinforced road design we assume to use
extruded biaxial geogrids, with 20 x 20 kN/m tensile
strength (GG20) for base reinforcement, and with
40x40 kN/m tensile strength (GG40) for subbase
reinforcement.
For these geogrids Manufacturer’s technical data
report the following Layer Coefficient ratio (LCR):

LCRGG20 = 1.506 (38)

LCRGG40 = 1.800 (39)

Design with AASHTO 1993 method results in the

unreinforced road structure shown in Fig. 3, and the
reinforced road structure shown in Fig. 4.
Note that the modified AASHTO 1993 method
assumes that both base and subbase are reinforced
with 1 layer only of geogrid.
Now let’s apply the geogrid design method
above explained.
Let’s use extruded biaxial geogrids with the
tensile strenths at given strain εr reported in Table 5.
The input data for calculation, related to traffic loads
and to materials and soils properties are reported in Fig. 3 Unreinforced road structure resulting from
Table 6. calculation with AASHTO 1993 method

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GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

Table 6 Input data for the Example 1

Fig. 4 Reinforced road structure resulting from

calculation with modified AASHTO 1993
method

Table 5 Geogrids tensile characteristics for

the examples
GG20 GG40
εr (%)
Tr (kN/m) Tr (kN/m)

1 4.90 10.00
2 7.00 14.00
3 9.80 19.00
4 12.60 25.00
5 14.00 34.00
Table 7 Vertical stresses at layers interfaces for the
Example 1
The vertical stresses at layers interfaces are reported
in Table 7.
Geogrid design calculations, carried out according to
the method and equations shown in the present
paper, are reported in Tab. 8 for base reinforcement
and in Table 9 for subbase reinforcement.

Hence the final layout is the following:

- the road structure shall include a 0,33 m thick
subbase, a 0,66 m thick base and 0,12 m thick
asphalt layer;
- the subbase shall be reinforced with a 40x40 kN/m
extruded biaxial geogrid, working at 2 % strain, Table 8 Geogrid design for base course in Example1
placed at subbase - subgrade interface;
- the base course shall be reinforced with 2 layers of
20x20 kN/m extruded biaxial geogrids; the first one
shall be placed at subbase – base course interface,
working at 1 % strain; the second one, working at
1 % strain as well, shall be placed 0,33 m above the
first one.
The design layout is shown in Fig. 5.

The example clearly shows that the geogrid

reinforcement required for thick base and / or
subbase layers may require more than the 1 only
layer supposed to be enough by road design
methods.

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 GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

Fig. 5 Design layout for Example 1

We select the geogrid reinforced road, for which
Table 9 Geogrid design for subbase course in the base thickness shall be equal to 0.60 m.
Example 1 Note that also the Leng - Gabr method assumes
that the base is reinforced with 1 layer only of
geogrid.
Now let’s apply the geogrid design method
above explained: since the base thickness is high, we
check the reinforcement with 2 layers of geogrids.
Such geogrid design is reported in Table 13 and
shown in Fig. 6:
- the base course shall be reinforced with 2 layers of
40x40 kN/m extruded biaxial geogrids; the first one
shall be placed at subgrade – base course interface,
working at 3 % strain; the second one, working at
5 % strain, shall be placed 0,35 m above the first
one.
Hence also this example clearly shows that the
geogrid reinforcement required for thick base and /
or subbase layers may require more than the 1 only
layer supposed to be enough by road design
methods.
EXAMPLE 2 Table 10. Input data for Example 2
Let’s design an unpaved road structure for
construction site access, where very heavy trucks
need to pass for many months. The subgrade is made
up of very soft clay with CBRSG = 1.3 (Cu = 40 kPa).
Design of the unpaved road structure is carried
out with the Leng - Gabr method (Leng and Gabr,
2006).
Input data shown in Table 10; both a light woven
geotextile and an extruded biaxial geogrid with
40x40 kN/m tensile strength (see Table 5) are
considered for road reinforcement.
Calculated data are reported in Table 11; base
thickness design for unreinforced road, road
reinforced with geotextile reinforcement and road
reinforced with geogrid reinforcement are reported
in Table 12.

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GEOSYNTHETICS ASIA 2012
5th Asian Regional Conference on Geosynthetics
13 to 15 December 2012 | Bangkok, Thailand

Table 11 Calculated data for Example 2 Table 13 Geogrid design for Example 2

LIMITATIONS
Table 12 Base thickness design for Example 2
The design method herein presented is based on
static stress distribution, and has to be used once the
empirical methods based on dynamic stress
distribution has already been applied to set the base /
subbase required thickness.
Laboratory and field testing are still required for
the full validation of the present design method.

REFERENCES

American Association of State Highway and Leng, J. E Gabr, M. A., (2006), Deformation-
Transportation Officials, AASHTO Guide for resistance model for geogrid-reinforced unpaved
Design of Pavement Structures, 1993. road, Journal of Transportation Research Board,
Giroud, J.P., Bonaparte, R., Beech, J.F., and Gross, National Research Council, Washington, D.C.,
B.A. (1990), Design of soil layer-geosynthetic 1975:146-154.
systems overlying voids. Geotextiles and Rodin, S. (1965), Ability of a clay fill to support
Geomembrane, Elsevier, 9(1). construction plant, Journal of Terramechanics, 2:
51-68.

Fig. 6 Geogrid layout for Example 2

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