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A geosynthetic reinforcement solution to prevent the formation of localized
sinkholes
Article in Canadian Geotechnical Journal · January 2011
DOI: 10.1139/cgj-37-5-987
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987
A geosynthetic reinforcement solution to prevent
the formation of localized sinkholes
P. Villard, J.P. Gourc, and H. Giraud
Abstract: To prevent the appearance of localized sinkholes under roads and railway lines in areas at risk, a research
program testing a geosynthetic reinforcement solution was carried out by a group of laboratories. The aim of the reinforcement is to limit surface deformation after the appearance of a sinkhole by making the surface settlement as compatible as possible with the geometrical safety criteria of the road or railway line until earth filling and repair works
can be scheduled. Full-scale tests were carried out on reinforced, instrumented road and railway structures subjected to
localized collapse. At the same time, a numerical study was carried out to gain a better understanding of the mechanisms involved (arch effect, membrane effect, and collapse mechanisms). The experimental results of the full-scale tests
were analyzed and compared with the results of three-dimensional finite element modeling.
Key words: localized sinkhole, karstic cavity, reinforcement, geosynthetic.
Résumé : Pour lutter contre l’apparition des effondrements localisés sous les voies ferroviaires et routières dans les
zones à risque, un vaste programme de recherche consistant à tester une solution de renforcement par géosynthétique a
été mené par un groupement de laboratoires. L’objectif du renforcement est de limiter les déformations de surface après
l’effondrement, en les rendant le plus possible compatibles avec les critères géométriques de sécurité des voies et ce,
jusqu’à ce qu’une intervention de remblaiement et de remise en état puisse être programmée. Des essais en vraie grandeur sur des structures de voies renforcées et instrumentées, soumises à des effondrements localisés, ont été réalisés.
Conjointement une étude numérique a été développée pour permettre une meilleure compréhension des mécanismes mis
en jeu (effet voûte, effet membrane, et mécanismes d’effondrement). Les résultats expérimentaux des essais en vraie
grandeur sont analysés et confrontés aux résultats d’une modélisation par éléments finis tridimensionnelle.
Mots clés : effondrement localisé, cavité karstique, renforcement, géosynthétique.
Introduction
The presence of underground cavities in certain areas suitable for development represents a risk of sinkhole formation,
which can be potentially detrimental to the smooth operation
of infrastructure and the safety of users. It is difficult to detect cavities either before or after installation of the infrastructure concerned because the nature of the phenomenon
changes constantly and it is difficult to locate small to moderate diameter deep cavities using current detection methods.
The major problems frequently encountered on French
road and rail networks are mainly due to (1) karstic cavities,
which, as a result of gradual collapse, lead to the formation
of a sinkhole rising to the surface; (2) old trenches dating
back to the last world war that were not properly filled in;
and (3) underground cavities resulting from subsoil excavations (galleries, tunnels, mines, or marl pits).
To guard against the risk of accidents linked to the presence of small diameter cavities under both roads and railway
lines (where the diameter L < 4 m), a reinforcement system
based on the use of geosynthetics has been considered. The
purpose of the reinforcement is to limit surface deformation,
Received June 6, 1999. Accepted January 10, 2000. Published
on the NRC Research Press website on October 6, 2000.
P. Villard, J.P. Gourc, and H. Giraud. Laboratoire
Interdisciplinaire de Recherche Impliquant la Géologie et la
Mécanique (LIRIGM), Université Joseph Fourier, 38041
Grenoble CEDEX 9, France.
Can. Geotech. J. 37: 987–999 (2000)
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Villard et al.
999
after collapse of the underlying fill, to values compatible
with the geometrical safety criteria of the road or railway
line. To achieve this, reinforcements with a high degree of
tensile stiffness were installed under the embankments at an
average depth of H = 1.5 m. To the authors’ knowledge, this
reinforcement concept for this particular purpose has
scarcely been used in full-scale applications (Kempton et al.
1996; Alexiew 1997).
There have been very few full-scale experiments on the
problems of sinkhole formation under reinforced cavities.
Those which come closest to the spirit of the work presented
here are the two-dimensional sinkhole tests (Kinney 1986)
conducted under narrow trenches (L = 1.22 to 2.07 m) with
an overlying fill height H of 0.76 m. The procedure used to
simulate the formation of the cavity (progressive melting of
a block of ice in the trench) is different from that used here,
but gives rise to the formation of an underlying cavity in a
manner similar to that of the process described in this paper.
However, the stiffness of the geosynthetic reinforcements
used (J = 73 to 180 kN/m) is much lower than the stiffness
of the reinforcement used here (J = 1818 to 3600 kN/m).
This obviously leads to different soil collapse mechanisms
and considerable surface deformations that do not meet the
traffic stability criteria currently imposed in France. Fullscale experiments (Kinney and Connor 1987; Kinney and
Connor 1990) concerning the use of geosynthetic reinforcements as a means of crossing trenches have also been conducted (e.g., excavation of trenches, installation of a
geosynthetic sheet, and backfilling). These applications,
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988
Fig. 1. Road experiment (SCET1 to SCET3).
Can. Geotech. J. Vol. 37, 2000
Fig. 2. Railway experiment (SNCF1 to SNCF4).
Fig. 3. Cavity instrumentation.
while of considerable interest with regard to the membrane
behavior of geosynthetic sheets, do not address the complex
problem of behavior of the overlying fill in the event of
sinkhole formation (arch effect, expansion, etc.) given that
the membrane deformation of the geosynthetic results from
progressive loading of the overlying soil layer and not from
collapse of the underlying soil.
To conduct this reinforcement study, a research program
entitled RAFAEL (from the French Renforcement des
Assises Ferroviaire et Autoroutière contre les Effondrements
Localisés or reinforcement of road and railway foundations
against localized sinkholes) was set up among French companies Societé Nationale des Chemins de Fer (SNCF), Paris,
France; Scetauroute, Guyancourt, France; and BIDIM
Geosynthetics, Bezons, France, and research bodies
Laboratoire Central des Ponts et Chaussées (LCPC), Paris,
France; and Laboratoire Interdisciplinaire de Recherche
Impliquant la Géologie et la Mécanique (LIRIGM),
Grenoble, France. Full-scale tests were carried out on instrumented motorway and railway structures (Gourc et al. 1999).
Cavities between 2 and 4 m in diameter, filled beforehand
with clay beads and reinforced by one or two geotextile
sheets of different tensile stiffnesses, were placed at the base
of the fill 1.5 m beneath the road or railway (four cavities
under railway lines and three under roads). The tests during
the road experiments (Fig. 1) were carried out directly without surfacing on top of the road bed so that localized sinkhole phenomena could be more easily assessed. For the
railway experiment, a conventional track structure (ballast,
concrete sleepers, and rails) was reconstructed so that trains
could pass over it (Fig. 2). The localized sinkholes were
simulated by pumping out the clay beads filling the artificial
cavity. When the cavity did not collapse after removal of the
beads, traffic stability tests (passage of trucks or trains) were
carried out.
Each cavity was fitted with the following instruments (Fig. 3):
(1) vertical displacement sensors (V1, V2, V3, and V4) to
measure the deflection of the geosynthetic material, positioned at the center and near mid-radius of the cavity; (2) cable-type displacement sensors initially placed horizontally
along the geosynthetic sheet (C1, C2, C3, C4, and C5 being
the cable fixing points on the geosynthetic sheets) and strain
gauges (D1, D2, D3, D4, and D5) to measure sheet strain;
(3) horizontal inclinometers to measure displacement within
the fill; and (4) topographical survey apparatus to measure
surface settlement.
The fill material was a 0–300 mm coarse alluvial material
(uniformity ratio Cu = 50) with a unit weight of γ d = 21.1
kN/m3. The internal angle of friction φ and cohesion c of the
material were estimated using drained direct shear tests in a
large shear box (1 × 1 m), with φ = 38° and c = 40 kPa. The
reinforcements used were unidirectional geosynthetic sheets
(nonwoven sheets reinforced by extra fibres in the direction
of geosynthetic production) unrolled continuously in the direction of the road or railway much wider than the diameter
of the cavities (5.3 m for 2 m diameter cavities and 7 m for
4 m diameter cavities). Several types of sheets were used for
comparative purposes on the various cavities tested. The
main characteristics of the tests carried out are presented in
Table 1. J is the secant stiffness in the direction of
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Table 1. Characteristics of the experiments.
Type of test
Cavity diameter (m)
No. of sheets
Stiffness J of the
geosynthetic (kN/m)
Failure tension Tf of the
geosynthetic (kN/m)
SCET1
SCET2
SCET3
SNCF1
SNCF2
SNCF3
SNCF4
2
4
4
2
4
4
2
1
1
1
1
1
2
1
1818
1818
3600
455
1818
1818
1818
200
200
230
50
200
200
200
Fig. 4. Sinkhole mechanisms.
geosynthetic production (reinforcement direction) obtained
at 5% strain. The secant stiffnesses obtained in the transverse direction were smaller; for all of the geosynthetics
tested they were 25 kN/m.
Behavior of reinforced fill under a cavity
In real cases, surface sinkholes are linked to the formation
of underground cavities; a slow, gradual phenomenon resulting from soil erosion following runoff water infiltration (dissolution of rock by water loaded with carbon dioxide or as a
result of the presence of galleries or tunnels). Beginning in
underlying cavities, the sinkhole tends to expand towards the
surface as the soil gradually collapses. Depending on the
size and depth of the cavity, either the sinkhole stabilizes or
the subsidence gradually rises to the surface. At the final
stage the topsoil layer can collapse suddenly.
The presence of a geosynthetic reinforcement in the fill
will hinder the subsidence as it rises towards the surface and
will help limit surface settlement and deformation. The way
the phenomenon evolves depends on the underlying erosion
mechanism (slow or sudden collapse) and the scale of the
sinkhole.
Depending on the diameter L of the cavity formed and the
depth H corresponding to the geosynthetic reinforcement,
the sinkhole mechanisms can evolve in one of two ways:
(1) complete collapse of all of the soil on top of the sheet
when H/L is small (Fig. 4A), or (2) formation of a soil arch
of variable stability when H/L is large (Fig. 4B).
Five distinct zones can be defined in the reinforced fill:
Zone 1: the geosynthetic sheet, which deforms like a
membrane under the action of the soil in zone 3.
Zone 2: the support soil, which is assumed to be stable, on
the sides of the cavity.
Zone 3: the collapsed soil, which places a load on the
geosynthetic sheet.
Zone 4: the intermediate layer of fill where the arch is
formed. The shape of zone 4b is such that the loads (individual weight of zone 5b and surface loads) can be transferred
to stable supports (zone 2). Zone 4a provides lateral support
for zone 4b.
Zone 5: the top layer of fill. Zone 5b is prevented at the
base from collapsing vertically under its own weight and under the action of the surface service loads by the arch (zone
4b) and laterally through friction from zone 5a.
For a reinforcement solution to be considered acceptable
it must meet the design criteria, which are surface geometric
criteria: even after collapse, an acceptable continuity of traffic movement must be guaranteed until surface filling work
can be envisaged. Several stages of calculation are needed to
check the surface geometric criteria: (1) evaluation of the
loads on the geosynthetic sheet (soil action and traffic overloads); (2) evaluation of geosynthetic sheet displacements
(stiffness modulus is selected taking into account the type of
loading: static and traffic loads); and (3) evaluation of surface displacements.
Evaluation of geosynthetic sheet
displacements (membrane effect)
Because of their structure, geosynthetics have a low bending rigidity and therefore can be strained only by tensile
forces. When subjected to stress perpendicular to their horizontal plane, they deform like a membrane so that the tensile
forces guarantee the static equilibrium of the sheet.
Analytical formulations of the membrane effect, which
can be used to evaluate tensile forces and sheet strain, have
been developed for homogeneous and isotropic sheets, and
for simple load geometries: vertical distributed loads or
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Can. Geotech. J. Vol. 37, 2000
Fig. 5. Characteristic angles of fibre orientation.
loads normal to the horizontal plane of the deformed sheet
(plane or axisymmetrical volume of revolution case). Authors who have studied this topic are Delmas (1979),
Matichard (1981), Perrier (1983), Gourc et al. (1982), and
Giroud et al. (1990, 1995, 1996).
The fibrous structure of geosynthetics, sheets composed of
nonwoven fabric (two-dimensional uniform distribution of
the fibres in a horizontal plane) providing reinforcement in a
given direction, was taken into consideration here by developing an original calculation method based on the finiteelement principle. The calculations consider large strains
and enable any sheet geometry and load to be studied. A triple-node triangular element has been developed specifically
for the membrane behavior of geosynthetics (Villard and
Giraud 1998). The main hypotheses concerning formulation
of the element are as follows:
(1) Each element consists of a group of fibres with various
orientations initially forming a horizontal plane.
(2) There is no slip between the fibres at intersections.
(3) The stresses absorbed in each fibre direction (characterized in the general reference by the angles α and β) are
orientated in the direction of the fibres after strain (characterized in the general reference by the angles α ′ and β ′,
Fig. 5).
(4) The tensile compression behavior of each fibre is nonlinear elastic; the compression elasticity modulus is considered to be very low compared with the tensile elasticity
modulus.
The calculations resulted in the formulation (for each fibre
direction considered) of a specific matrix system of a triplenode three-dimensional element written as {F} = [K]{u} +
{R}, with {F} being the stresses at the element nodes, {u}
the nodal displacements, [K] the elementary rigidity matrix,
and {R} a corrective term for taking large strains into account.
[1]
 F1 x 
 u1 x 
F 
u 
 1y 
 1y 
 F1 z 
 u1 z 
F 
u 
 2 x  EeD
 2 x  EeDG
[K′ ]  u2 y  +
 F2 y  =
2
2
 F2 z 
 u2 z 




 F3 x 
 u3 x 
 F3 y 
 u3 y 




 F3 z 
 u3 z 
 B1 cos(β ′ ) cos(α ′ ) 
 B cos(β ′ ) sin(α ′ ) 

 1
B1 sin(β ′ )


 B cos(β ′ ) cos(α ′ ) 

 2
 B2 cos(β ′ ) sin(α ′ ) 


B2 sin(β ′ )


 B3 cos(β ′ ) cos(α ′ ) 
 B cos(β ′ ) sin(α ′ ) 

 3
B3 sin(β ′ )


where E is the secant elasticity modulus of all the fibres with
orientation α and β, e is the element thickness, and G, Bi, D,
and K′ (i,j) are coefficients defined by
[2]
G = cos(β) cos(α) [cos(β ′) cos(α′)
– cos(β) cos(α)] + sin(β) [sin(β ′) – sin(β)]
+ cos(β) sin(α) [cos(β ′) sin(α′) – cos(β) sin(α)]
[3]
B1 =
X m2 −X m3
D
B2 =
X m3 −X m1
D
and B3 =
[4]
X m1 −X m2
D
D = (XL2 Xm3 + XL3 Xm1 + XL1 Xm2 – XL2 Xm1
– XL3 Xm2 + XL1 Xm3)
K′[3i – 2, 3j – 2] = BiBj cos2(β ′) cos2(α′)
K′[3i – 2, 3j – 1] = BiBj cos2(β ′) cos(α ′) sin(α′)
Kv[3i – 2, 3j] = BiBj cos(β ′) sin(β ′) cos(α′)
K′[3i – 1, 3j – 2] = BiBj cos2(β ′) cos(α ′) sin(α′)
K′[3i – 1, 3j – 1] = BiBj cos2(β ′) sin2(α′)
K′[3i – 1, 3j] = BiBj cos(β ′) sin(β ′) sin(α′)
K′[3i, 3j – 2] = BiBj cos(β ′) sin(β ′) cos(α′)
K′[3i, 3j – 1] = BiBj cos(β ′) sin(β ′) sin(α′)
K′(3i, 3j) = BiBj sin2( β ′)
XL1, Xm1 XL2, Xm2, XL3, Xm3 are, respectively, the coordinates
of nodesr 1,r 2, rand 3 of the element in the local reference
frame ( L, M, T ) linked to the direction of fibre α and β
(Fig. 6).
The characteristic behavior matrix of a geosynthetic sheet
with several fibre directions is obtained by finding the sum
of the elementary rigidity matrices of each fibre direction.
The matrix obtained is then inserted into a finite element
computation code. The system obtained depends on the initial fibre distribution (spatial orientation and behavior of
each fibre direction) and on the final solution after element
strain. The problem is solved iteratively. The model can be
satisfactorily compared with existing analytical solutions
(Villard and Giraud 1998), and the proposed method was
therefore theoretically validated.
A parametric study of the membrane effect focusing on
the influence of the textile type and cavity shape was carried
out (Giraud 1997). This enabled one economically important
aspect of the project to be justified, namely, that unidirectional sheets (nonwoven geosynthetic reinforced in one single direction) unrolled continuously in the direction in which
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Fig. 6. Local reference frame related to an element.
991
Fig. 8. Sinkhole mechanism according to a vertical shear surface.
Fig. 7. Design chart.
Evaluation of loads on the geosynthetic
sheet
The loads on the geosynthetic sheet were evaluated using
a limit equilibrium method, which was relatively elementary
given the difficulties encountered in modeling arch formation using conventional finite element methods.
The loads likely to affect the geosynthetic sheet during a
total collapse (Fig. 4A) result from the weight of the soil
above the cavity and any surface overloads. This is the simplest case. When an arch forms (Fig. 4B), the load absorbed
by the sheet is lower because some load is transferred to stable supports. The case of a stable arch will be considered
and its equilibrium studied as a function of the loads applied
to it (actions of zones 5b and 4a).
traffic passes along the road or track were technically and
economically the most efficient for this type of application.
They were easy to manufacture and install, guaranteed anchorage parallel to the road or track, and provided optimum
reinforcement (compared for example to reinforced sheets
with a similar total number of fibres in two directions, direction of traffic and crosswise). The results of this parametric
study (Villard and Giraud 1998) are the reason for the technical choices made in initially defining the size of the cavities tested (Table 1). A typical design chart is given in Fig. 7
for circular cavities of diameter L, reinforced with unidirectional geosynthetic sheets assuming non-slipping of the
sheet around the circumference of the cavity. This assumption is based on full-scale experimental results, which show
that no significant slipping of the anchorage system was recorded during the tests (zero displacement measured on the
C5 sensor (Fig. 3) located inside the fill at a distance of
0.26 m from the edge of the cavity). Note that, in any case,
it is very easy to make allowance for anchor slipping in the
proposed calculation method. The uniform vertical stress, q,
acting on the geosynthetic sheet (soil action and traffic overloads) is noted, and f is the permissible sag in the middle of
the geosynthetic sheet. The chart in Fig. 7 is used to determine both the stiffness, J, of the geosynthetic and the tension, T, that it has to withstand for given values of f/L and
qL (e.g., for L = 2 m, q = 21 kN/m2, and f = 0.15 m, the values obtained are J = 5400 kN/m and T = 74 kN/m).
Load transmitted to the arch (action of zone 5b)
The static equilibrium of zone 5b was studied to evaluate
the limit vertical stresses σz that will be borne by the upper
part of the arch. The equilibrium mechanism adopted
(Fig. 8) results from the limit equilibrium method originally
developed by Terzaghi (1943), which assumes that the soil
immediately above the arch (zone 5b) tries to move in a vertical column between the adjacent masses of soil which have
remained stable (zone 5a). The shear strength along the slip
lines resists the displacement of the active soil mass (zone
5b), reducing stresses on the upper part of the arch (zone 4b)
and increasing stresses on the stable adjacent support (zone 2).
The axisymmetrical case will be considered and it will be
assumed that the shear lines are vertical. It is then possible
to estimate the value of the stresses acting on the arch (zone
4b) by studying the limit equilibrium of the soil cylinder in
the active zone (zone 5b).
The limit equilibrium of the driving forces and the resistive forces applied to the elementary cylinder of zone 5b can
be used to evaluate the vertical stress σz acting at a given
depth z.
The driving forces (individual weight and upper part
stresses σz) acting on the elementary cylinder of radius R =
L /2 and of thickness dz are defined by (π R2) γ dz + (π R2) σz,
where γ is the unit weight of the soil considered.
The resistive forces are a function of the shear stress
along the vertical sheared interface (τ = c + σr tan φ) and the
stresses in the lower part (σ z + dσ z):
[5]
τ2 πRdz + ( π R2)(σ z + dσ z)
where c is the cohesion, φ the soil internal angle of friction,
and σr the normal stress at the sheared surface at depth z.
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Can. Geotech. J. Vol. 37, 2000
Fig. 9. Static equilibrium of the arch (axisymmetrical case).
The ratio between the vertical stress σz and the normal stress
σr is assumed to be independent of z and equal to the active
earth coefficient K (i.e., σr = K σz). This value of K is justified by the kinematics observed during creation of the void,
i.e., a horizontal extension of the lateral fill material towards
the sinkhole (ground thrust towards the cavity).
The equilibrium of the driving and resistive forces can be
written as
[6]
Fig. 10. Ratio h/L as a function of the ratio H/L.
π R2 (γ dz + σz) = (c + σr tan φ)2 π R dz
+ π R2(σz + dσz)
i.e.,
[7]
dσ z
c
tan φ
= γ − 2 − 2Kσ z
dz
R
R
Considering that for z = 0, σz = p (overload area) the following is obtained after integration:
R( γ − 2c / R)
(1 − e− K tan φ 2 z/ R) + pe− K tan φ 2 z/ R
2K tan φ
R(γ − 2 c / R)
by adding k 0 =
k 1 = 2Ktan φ z / R
2 K tan φ
[8]
σz =
and k 2 = p − k0
surface loads towards the supports and from the stresses τ
acting on the periphery of the cylinder. If a horizontal component of the supporting stress is considered at the base of
the arch, this would give h values lower than those obtained
assuming a vertical supporting stress only.
The static equilibrium of a portion dθ of arch gives
r =R
[11]
Σ Rz = 0
– dFz + ∫ σ z d r dθdr = 0
r =0
r =R
[12]
Σ M(A) = 0
z= H
∫ rσ z d r dθdr +
r =0
eq. [8] becomes
[9]
σ z = k 0 + k 2 e− k 1 z
At depth d, the crown arch,
[10]
σ zd = k 0 + k 2 e− k 1 d
Equilibrium of the arch
Arch formation results from the reorientation of stresses
such that all of the grains involved constitute a stable arrangement. The arch height, h, and the topsoil thickness, d,
can be evaluated by considering the overall equilibrium of
the grains forming the arch (Fig. 9). If the arch soil weight
(zone 4b in Fig.4) is ignored, the only stresses to be considered in the arch equilibrium are σzd the vertical stress at
depth d supported by the arch (action of zone 5b on zone
4b), σr the lateral stress at depth z due to soil thrust in zone
4a (σr = K σz), dFz the vertical stress acting on the supposedly stable supporting soil, and dFr the horizontal stresses
borne by the crown. dFz results from the reorientation of the
∫
(z + h − H )
z = ( H − h)
× σr Rdθdz − Rd Fz = 0
with
σ z = k0 + k2 e
−k 1 z
and σr = K σz.
Replacing σzd by its value (eq. [10]) in eqs. [11] and [12]
gives, after integration:
[13]
with
[14]
R2
(k0 + k 2 e− k 1 ( H − h) dθ
2
Kk2 R
K k0 Rh 2
C1 =
and C2 =
2
k1k1
dFz =
C 1 + C 2 ( e − k 1 ( H − h) − e − k 1 H )
+
R3
( k 0 + k 2 e − k 1 ( H − h) ) = 0
6
Once solved, eq. [14] can be used to determine the height
h of the stable arch. For p = 0 (i.e., k2 = –k0) height h is independent of c and γ (eq. [14] is independent of k0). In these
conditions, h can be determined as a function of the fill
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Table 2. Main results of experiment SCET1 (H/L = 0.75).
After emptying
After traffic
J (kN/m)
f (m)
ε max1 (%)
ε max2 (%)
s (m)
h (m)
h/L
1818
1818
0.21
0.22
5.1
4.3
1.97
2.15
0
0
1.07
0.535
Fig. 11. Total and sudden collapse.
height H and cavity diameter L (L = 2R). Figure 10 gives the
curve h/L as a function of the ratio H/L for K = (1 – sinφ) /(1
+ sin φ) and φ = 38°. In the plane case, analytically the most
simple, the arch is demonstrated to be a semi-ellipse.
When H is large compared to L (i.e., a very deep cavity)
eq. [14] shows that the arch height is h∞ = L/(2 3K ), i.e.,
for the previous numerical application, h∞ /L = 0.592. The
arch height h generally obtained using eq. [14] is therefore
always less than h∞ (asymptote of the curve), which can be
considered to be the maximum height of soil that is likely to
collapse and possibly act on the geosynthetic sheet.
Evaluation of surface displacements (soil
expansion)
When a granular material is decompacted, disimbrication
occurs and its particles are reorganized, increasing its apparent volume. Little is known about this expansion under very
little confinement and knowledge is limited to empirical
findings made by earthwork specialists. The increase in soil
volume is linked to the nature, granular distribution, initial
compactness, and state of the stresses applied to the material. The ratio between the decompacted soil volume Vse and
the initial soil volume prior to decompacting Vs is called the
expansion coefficient: Ce = Vse /Vs.
Soil expansion will govern the extent to which surface deformation is limited depending on the rigidity of the reinforcement used and the observed sinkhole formation
mechanism (gradual or sudden collapse). Under the weight
of the expanded soil, the geosynthetic sags like a membrane.
As it deforms it liberates a space ∆Vg that can be partially or
completely filled by the increasing expanded soil volume
∆Vs: ∆Vs = Vse – Vs = (Ce – 1)Vs.
If there is a complete collapse (Fig. 4A), the surface settlement, s, will be no more than the displacement, f, corresponding to the membrane sagging of the geosynthetic (Fig. 11).
If an arch is formed (Fig. 4B), a gap is created between
the arch-shaped surface soil and the collapsed, expanded soil
(Fig. 12A). The greater the extent of soil expansion, the
smaller the gap will be. The foreseeable surface settlement
depends on the characteristics of the fill and is no more than
the height left free between the arch and the collapsed soil.
If the soil expands sufficiently, there will be no loss of con-
Fig. 12. Formation of an arch.
tact between the arch and the expanded collapsed soil
(Fig. 12B). Observations on the experimental site implied
that this phenomenon may contribute to stabilizing the arch
by preventing the grains on the top of the arch from becoming detached, especially under dynamic loads.
An arch stability criterion can be defined as a function of
the geosynthetic sheet characteristics (stiffness J) and the
soil characteristics (expansion coefficient Ce):
∆Vs < ∆Vg: formation of a gap under the arch and possibility of a reduction in the arch crown thickness d,
∆Vs ≥ ∆Vg: contact between the arch and the expanded
soil and formation of a stable equilibrium.
Results of the experiments
Fairly similar results were obtained on all of the cavities
with the same diameter, in both the road and railway experiments. Only the results concerning road experiments will be
analyzed in detail, because they were considered more representative of the mechanisms of sinkhole formation given that
the stiffening structure of the tracks in the case of the railway experiments no doubt interfered slightly with the basic
mechanisms. The complete results of the experiments are
presented in Gourc et al. (1999).
Cavity L = 2 m: SCET1
Measurements were taken continuously during the emptying stage and following traffic stability tests. In total, a truck
with a 13 t load per axle was driven over the cavity 74 times
without any visible surface settlement, s. The main results
obtained after emptying and traffic stability tests are presented in Table 2. On the table, f is the deflection at the center of the sheet, εmax1 is the maximum strain deduced from
the cable-type displacement sensor measurements, εmax2 is
the maximum strain given by the strain gauges, s is the central surface settlement, and h is the maximum collapsed soil
height.
To find out more about the arch effect mechanisms, it was
decided in this case only, given the scale of the experiment,
to excavate the cavity meticulously using a mechanical digger. After dismantling at the end of the test, an arch had
formed and the soil had collapsed to a depth of about
1.07 m. A small gap of a few centimetres was observed between the lower surface of the arch and the soil in the collapsed zone. This gap corresponds to the actual expansion of
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Can. Geotech. J. Vol. 37, 2000
Table 3. Main results of experiments SCET2 and SCET3 (H/L = 0.375) after emptying.
SCET2
SCET3
SCET3
J (kN/m)
f (m)
ε max1 (%)
ε max2 (%)
s (m)
h/L
1818
3600
3600
> 0.6
0.46
0.48
5.5
4
4.6
5
4.8
5.2
0.25
0
0.25
0.375
< 0.375
0.375
Fig. 13. Fill geometry for SCET2 after emptying (J = 1818 kN/m, H/L = 0.375).
Fig. 14. Fill geometry for SCET3 after emptying (J = 3600 kN/m, H/L = 0.375).
Fig. 15. Fill geometry for SCET3 after a truck has passed over once (J = 3600 kN/m, H/L = 0.375).
the collapsed soil which, given the geosynthetic sheet deflection f of 0.22 m, can be estimated at Ce ≈ 1.16.
Cavities L = 4 m: SCET2 and SCET3
Two 4 m diameter cavities were tested during the road
tests. Only the stiffnesses of the geosynthetic sheets used
differed from one cavity to the other: 1818 kN/m for cavity
SCET2 and 3600 kN/m for cavity SCET3.
The result of emptying the least reinforced cavity
(SCET2) was a sudden collapse of all of the fill soil onto the
sheet following a mechanism similar to that presented in
Fig.13. The main results obtained are (Table 3) deflection in
the sheet center, f, greater than 0.6 m (off the top end of the
sensor scale), a surface settlement, s, of 0.25 m, and maximum geosynthetic strain of about 5.5%.
Unlike cavity SCET2, cavity SCET3, reinforced by a
stiffer geosynthetic sheet (J = 3600 kN/m), did not collapse
on emptying. The main results obtained are (Fig.14 and
Table 3) deflection at the sheet center, f of 0.46 m, very little
surface settlement, s, and maximum geosynthetic sheet
strain of about 4.8%. At first glance, this difference in the
results can be explained by the fact that the geosynthetic
sheet in cavity SCET3 is stiffer than the one in cavity
SCET2 and, consequently, its membrane strain, f, is reduced.
Given the strain measured by the strain gauge, a thin arch
formed in this case.
Traffic stability tests were carried out. The first time the
truck passed over, the surface collapsed suddenly by about
0.25 m (Fig. 15), although this was confined to the central
part and corresponded to the failure of the arch crown. On
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Villard et al.
Fig. 16. Finite element meshing adopted for numerical modelling.
995
Table 4. Model–experiment comparison for cavity SCET1 after
trucks have passed over 74 times.
Sensor V1 (∆z m)
Sensor V2 (∆z m)
Sensor V3 (∆z m)
Sensor V4 (∆z m)
Sensor D1 (ε%)
Sensors C1–C2 (ε%)
Sensor D2 (ε%)
Sensor D3 (ε%)
Sensors C2–C3 (ε%)
Sensor D4 (ε%)
Sensors C3–C4 (ε%)
Sensor D5 (ε%)
Fig. 17. Comparison of sheet vertical displacements (traffic direction–zox plane)
the other hand, the deflection, f, and strain, ε, measurements
barely changed (f = 0.48 m and εmax2 = 5.2%).
According to the strain measured (Table 3), the tensile
forces obtained in the sheet correspond to some 40% of the
failure tensile force, Tf, so there is relatively little risk of the
geosynthetic sheets tearing (which would cause a catastrophic collapse). Therefore, it was considered reasonable
to continue the experiment.
To enable traffic to resume, the surface subsidence was
leveled with fill. In these conditions, the truck could be
driven over the site again without any significant change in
the geosynthetic sheet strain.
If the possibility of filling in the surface is accepted, this
reinforcement technique appears to be very efficient since,
after having filled in the sinkhole area, traffic can resume
without any major problems, with the geosynthetic sheet
bearing the overall load (weight of collapsed soil and dynamic overload from traffic).
Comparison of experiments and modelling
(membrane effect)
The compatibility of the theoretical results with the measurements taken (geosynthetic sheet deformation and strain
measurements) was analyzed using a three-dimensional finite element model of a circular sheet subjected to a load
distributed normal to its initial plane, following the method
described above. As the behavior of the membrane is validated by calculation before the passage of traffic, the loading
and mechanical behavior characteristics of the geosynthetic
correspond to static loads.
Experiment
Model 1
Model 2
0.218
0.146
0.186
0.186
2.15
4.3
0.9
–0.023
2.4
1.12
2.2
1.63
0.212
0.137
0.172
0.184
2.82
2.82
2.86
2.91
2.90
2.98
3.03
3.04
0.204
0.123
0.153
0.168
2.47
2.47
2.51
2.56
2.55
2.62
2.62
2.63
Fig. 18. Sheet vertical displacements (perpendicular to traffic direction–zoy plane)
Cavity L = 2 m: SCET1
The meshing adopted to discretize the problem (Fig. 16)
includes 1712 triple-node triangular elements and 889 nodes.
The boundary conditions are zero displacement on the cavity
periphery (fixed supports and perfect anchorage for the
geosynthetic). The mechanical properties of the geosynthetic
sheet follow: tensile stiffness in the traffic direction of 1818
kN/m and stiffness in the transverse direction of 25 kN/m.
Experiment SCET1, which was meticulously dismantled
after the test, gave a fairly precise estimate of the forces actually applied to the sheet (maximum collapsed soil height
h = 1.07 m and unit weight γ = 21.1 kN/m3).
Two types of load were modeled: a uniform distributed
load equivalent to a soil height h of 1.07 m (model 1) and a
load distributed in a paraboloid of revolution closer to the
shape of the arch observed (model 2) defined by a soil
height of 1.07 m in the center of the paraboloid and soil
heights of zero on the edges.
The results obtained experimentally and numerically for
the geosynthetic sheet at the sensors (Fig. 3) are summarized
in Table 4: displacement sensors (V1, V2, V3, and V4), cabletype strain sensors (C1, C2, C3, C4, and C5), and strain
gauges (D1, D2, D3, D4, and D5). The results obtained are not
symmetrical because the position of sensors V3 and V4 at
mid-radius of the sheet is approximate.
Figures 17 and 18 present the longitudinal and cross sections obtained numerically in the two load cases considered.
The fact that there is one favored reinforcement direction
makes the longitudinal and cross sections different. The experimental results from the vertical displacement sensors tie
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Fig. 19. Comparison of sheet strain elements (traffic direction).
Can. Geotech. J. Vol. 37, 2000
Table 5. Comparison of experimental and theoretical results after
collapse.
SCET3 (J =
3600 kN/m) after
traffic (1 passage)
SCET2 (J =
1818 kN/m)
f (m)
ε max (%)
in well with the theoretical results, which are fairly similar
from one model to another.
Figure 19 compares the experimental and numerical
strains of the geosynthetic sheet obtained along the reinforcement in the traffic direction. Numerically, these elongations vary little compared with the experimental values,
which are fairly scattered, without doubt due to the experimental difficulties encountered in measuring strain on a fibrous sheet.
Cavities L = 4 m: SCET2 and SCET3
Only the experimental results after collapse of the cavities
will be used for the comparison with modeling, since fill
was not excavated during SCET3 and the thickness d at the
arch crown before traffic (d = H – h) could therefore not be
measured. Simulations similar to those presented for cavity
SCET1 (model 1) were carried out assuming that the distributed load acting on the sheet is the result of the fill completely collapsing onto the sheet, giving a soil height h =
1.5 m.
The results of the modeling (deflection at the sheet center,
f, and the maxima, εmax, of the maximum strains obtained
using one of the two measuring devices: max of strains εmax1
and εmax2) are compared with the experimental results in Table 5. Here again, the two sets of results tie in well.
Therefore, it may be deduced that the membrane effect is
correctly evaluated by the model proposed and that the collapsed soil volume can be used to evaluate geosynthetic
sheet deflection correctly. Subsequently, a reverse calculation can be used to estimate the height h of the arch formed
based on the geosynthetic sheet strain measurement.
Comparison of experiment and model (arch
effect)
The mechanisms of sinkhole formation obtained experimentally are fairly similar from one test to another for a
given cavity diameter and for either type of experiment (road
or railway). The following were observed: formation of stable arches (Fig. 4B) for 2 m diameter cavities (H/L = 0.75);
whereas for 4 m cavities (H/L = 0.375), all of the fill completely collapsed on to the sheet (Fig. 4A), either after emptying or during the traffic stability tests. This confirms the
importance of the ratio H/L in arch formation mechanisms.
The heights, h, of soil that collapsed after the cavities
were emptied, were either directly measured on site (cavities
that were dismantled (SCET1) or collapsed completely up to
the surface) or deduced from sag measurements obtained experimentally at the center of the sheet. In this case, h was es-
Exp.
Theor.
Exp.
Theor.
> 0.6
5.5
0.62
6.4
0.48
5.2
0.49
3.93
Fig. 20. Comparison of theoretical and experimental arch heights
h, after emptying.
timated based on an inverse calculation using the finite element model presented above (model 1). This entailed finding the soil height overload required to obtain a theoretical
deflection in the center of the sheet that is identical to the
experimental deflection, f. For all of the tests carried out, the
collapsed soil heights, h, measured or estimated at the end of
emptying are presented in Table 6.
According to the numerical developments described above
(eq. [14]), the theoretical heights of soil that collapsed onto
the sheet are h = 0.89 m for cavities of diameter L = 2 m
(H/L = 0.75, h/L = 0.445) and h = 1.23 m for cavities of diameter L = 4 m (H/L = 0.375, h/L = 0.3075). As a result, at
the center of the 2 and 4 m diameter cavities, the theoretical
thicknesses of the arch crown (d = H – h) are 0.61 m and
0.27 m, respectively. The theoretical and experimental ratios
h/L obtained after emptying on all of the cavities tested
(H/L = 0.75 and H/L = 0.375) are grouped together in
Fig. 20. Given the H/L value, the difference on the Y-axis between the bisectrix and the curve h/L corresponds to the soil
thickness at arch crown d/L.
A comparison of the results obtained on all of the 2 m
cavities (H/L = 0.75) shows that the results from identically
reinforced cavities SCET1 and SNCF4 are fairly similar to
the expected theoretical results. Test SNCF1, with the least
reinforced cavity (J = 455 kN/m), has a very small arch
height h, which, moreover, is not compatible with the theoretical estimate.
A comparison of the results obtained on emptying on all
of the 4 m cavities (H/L = 0.375) shows a fairly good correlation between the theory and the experiments. With total
collapse, the corresponding experimental points are on the
bisectrix. The smallest arch heights were found on the railway experiments, probably because of the presence of a ballast layer and a rolling system in the upper part of the fill.
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Table 6. Soil heights h measured or estimated (*) at the end of emptying, in the cavity axis.
SCET1
SCET2
SCET3
SNCF1
SNCF2
SNCF3
SNCF4
L (m)
J (kN/m)
f (m)
h (m)
d = (H – h) (m)
h/L
2
4
4
2
4
4
2
1818
1818
3600
455
1818
2 × 1818
1818
0.21
> 0.60
0.46
0.26
> 0.51
> 0.51
0.2
1.07
1.5
1.35 (*)
0.5 (*)
> 0.91 (*)
1.5
0.91 (*)
0.43
0
0.15
1
< 0.59
0
0.59
0.52
0.375
0.3375
0.25
0.2275
0.375
0.455
Fig. 21. Arch stability criteria (Cemin as a function of h/L).
The soil thicknesses at arch crown d are relatively small, and
it is fairly easy to see how fragile they are. This explains
why the cavities that did not fail on emptying collapsed during the traffic stability tests.
The case of experiment SNCF3 (H/L = 0.375) corresponding to a cavity reinforced by two geosynthetic sheets (J = 2
× 1818 kN/m) separated vertically by a 0.5 m thick layer of
soil is interesting, although surprising at first sight. This
technique, suggested by the experts, proved less efficient
than a reinforcement using a single sheet (positioned at the
base of the fill) of similar rigidity to that of the two sheets
(SCET3, H/L = 0.375, J = 3600 kN/m) but even less efficient than a reinforcement by a single sheet (SNCF2, H/L =
0.375, J = 1818 kN/m).
As shown by the previous theoretical approach, the presence of the second sheet inside the fill disrupted the arch
formation mechanisms. The arch can only form above the
upper geosynthetic sheet situated at a depth H ′ of 1 m, with
the soil between the two geosynthetic sheets collapsing by
almost vertical shear. Therefore, it seems more appropriate
to consider a fill height H ′ of H – 0.5 m. For H ′/L = 0.25
(SNCF3*), the graph in Fig. 20 gives a very small theoretical arch crown thickness d ′ (d ′ = H ′ – h), hence the sinkhole
observed, unlike the case where a single geosynthetic sheet
is used.
As shown by the experimental and theoretical results, arch
stability is directly linked to the soil thickness at arch crown
d, which itself is a function of the ratio H/L. However, depending on the tensile stiffness of the geosynthetic sheet,
sinkholes were observed on 4 m cavities (H/L = 0.375) after
emptying (J = 1818 kN/m) or after the traffic stability tests
(J = 3600 kN/m). As a result, a second arch stability crite-
rion was introduced to take into account the geosynthetic
sheet stiffness J and the soil expansion aptitude Ce as proposed above. If the collapsed soil manages to stay in contact
with the arch, through soil expansion, the regressive erosion
of the arch will be slowed down. It is particularly easy to
obtain this contact if there is little geosynthetic sheet sag
(low ∆Vg) and the soil expands extensively (high ∆Vs).
A graph illustrating the potential for expanded soil – arch
contact can be defined using a minimum expansion coefficient Cemin required to fill the volume created by sheet sag
∆Vg using the volume created by soil expansion ∆Vs: ∆Vs =
∆Vg.
For a given cavity diameter L, eq. [14] gives the estimated
height h of soil collapsed onto the sheet, and consequently,
the load borne by the sheet: q = γ d h. The numerical model
of membrane behavior under a uniform load (model 1,
Figs. 17 and 18), for a geosynthetic sheet stiffness J, can be
used to determine the deflection f at the center of the sheet
caused by load q. Assuming that volumes ∆Vs and ∆Vg are
paraboloids of revolution, the minimum expansion coefficient Cemin required to fill the cavity completely can be determined using the equation Cemin = (f + h)/h. The values of
Cemin presented in Fig. 21 were calculated for different J and
L values and for γ = 21.1 kN/m3 for the fill soil (before expansion). The complete graph obtained (Fig. 21) gives the
estimated mechanism of sinkhole formation as well as the
stability of any arch formed over time.
For a given ratio H/L, the theoretical soil height h/L likely
to collapse is obtained from the graph on the right. Using the
graph on the left, the minimum coefficient Cemin required to
fill the cavity completely is obtained for given L and J values.
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998
If Cemin ≤ actual Ce, contact between the arch and the expanded soil is maintained, which is favorable to arch stability over time.
If Cemin > actual Ce, a gap is created under the arch, which
is no longer in contact with the expanded soil and which is
unfavourable to arch stability over time.
For cavities of diameter L = 2 m (H/L = 0.75) and a
modulus J = 3600 kN/m, contact is maintained for Cemin =
1.175; whereas, with J = 1800, Cemin = 1.22 is required. Few
experimental results are available on Ce values, but it is
common to consider Ce = 1.15 for fill soils. This appears to
show that, for 2 m cavities, the arches formed are relatively
stable over time, especially if the sheet stiffness J is high.
For cavities of diameter L = 4 m (H/L = 0.375), the Cemin
values required to maintain collapsed soil – arch contact are
very high and unrealistic (Cemin = 1.36 and 1.495, respectively, for J values of 3600 and 1818 kN/m). Following the
traffic stability tests, the probability of 4 m diameter cavities
collapsing therefore seems to be confirmed.
The progressive arch regression mechanisms were actually
observed during these experiments. The diameter B of the
surface sinkhole area is always less than L, and the shape of
the sides is similar to a truncated arch (Fig. 22). This would
correspond to the regressive erosion of the arch with an initially thin (H – h), stable crown.
On the other hand, it could be pointed out that these observations do not agree with the sinkhole geometries used in
the design method proposed by the BSI (British Standard Institute BS 8006 1995), which assumes that the sinkhole is in
the shape of a truncated cone with a funnel-shaped top (B > L).
Design method
Once the reinforcement aims have been defined (temporary or permanent solution) and the design criteria have been
fixed (permissible surface settlement for a given warning
level and stability of the phenomenon), then it is possible to
draw up a dimensional design.
Evaluation of sheet loading
The chart in Fig. 20 is used to determine either of the
mechanisms that is likely to be encountered: either formation of a stable arch when the keystone width is high and the
soil expansion coefficient is greater than the requisite value,
or formation of an unstable arch and collapse of the entire
soil fill onto the sheet. The vertical stress, q, that the
geosynthetic sheet has to withstand (action of the collapsed
soil and traffic overloads) is then deduced. For example,
for L = 2 m, H = 1 m, g = 21 kN/m3, and Ce = 1.1, the chart
in Fig. 20 shows that the arch formed is unstable and leads
to collapse of the soil over the cavity, i.e., q = gH = 21
kN/m2.
Determination of permissible sag of the geosynthetic
sheet
In view of the considered soil expansion factor, Ce, and
maximum permissible surface settlement, s, the maximum
sag, f, sustained by the geosynthetic in the center of the
sheet is defined by comparing the volume of free volume of
soil on the surface, the expanded soil volume, Vs, and the
volume generated by the membrane deformation of the
Can. Geotech. J. Vol. 37, 2000
Fig. 22. Shape of observed sinkholes.
geotextile Vg. If the soil collapses in cylindrical form and the
surface deformation profile is similar to that of the
geosynthetic, then f = s + (Ce – 1)H, or for a permissible surface settlement of 0.05 m, a value of f = 0.15 m.
Choice of geosynthetic
Given the applied vertical stress, q, and the required sag, f,
at the center of the geosynthetic sheet, it is then possible to
define a stiffness value, J, and minimum tension, T, for the
geosynthetic from the chart in Fig. 7, i.e., values of J = 5400
kN/m and T = 74 kN/m, respectively, for the example considered (unidirectional sheet).
Conclusions
The mechanisms observed during the full-scale experiments are quantitatively and qualitatively similar to those described by the model. One of the key points of the results is
the formation of a stable arch for 2 m cavities and the formation of an unstable arch for 4 m cavities, for 1.5 m thick
fill consisting of granular material with a large grain size
(0/300 mm).
This study has made a valuable contribution in three different ways:
(1) Technical choices were proposed for reinforcing roads
and railways (type of geosynthetic chosen according to the
cavity diameters and fill thicknesses);
(2) Different types of reinforcements were proposed and
tested;
(3) More knowledge of the mechanisms involved (arch effect and membrane effect) has been gained.
Regarding the modeling of geosynthetic sheets, the model
proposed is especially well suited to the behaviour of
geosynthetic sheets of any type (woven or nonwoven with or
without a preferential reinforcement direction).
Regarding the use of this type of solution for reinforcing
roads and railways, the proposed technical solution is satisfactory for small diameter cavities at moderate depths, since
it respects fairly strict surface deformation criteria. For large
diameter cavities at moderate depths, this is not the case and
fairly large surface sinkholes are likely to form. Given the
way in which a membrane geosynthetic functions, selecting
a high tensile stiffness J does not avoid this problem. However, this type of system can be used to avoid large-scale
catastrophic sinkholes, and after filling works, the structure
can be restored to almost normal use.
References
Alexiew, D.A. 1997. Bridging a sink-hole by high-strength highmodulus geogrids. In Proceedings of the Geosynthetics’ 97
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Monday, October 02, 2000 1:55:49 PM
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Composite Default screen
Villard et al.
Conference, Long Beach, Calif., U.S.A., Vol. 1. Industrial Fabrics Association International (IFAI), St. Paul, MN. pp. 13–24.
British Standard. 1995. Code of practice for strengthened/reinforced soils and other fills. British Standard Institution, London,
U.K.
Delmas, P. 1979. Sols renforcés par géosynthétiques – premières
études. Ph.D. thesis, Université Scientifique et Médicale de Grenoble.
Giraud, H. 1997. Renforcement des zones d’effondrement localisé
– modélisations physique et numérique. Ph.D. thesis, Université
Joseph Fourier.
Giroud, J.P. 1995. Determination of geosynthetic strain due to deflection. Geosynthetics International, 2(3): 635–641.
Giroud, J.P. 1996. Closure of discussion of determination of
geosynthetic strain due to deflection. Gesosynthetics International, 3(1): 143–144.
Giroud, J.P., Bonaparte, R., Beech, J.F., and Gross, B.A. 1990. Design of soil layer-geosynthetic systems overlying voids.
Geotextiles and Geomembranes, 9(1): 11–50.
Gourc, J.P., Matichard, Y., Perrier, H., and Delmas, P. 1982. Bearing capacity of a sand-soft subgrade system with geotextile. In
Proceedings of the 2nd International Conference on Geotextiles,
Las Vegas, Nev., August 1982. Industrial Fabrics Association International (IFAI), St. Paul, MN. pp. 411–416.
Gourc, J.P., Villard, P., Giraud, H., Blivet, J.C., Khay, M., Imbert,
B., Morbois, A., and Delmas, P. 1999. Sinkholes beneath a reinforced earthfill – a large scale motorway and railway experiment. In Proceedings of the Geosynthetics’ 99 Conference, 28–
30 April, 1999. Boston, Mass., U.S.A. Industrial Fabrics Association International (IFAI), Roseville, MN.
999
Kempton, G.T., Lawson, C.R., Jones, C.J.F.P., and Demerdash, M.
1996. The use of geosynthetics to prevent the structural collapse
of fills over areas prone to subsidence. In Proceedings of the 1st
European Conference on Geosynthetics: Applications, Design
and Construction, Maastricht 1996. Edited by M.B. de Groot, G.
den Hoedt, and R.J. Termaat. A.A. Balkema, Rotterdam,
pp. 317–324.
Kinney, T.C. 1986. Reinforced roads bridging voids. In Proceedings of the 4th International Conference on Cold Regions Engineering, Anchorage, 24–26 February, 1986. American Society of
Civil Engineers, New York, pp. 320–329.
Kinney, T.C., and Connor, B. 1987. Geosynthetics supporting embankments over voids. Journal of Cold Regions Engineering,
American Society of Civil Engineers, 1(4): 158–170.
Kinney, T.C., and Connor, B. 1990. Geosynthetic reinforcement of
paved road embankments on polygonal ground. Journal of Cold
Regions Engineering, ASCE, 4(2): 102–112.
Matichard, Y. 1981. Sol bicouche renforcé par géosynthétique. Application aux chaussées provisoires. Ph.D. thesis, Université
Scientifique et Médicale de Grenoble.
Perrier, H. 1983. Sol bicouche renforcé par geotextile. Rapport de
recherche LPC No. 125. Presse du Laboratoire Central des Ponts
et Chaussées. Paris, France.
Terzaghi, K. 1943. Theoretical Soil Mechanics. John Wiley and
Sons Inc. New York, U.S.A.
Villard P., and Giraud H. 1998. Three-dimensional modeling of the
behavior of geotextile sheets as membranes. Textile Research
Journal, 68(11): 797–806.
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