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FFDM Software Development Series 13 1 2025-01-07
FFDM Software Development Series 13
Modelling Reinforcing Material Subjected to Pullout
Ching-Chuan Huang
Professor Emeritus
Department of Civil Engineering,
National Cheng Kung University, Tainan, Taiwan
Email: samhcc@mail.ncku.edu.tw
2025/01/07
FFDM Software Development Series 13 2 2025-01-07
INTRODUCTION
In displacement-based analyses using FFDM, mobilized pullout forces of
reinforcement are functions of shear displacements along the potential failure surface.
Based on past studies on the tensile stress vs. pullout displacement of reinforcing
material subjected to pullout, the tensile stress vs. pullout displacement relationship can
be well-simulated using hyperbolic curves. To establish a hyperbolic curve-based
reinforcement pullout model, some well-instrumented pullout tests on polymer or non-
polymer reinforcement are analyzed using a curve fitting technique. Huang (2013) and
Huang et al. (2017) conducted preliminary study on using hyperbolic curves in
modelling pullout behavior of geosynthetic material in some reduce-scaled pullout test.
In the following, the hyperbolic curve-based pullout model is extended to accommodate
a wide variety of materials currently used as reinforcing materials. Correlations
between the soil types and the parameters governing the hyperbolic pullout curves are
identified.
13.1 BOND COEFFICIENT
Experimental studies on soil-reinforcement interactions using pullout boxes (Table
13.1.1) provide information in terms of bond coefficient, fb defined by:
𝑓=𝜏
𝜏 (13 − 1 − 1)
τmax: peak value of shear stress mobilized at peak pullout force.
τf: shear strength of soils
Values of fb obtained in these pull-out tests shown in Fig. 13.1.1 reveal the
following:
(1) A consistent trend of decreasing fb with the increase of σn’ is for all tested materials,
except the geogrid/clayey silt which exhibits no pressure-dependent values of fb.
(2) The values of fb for the smooth steel/sand interface are close to those for
geogrid/sand and geotextile/sand.
(3) Ribbed materials, such as ribbed geostrips and ribbed steel strips have values of fb
which are distinct from those with smooth faces.
(4) The values of fb for the ribbed geostrip/sand have a relatively highly variated fb,
compared with other materials tested. This is shown by the line of the upper limit
for ribbed geostrip/sand interface.
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Table 13.1.1 Summary of pullout tests
Reference Soil type
(USCS)
Pullout material Lf *
(m)
c **
(kPa)
φ**
()
Sugimoto &
Alagiyawanna (2003)
Silica sand
(SP)
Integrated geogrid 0.68 0 29.9
Sieira et al. (2009) Sandy silt (SM), silty
clay (MC)
Woven geogrid 1.0 15-30
21-37
Moraci et al. (2014) Silica sand (SP) Geogrid 1.15
Tajabadipour &
Lajevardi (2021)
Silica sand
(SP)
Geosynthetic, Steel,
Ribbed steel strips
0.85 0 38
Ismail et al. (2021) Silica sand
(SP)
Biaxial geogrid,
Wonen geotextile
0.70 0 46.8-
52.6
Park & Hong (2021)
Well-graded sand (SW) Geosynthetic strip 1.25 8.7 35.5
Vieira & Pereira
(2022)
Re-cycled construction
materials
Woven geogrid,
Woven geotextile
0.75 12.4-
21.1
37.5-
40.5
* Full embedment length of pullout specimen
** Cohesion intercept and internal friction angle of soils
Fig. 13.1.1 Bond coefficients obtained for various materials
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An important issue to be addressed in using the above-mentioned values of fb in
the analysis is the length of reinforcement embedded in the potential pullout zone, i.e.,
use the full length of reinforcement embedded (Lf) or use the so-called ‘effective length’
(Le). The latter one has been observed and proposed in recent research (Cardile et al.,
2016). Table 13.1.1 shows that only very limited number pullout tests using Lf>1.0 m
along with local strain (or displacement) sensors. Therefore, an assumption of Le≦1.0
m is used here to derive the bond coefficients shown in Fig. 13.1.1. Another fact that
supports the use of Le≦1.0 m is that under the peak pullout state, the local axial stresses
(or strains) at a distance larger than 1.0 m from the pullout end are negligibly small
(Cardile et al., 2016, Ferreira et al., 2020).
13.2 HYPERBOLIC PULLOUT FORCE-DISPLACEMENT RELATIONSHIPS
The hyperbolic pullout force vs. displacement curve can be expressed as:
𝑇=𝛿
𝑎+𝑏∙𝛿 (13 − 2 − 1)
𝑎= 1
𝑘 (13 − 2 − 2)
𝑏= 1
𝑇 = 𝑅
𝑇 (13 − 2 − 3)
δ: pullout displacement
ki: initial pullout stiffness
Rt: asymptote factor (ratio between failure strength and asymptote strength)
Tspt: asymptote strength at infinite displacement
Tf: failure strength determined by the smaller of tiebreak and pullout strength
𝑇= 𝑀𝑖𝑛.𝑜𝑓 𝑇,𝑇 (13 − 2 − 4)
𝑇 = 𝑓∙𝜎
∙𝐿 (13−2−5)
σn’: Effective normal stress
Le: Effective pullout length of reinforcement (≦1.0 m)
Ttiebreak: tie-break strength of reinforcement
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13.3 STRESS DEPENDENCY OF INITIAL PULLOUT STIFFNESS
The initial pullout stiffness (ki) can be expressed as a power function of effective
normal stress (σn’) on the failure surface:
𝑘=𝐾∙𝐺𝜎
𝑃 (13 − 3 − 1)
Kt: initial pullout stiffness number (a non-dimensional material constant)
Pa: atmospheric pressure (= 101.3 kPa)
G: reference pullout stiffness (= 101.3 kN/m/m)
nt: exponent of stress dependency
Based on a series of curve-fitting using pullout resistance vs. pullout displacement
curve reported in the studies shown in Table 13.1.1, hyperbolic curve parameters, Kt, nt,
Rt are summarized in Figs. 13.3.1 (and 13.3.2), 13.3.3, and 13.3.4, respectively. In each
figure, median line and 95% confidence intervals are shown. Soil types (type1: SW, 2:
SP, 3: SM, 4: MC) according to Unified Soil Classification System (USCS), rather than
friction angles (φ) are used because one of the soils investigated here is a cohesive soil
(with a non-zero cohesion intercept). Therefore, friction angles are not the only
parameters for soil strength.
Figure 13.3.1 shows Kt vs. soil type relationship obtained in the pullout tests. An
overall trend of descending value of Kt with the decrease of soil strengths (or the
decrease of particle size) can be seen. Figure 13.3.2 provides another version of Kt vs.
soil type relations. In this case, a normalized parameter (Kt
·
G)/J2% is used as the ordinate,
rather than Kt. The J2% is the in-air tensile stiffness of the pullout material. Data points
in Fig. 13.3.2 are with less scattering than those in Fig. 13.3.1.
Figure 13.3.3 shows the stress level dependency exponent (nt) vs. soil type
relationships. The value of nt tends to decrease with the decrease of soil strengths (or
the decrease of particle size). Figure 13.3.4 shows asymptote factor (Rt) vs. soil type
relationships for various types of soils investigated. A similar trend to those observed
in Fig. 13.3.1 through 13.3.3 can be seen.
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Figure 3.3.1 Initial pullout stiffness number K vs. Soil type relationship
Figure 13.3.2 Normalized initial pullout stiffness number Kt vs. Soil type relationship.
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Figure 13.3.3 Pressure dependency exponent (nt) vs. Soil type relationships
Figure 13.3.4 Asymptote factor (Rt) vs. Soil type relationships
13.4 RELATIONSHIP BETWEEN PULLOUT AND SHEAR DISPLACEMENTS
Figures 13.4.1(a) show a zero-shear displacement and a large shear displacement
condition, respectively, of a shear band intersecting with a reinforcement layer. Fig.
13.4.1(b) shows that the pullout displacement of reinforcement (δ) is identical to the
shear displacement of the base of slice No. i (Δi):
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𝛿=∆ (13 − 4 − 1)
The increment of reinforcement pull-out displacement (
incr) is the difference
between the post-loading pullout displacement (
b) and pre-loading pullout
displacement (
a), expressed as:
𝛿 =𝛿−𝛿 (13 − 4 − 2)
Corresponding to the incremental pull-out displacement, an incremental pull-out
force (Tincr) is expressed as:
𝑇 = 𝑇−𝑇 (13 − 4 − 3)
Where Ta and Tb are pull-out forces mobilized at the pre-loading and post-loading
conditions, respectively.
Fig. 13.4.1 Pullout displacement of reinforcement intersecting with a shear band.
(a) zero shear displacement condition, (b) large shear displacement condition.
(b)
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REFERENCES
Cardile, G., Moraci, N. and Calvarano, L.S. (2016) “Geogrid pullout behaviour
according to the experimental evaluation of the active length” Geosynthetics
International, Vol. 23, No.3, 194-205.
Ferreira, F. B., Vieira, C. S. and Lopes, M. L. (2020) “Pullout behavior of different
geosynthetics- Influence of soil density and moisture content” Frontiers in Built
Environment, Vol. 6, No. 12, 1-13. Doi: 10.3389/fbuil.2020.00012
Huang, C.-C. (2013) “Force equilibrium-based finite displacement analyses for
reinforced slopes: Formulation and verification” Geotextiles and Geomembranes,
Vol. 42, pp. 394-404.
Ismail, M.K.A., Joohari, M.I., Habulat, A. and Azizan, F.A. (2021) “Pull-out resistance
of sand-geosynthetics reinforcement” The International Journal of Integrated
Engineering, Vol. 13, No.3, 87-93. Doi: doi/org/10.30880/ijie.2021.13.03.010
Moraci, N., Cardile, G., Gioffre, D., Mandaglio, M. C., Calvarano, L.S., Carbone, L.
(2014) “Soil geosynthetic interaction: Design parameters from experimental and
theoretical analysis” Transport Infrastructure and Geotechnical Engineering, Vol.
1, 165-227. Doi: 10.1007/s40515-014-0007-2
Park, J. and Hong, G. (2021) “Effective length prediction and pullout design of
geosynthetic strips based on pullout resistance” Materials, Vol. 14, 6151.
Sieira, A.C.C.F., Geoscovich, D.M.S, Sayao, A.S.F.J. (2009) “Displacement and load
transfer mechanisms of geogrids under pullout condition” Geotextiles and
Geomembranes, Vol. 27, 241-253.
Sugimoto, M. and Alagiyawanna, A.M.N. (2003) “Pullout behavior of geogrid by test
and numerical analysis” Journal of geotechnical and geoenvironmental engineering,
ASCE, Vol. 129, No. 4, 361-371. Doi: 10.1061/(ASCE)1090-
0241(2003)129:4(361)
Tajabadipour, M. and Lajevardi, S.H. (2021) “Laboratory large-scale pullout
investigation of a new reinforcement of composite geosynthetic strip” Journal of
Rock Mechanics and Geotechnical Engineering, Vol. 13, 1147-1159.
Vieira, C. and Pereira, P.M. (2022) “Influence of the geosynthetic type and compaction
conditions on the pullout behaviour of geosynthetics embedded in recycled
construction and demolition materials” Sustainability, Vol. 14, 12070. Doi:
doi.org/10.3390/su14031207