Technical Paper by SCR Lo

Technical Paper by S.C.R. Lo

PULL-OUT RESISTANCE OF POLYESTER STRAPS AT LOW OVERBURDEN STRESS ABSTRACT: The pull-out resistance of a high tenacity polyester strap at a low overburden stress of less than 100 kPa was studied with a large-scale pull-out box. Three different types of soil hauled from active construction sites were used. The test results indicated that the friction factor, as defined by the ratio of the average failure shear stress to average normal stress, increased with a reduction in the overburden stress. This increase was observed to be more significant for the soil with a high dilatancy. The difference in the friction factor between the Grade 20 and 30 straps was slight. These observations can be consistently explained by the constrained dilatancy hypothesis. KEYWORDS: Geosynthetic strap, Polyester, Reinforced soil, Pull-Out testing, Friction factor, Dilatancy. AUTHOR: S.C.R. Lo, Senior Lecturer, School of Civil Engineering, University College, University of New South Wales, Canberra, ACT, 2600, Australia, Telephone: 61/2-268-8349, Telefax: 61/2-6268-8337, E-mail: [email protected] PUBLICATION: Geosynthetics International is published by the Industrial Fabrics Association International, 1801 County Road B West, Roseville, Minnesota 55113-4061, USA, Telephone: 1/612-222-2508, Telefax: 1/612-631-9334. Geosynthetics International is registered under ISSN 1072-6349. DATES: Original manuscript received 28 August 1997, revised version received 27 February 1998 and accepted 7 March 1998. Discussion open until 1 March 1999. REFERENCE: Lo, S.C.R., 1998, “Pull-Out Resistance of Polyester Straps at Low Overburden Stress”, Geosynthetics International, Vol. 5, No. 4, pp. 361-382.

GEOSYNTHETICS INTERNATIONAL

S 1998, VOL. 5, NO. 4

361

Lo D Pull-Out Resistance of Polyester Straps at Low Overburden Stress

1

INTRODUCTION

High-tenacity polyester straps have recently been successfully used as the reinforcing elements for geosynthetic-reinforced soil walls. A typical cross section of a high-tenacity polyester strap is shown in Figure 1. It consists of a number of groups (referred to as lanes) of high-tenacity polyester yarns individually encapsulated in a modified polyethylene. The polyester yarns are the load carrying elements, whereas the sheathing is for protection against construction damage. In addition to possessing the common advantages of geosynthetic reinforcement, high-tenacity polyester straps have the additional advantages of possessing high strength and stiffness, and display low creep. However, the pull-out resistance of high-tenacity polyester straps often controls the reinforcement length at low overburden stress because of the high load capacity and smaller perimeter of a typical polyester strap. This is particularly true for reinforced soil walls supporting a major highway due to either horizontal loading on a sill beam or side loading on a parapet/noise barrier. The pull-out resistance of geosynthetic sheets or grids has been studied by a number of researchers (e.g. Bergado and Chai 1994, Farrag et al. 1993, Fannin and Raju 1993, Jewell et al. 1985, Juran et al. 1988, and Ochai et al. 1996), but experimental studies on the pull-out resistance of geosynthetic straps is limited. In the context of continuum mechanics, the pull-out resistance of a reinforcing element, dξ, is given by: Rp =

 τ p dξ

(1)

where: Rp = pull-out resistance of the reinforcement; τ = soil-reinforcement interface shear stress at reinforcement pull-out; p = perimeter of the reinforcement; and integration is performed over Lp , the length of the reinforcement embedded in the resistance zone (as defined by the location of maximum reinforcement tension). In design, the following simplified equation is commonly used (Christopher et al. 1989a, 1989b):

1.5 to 2 mm 4 to 6 mm

~7.5 mm Polyester yarns

Low Low density density polyethylene polyethelene (with carbon carbon black) black) (with

85 or 90 mm Figure 1.

362

Cross section of a typical polyester strap.


S 1998, VOL. 5, NO. 4


R p = α F σ0 p L p

(2)

where: σo = overburden stress acting normal to the reinforcement surface; F = pull-out resistance factor; and α = scale effect correction factor. The parameter F is the basic parameter in characterising the interface shear strength of a particular soil-reinforcement combination. The α factor takes into account the effect of nonuniform mobilisation of interface shear stress and, hence, progressive failure along the length Lp . The value of α is bounded by: 1 ≥ α ≥ Min  tan δ∕ tan δ res , tan φ∕ tan φ res 

(3)

where: tanδ = peak interface friction angle at the soil-reinforcement interface; and the subscript “res” denotes a residual value. Note that tanδ and tan δres are used in the context of element properties despite the fact that α is scale dependent. The term α F in Equation 2, which is the ratio of the average shear to normal stress at pull-out failure, is referred to as the “friction factor” in the current paper. It is recognised that the α factor and, hence, the measured friction factor in pull-out testing, is dependent on the length of the pull-out box, which can be considerably shorter than the anchored lengths of the reinforcing elements of a full-scale wall. However, the soil displacement along the reinforcement in a pull-out box is small and has a near zero value at the pull-out end. Such a displacement field generates the most severe progressive failure along the soil-reinforcement interface, but will not be realised in a fullscale, geosynthetic-reinforced soil wall as illustrated in Figure 2. This, in addition to a more favorable stress field in a full-scale wall (Bergado et al. 1992), will lead to a higher pull-out resistance in the field. This means that the friction factor, as measured in a pull-out box, actually corresponds to that of a longer anchorage length under fullscale conditions. Thus, the test results are still relevant to the design of a full-scale wall. It is pertinent to note that Equation 2 is commonly used in the context of a two-dimensional design model, with σo being deduced by a simplified two-dimensional stress analysis. Such an assumption is consistent with the interpretation of pull-out test results: σo is taken as the test pressure applied to the top boundary. However, the stress around a polyester strap is three-dimensional and this may lead to a significantly higher pullout resistance. The broad objective of the current study was to experimentally examine the pull-out resistance of a high-tenacity polyester strap at low overburden stress. The polyester strap had a textured surface and is referred to as the P-strap. The test results were synthesized on the assumption that Equation 2 can be used in the context of a two-dimensional design model. The question of factoring the three-dimensional stress field around a polyester strap into a two-dimensional design model was addressed. To remove the limitations associated with using standard laboratory sand, soils from active construction sites were used.

2

CONSTRAINED DILATANCY

The effects of a three-dimensional stress state around a polyester strap can be best captured by the dilatancy behaviour of the soil in the immediate vicinity of the strap.


S 1998, VOL. 5, NO. 4

363


Embedded end

Pull-out end

Displacement of reinforcement or soil

Relative interface displacement in pull-out box Relative interface displacement in prototype wall

Reinforcement displacement

Soil displacement displacement resistancezone zoneofof in resistant prototype wall wall prototype

Soil displacement in pull-out box

0

1

Distance along reinforcement / Anchorage length of reinforcement Figure 2. Illustration of the difference in displacement fields for a pull-out box test and an actual geosynthetic-r einforced wall.

As the strap is being “pulled out”, the soil in the vicinity of the strap will be subject to considerable shearing. For a well-compacted granular soil, subject to a constant confining stress state, shearing will lead to volumetric dilation. However, the volumetric dilation of the soil elements in the vicinity of the strap will be constrained by the surrounding soil (Figure 3). This interaction locally increases the normal stress, σn , acting directly on the strap to a value in excess of the average overburden stress acting on the surrounding soil. The latter is the σo value obtained by a two-dimensional stress calculation. Expressing the normal stress acting on the strap as σn = σo + Δ σ, the interface shear stress at failure, τ, for an infinitesimal element dξ is given by τ = (σ o + Δσ) tan δ = σo (1 + [Δσ ∕ σo ]) tan δ

(4)

where tanδ is the interface friction angle between the soil and the reinforcement. Equation 4 is to be used for an infinitesimal element and tanδ is an element property. If Equation 2 is used in the context of a two-dimensional design model, it can be reformulated for an infinitesimal element as: τ = σo F

(5)

where: F = pull-out resistance factor; and σo is deduced from a two-dimensional stress calculation. Equating 4 and 5 for a two-dimensional design model yields:

364


S 1998, VOL. 5, NO. 4


Dilation constrained by surrounding soil Tendency to dilate

Soil element in shear

Reinforcement tension Reinforcement strap

Vertical stress distribution ∆σ σo Reinforcement strap Figure 3.

Constrained dilatancy effects.

F = (1 + [Δσ ∕ σo]) tan δ

(6)

f = α (1 + [Δσ ∕ σo ]) tan δ

(7)

R p = f σo p L p

(8)

Defining f = α F, then:

where f is referred to as the friction factor or apparent coefficient of friction (BS 8006). Thus, the increased shear resistance at the interface can be indirectly modelled by an increase of the friction factor. Equation 7 indicates that the friction factor is the product of three separate terms. The first term is the α factor, which considers the effects of scale and progressive failure. The second term, 1 + ∆σ / σo , is the increase in the friction factor at low overburden stress due to the constrained dilatancy effect, and the last term represents the basic interface characteristics (as an element property). This implies that the relative increase in the friction factor at low overburden stress is independent of the anchorage length or extent of progressive failure. It is also evident that the increase in the friction factor due to the constrained dilatancy effect will only be significant at a low overburden stress, but will be of a negligible extent at a high overburden stress. The above analysis is also applicable to ribbed steel strips. For geosynthetic straps, there are two additional complicating factors. The first one is whether an adequate constrained dilatancy effect can be generated by direct shear stress transfer along the


S 1998, VOL. 5, NO. 4

365


interface. The second factor relates to the critical stress ratio before the onset of dilation. Even for a dense soil, the mobilised stress ratio has to exceed a critical value before the onset of dilation. This is illustrated by the schematic volumetric strain response of a dense sandy soil presented in Figure 4. Thus, ∆σ will be generated only if the stress ratio can exceed the critical value, meaning that the reinforcement surface must be adequately rough to ensure that the local interface stress ratio, τ / σn , can exceed the critical value. 3

TESTED MATERIALS

3.1

Polyester Strap (P-Strap)

A cross section of the polyester strap used in the current study is presented in Figure 1. The sheathing has a textured surface to provide good interface characteristics. The P-strap has a width of 85 to 90 mm, depending on the strength grade. The strap comes in nominal strength grades of 20, 30, 50, and 100 kN. The characteristic short-term tensile strength as defined by the 95% fractile is approximately 15% higher than the respective nominal strength grade. The short-term tensile strength is measured in accordance with BS 6906 using a 1 to 2 m long specimen length and a displacement rate of 100 to 150 mm per minute, respectively. Different strength grades are achieved by varying the number of yarns per lane, but using the same type of polyester and the same sheathing material. The strap is manufactured in 100 m long rolls. There are several products on the Australian market that are of a form similar to the P-strap. The testing program reported in the current paper was focused on Grade 20 and 30 straps as these grades are most commonly used at low overburden stress. 3.2

Soils Tested

Three types of soils, hauled from active construction sites and referred to as “PR”, “SW”, and “M”, were used in the current study. Soil PR was considered to be a highquality fill soil, whereas the Soils SW and M were considered to be “average” fill soils

τ / σn

Critical stress ratio = τ / σn

Dilation

Compression

Negative strain

Positive strain Volumetric strain

Figure 4.

366

Volumetric strain response of the dense sandy soil.


S 1998, VOL. 5, NO. 4


that are used in the reinforced zones of geosynthetic-reinforced soil walls in Australia. The particle size distribution curves of the three soils are shown in Figure 5. Soil PR was a well-graded, sandy gravel with less than 5% fines (i.e. particles passing through a 75 µm sieve). Although some of the larger particles were crushed during compaction, the increase in fines content due to compaction was minimal. Soil SW was a well-graded, gravelly sand, however, a significant portion of the gravel-sized particles were crushed into fines upon compaction and shearing. This can be seen by comparing the grading curves of the virgin soils and those retrieved from the pull-out box upon completion of testing (Figure 5). Soil M was a well-graded sand with some gravels. It was obtained by crushing quarried sandstone. The gravel-sized particles tended to disintegrate during compaction. The physical properties of Soils PR, SW, and M are summarized in Table 1. The soil friction angles were measured using consolidated drained direct shear tests in accordance with ASTM D 3080 and with particles > 2.6 mm removed. The target density of the direct shear soil specimens was 95% of the maximum dry density, ρd-max , as determined by Standard Proctor tests. The normal stress range adopted for the direct shear tests was 50 to 450 kPa. A tangent definition of the friction angle was adopted. Strength and friction angles were consistent with construction specifications in the direct shear tests. 4

TEST CONFIGURATION

4.1

Pull-Out Box

The pull-out box (Figure 6a) had nominal plan dimensions of 1 m × 1 m. The box was designed for testing metallic or geosynthetic reinforcement in the form of straps/ strips, mesh, grids, and sheets. The design and performance evaluation of the pull-out box are discussed in the paper by Lo (1990a). Minor details were added to the box to further improve pull-out tests for geosynthetic straps. The normal stress was applied to the top boundary using pressurized water acting on a flexible rubber membrane, which ensured an essentially uniform normal stress and negligible shear stress acting on the top boundary. However, stress uniformity along the top boundary does not necessarily guarantee uniformity of normal stress acting on the soil-strap interface, particularly near the front wall, due to wall friction (if significant) and normal stress induced by the pullout force (Juran et al. 1988). This uncertainty was handled by using the following special features of the pull-out box: Table 1.

Physical properties of the soils used in the testing program.

Property ρd-max (kg/m3) wopt (%) φ (_) φres (_)

PR

Fill soil SW

M

1,930 15.5 40 38

1,880 15.0 40 30

1,950 11.5 38 33

Note: ρd-max = maximum dry density, wopt = optimum water content measured in Standard Proctor test; φ = peak friction angle of soil; φres = residual friction angle of soil.


S 1998, VOL. 5, NO. 4

367


(a)

100

% Passing

90 80

Soil PR

70 60 Tested soil Original soil

50 40 30 20 10

% Passing

(b)

% Passing

(c)

100 90 80 70

Soil SW

60 50 40 30 20 10 100 90 80 70 60

Soil M

50 40 30 20 10 0 0.01

0.10

1.00

10.00

100.00

Particle size (mm) Figure 5.

368

Particle size distribution curves: (a) Soil PR; (b) Soil SW; (c) Soil M.


S 1998, VOL. 5, NO. 4


S The vertical walls of the pull-out box were lined with greased rubber sheets in a manner similar to the free-ends in triaxial testing in order to achieve a smooth vertical boundary and, hence, eliminated the uncertainties associated with front wall friction on the observed behaviour. S The front 100 mm was debonded from the surrounding soil by a rubber sleeve and grease system (Figure 6b). Hence, the front zone, which may be subject to complex stress conditions, did not contribute to the shear stress transfer. The exit slit was designed to serve the apparently conflicting functions of containing the soil and allowing the reinforcement to be pulled out freely. After investigating the possible increase of the friction factor at low overburden stress, it was deemed absolute-

(a) Pressurized water

Diaphragm

Polyester strap

Soil Debonded length (see sleeve detail)

10 to 20

200

LVDT

Clamp

See exit detail 1,000 200 to 250

100 to 200 (b)

Grease

(c)

Rubber sheet

100

Soil Grease Polyester strap

Rubber sheet

Polyester strap

All dimensions in mm Figure 6.

Pull-out box: (a) cross section; (b) rubber sleeve detail; (c) exit detail .


S 1998, VOL. 5, NO. 4

369


ly essential that the exit slit resistance be minimal. The exit slit was formed by packing the exit gap with four layers of soft rubber with grease in between (Figure 6c). The rubber sheets fully contained the soil and pull-out of the strap was achieved by relative sliding between the lubricated rubber sheets. Extensive calibration tests were conducted to ensure that the resistance at the exit slit was minimal (Lo 1990b). An Instron jack was used to apply the pull-out force in a displacement-controlled mode at a programmed rate of 1 mm/minute. A linear variable displacement transducer (LVDT ) was mounted outside the exit slit to measure the displacement of the strap. 4.2

Specimen Preparation

The soils were hauled directly from active construction sites to the laboratory in drums. The specimen preparation technique took into account the following factors:

S It was not practical to oven-dry the soil due to the large volume of soil required. S The cost of hauling a large quantity of soil from active construction sites located several hundred kilometres away from the laboratory was high. S Reproducible specimen preparation was needed in order to investigate the influence of overburden stress on the friction factor. S The soil was subjected to heavy compaction at the construction site, which had to be simulated in the laboratory tests. The soil was first preconditioned in a separate box before being placed in the pull-out box. The soil was turned and spread, and water was added if necessary to achieve a target water content, w. The target w value, which was on the dry side of wopt , was selected based on the site conditions. This preconditioning process took approximately one day to enable the value of w to equalise in the specimen. The soil was placed and compacted in 33 mm thick layers with a standard percussion vibratory hammer fitted with a square plate for delivering the compaction energy. This compaction method was found to simulate the effects of heavy compaction, in particular, the particle breakdown during compaction of weaker soils used at a construction site. The bulk unit weight, γ, of the soil can be strictly maintained by controlling the weight of soil used for each layer. The target as-placed γ value was chosen to reflect construction conditions. Soil PR was compacted to γ = 19.5 kN/m3. The water content was equal to 5.5% and yielded a mean dry unit weight, γd-mean = 98% of ρd-max . Soil SW was compacted to γ = 19.5 kN/m3. The mean value of the as-placed water content was 9.8% and gave γd-mean = 96% of ρd-max . Soil M was placed at γ = 19.0 kN/ /m3. The mean value of the as-placed water content was 5%, which resulted in a dry unit weight, γd = 94% of ρd-max . For Soils SW and M, the water content values were determined from specimens retrieved after pull-out testing. The variability in w values between tests had a standard deviation of 1% for Soil SW and 0.5% for Soil M. For the Soil PR tests, the overburden stress was applied immediately after specimen preparation. For the Soils SW and M tests, a “preloading pressure” of 100 and 200 kPa, respectively, was applied prior to the application of the test pressure to simulate the overconsolidation effect induced by the heavy compaction equipment. The preloading pressure was selected based on the compaction equipment used. The preloading pressure was not applied for the Soil PR tests because information on the compaction equip-

370


S 1998, VOL. 5, NO. 4


ment was not available at the time of testing. The test pressure was applied for a minimum period of two hours prior to application of the pull-out force. 4.3

Testing Program

The testing program for all three fill soils is presented in Table 2. The test pressure used was in the range of 15 to 100 kPa. It was recognized that previous studies (Fannin and Raju 1993) report pull-out tests at pressures as low as 5 kPa; however, the overburden stress on the uppermost strap in a full-scale P-strap reinforced soil wall is seldom less than 20 kPa. Hence, 15 kPa was adopted as the minimum overburden stress to be used in the test program. Most of the tests were conducted using Grade 20 or 30 straps, although a Grade 50 strap was also used in one test series (Soil M) at a test pressure of 100 kPa. Table 2.

Summary of the test program. Test reference

Strap grade

Test pressure (kPa)

PR-3

20

95

PR-4

20

53

PR-5

20

93

PR-7

30

65

PR-8a

20

26

PR-9

30

30

SW-1

30

50

SW-2

30

25

SW-3

30

15

SW-4

20

80

SW-5

20

35

SW-6

20

100

M-1

30

30

M-2

30

15

M-3

30

20

M-4

30

50

M-5

30

40

M-6

50

100

M-7

30

80

Soil PR test series

Soil SW test series

Soil M test series


S 1998, VOL. 5, NO. 4

371


5

LOAD-DISPLACEMENT CURVES

5.1

Soil PR Tests

The applied force versus displacement curves for Soil PR are presented in Figure 7. For the Soil PR tests only, the LVDT was mounted on the clamp used to connect the strap to the jack. Hence, corrections were applied to account for slippage at the clamp and extension of the length of strap between the exit point and the clamp. This, in conjunction with a semi-automatic data-logging system, led to noisy force-displacement curves. The only exception was test PR-9, which used a fully automated data-logging system. Only the load-displacement curves at applied loads larger than 2.0 kN were considered as reliable data because the applied correction can be significant when compared to the magnitude of recorded displacements at a low applied force. Thus, there may be uncertain, although small, initial errors in the displacement data. Despite this fact, it is evident that the load-displacement curves are nonlinear, and the mobilisation of the pull-out resistance was ductile. However, it should be noted that the overall load-displacement response may not be indicative of the interface shear stress versus relative displacement characteristics at an element level. The load-displacement curves can have a significantly higher stiffness, higher peak shear stress, and can display significant strain softening (Long et al. 1997). The maximum pull-out force in test PR3 was “abnormally low”

10.00

Force (kN)

Soil PR

5.00 PR--3 PR--4 PR--5 PR--6 PR--7 PR--9

0.00 0

Figure 7.

372

5

10 15 20 25 30 Displacement at exit (mm)

35

Force-displacement curves for Soil PR.


S 1998, VOL. 5, NO. 4

40


relative to other test results in the same test series; although a definitive explanation could not be found, it appeared to be due to clamp slippage. 5.2

Soils SW and M Tests

For these two test series, the LVDT at the exit was mounted directly on the strap. This arrangement gave more reliable measurements of the pull-out displacement. The test results for the two soils are discussed together because the observed responses followed a similar pattern. The applied force versus displacement curves for Soil SW are presented in Figure 8, and the curves for Soil M are presented in Figure 9. The load-displacement responses of tests SW-1 and M-6 were lost. The former was caused by retightening of the clamp during testing, and the latter was due to a malfunction of the LVDT. Note that for the Soil SW tests, the zero displacement was taken when the strap was slightly tensioned and, thus, a small force was registered at zero displacement. In the Soil M tests, zero displacement was taken when the strap was just tightened in an attempt to measure the load-displacement curve immediately after onset of loading. However, the strap slightly sagged under the weight of the LVDT that was mounted on the strap. With the application of tension, the sagging diminished, which led to a slight rotation of the LVDT mounting and, hence, a negative displacement signal. This gave a false reduction in the displacement reading with the application of the pull-out force in the initial load application phase. Once the strap became adequately tight, the above aberration ceased and the displacement increased with the applied force. Ductile mobilisation of the pull-out resistance was observed in all of the tests. The force-displacement relationship for both Soils SW and M tests were relatively linear until the maximum resistance was approached. Again, this is an overall response and may not be representative of the shear stress and relative displacement characteristics at an element level. The two exceptions were the SW-4 and SW-6 test results (Figure 8). These two tests were conducted with the Grade 20 straps under higher overburden stress. The high overburden stress permitted the development of greater tension that, in conjunction with the lower stiffness of Grade 20 straps, led to a significant nonlinear response. For these two tests, the displacement required to mobilise the peak pull-out resistance, Xp , was also higher than the other tests. It needs to be mentioned that the maximum pull-out forces applied in these two tests are expected to be significantly higher than the design reinforcement tension of the Grade 20 straps. The maximum pull-out force for test SW-6 at a test pressure of 100 kPa was slightly lower than that of test SW-4 at a test pressure of 80 kPa. This small aberration is believed to be due to the inevitable variability associated with working with a large quantity of soil hauled from an active construction site. A small unloading-reloading loop occurred for test M-4, which was due to a slight amount of clamp slippage that was then arrested. The relationship between the pull-out displacement required to mobilise the maximum pullout force, Xp , and the pull-out resistance, Rp , were examined in Figures 10a and 10b for Soils SW and M, respectively. There is a clear correlation between Xp and Rp for both Soils SW and M test results. For Soil SW (Figure 10a), the data points for both the Grade 20 and 30 straps appear to follow the same trend. For Soil M (Figure 10b), the data points that correspond to a Grade 50 (stiffer) strap are located significantly below the trend line. For both test series, Xp increases with Rp . The influence of strap grade was uncertain. The above observations can be explained by hypothesizing that the change


S 1998, VOL. 5, NO. 4

373


6.00 Soil SW

5.00

Force (kN)

4.00 3.00 SW--2 @ 25 kPa 2.00

SW--3 @ 15 kPa SW--5 @ 35 kPa

1.00

SW--4 @ 80 kPa SW--6 @ 100 kPa

0.00 0 Figure 8.

5

10 15 20 25 30 35 40 Displacement at exit (mm)

Force-displacement curves for Soil SW.

6.00 Soil M 5.00

Force (kN)

4.00 3.00 2.00

M--1 @ M--2 @ M--3 @ M--4 @ M--5 @ M--7 @

1.00 0.00 0 Figure 9.

374

30 kPa 15 kPa 20 kPa 50 kPa 40 kPa 80 kPa

5 10 15 20 Displacement at exit (mm)

25

Force-displacement curves for Soil M.


S 1998, VOL. 5, NO. 4


(a)

30.00 Soil SW

Xp (mm)

20.00

10.00 Grade 30 strap Grade 20 strap 0.00

(b)

20.00 Xp (mm)

Soil M 10.00 Grade 30 strap Grade 50 strap 0.00 1.00

Figure 10.

2.00

3.00 4.00 5.00 Pull--out resistance (kN)

6.00

Xp versus Rp plot: (a) Soil SW; (b) Soil M.

in Xp values was due to the following effects: (i) deformation along the soil-strap interface; (ii) deformation of the surrounding soil; and (iii) strap extension along the embedded strap. Effect (ii) would cause the constrained dilatancy effect, which complicated the influence of the strap grade on the Xp versus Rp relationship. 6

FRICTION FACTOR

6.1

Force Correction

Apparent cohesion may contribute to the measured pull-out resistance because the tests were conducted with the soil in neither a fully saturated nor a completely dry state. This is particularly relevant for Soils SW and M as the soil particles of these two soil types possessed some fines. There may also be some resistance at the exit slit. At a low overburden stress, these additional resistances, although small in magnitude, may have had a significant influence on the friction factor calculated using the test results.


S 1998, VOL. 5, NO. 4

375


To correct for the above errors, calibration tests were conducted to measure the pullout resistance of a P-strap without any applied pressure. For Soil PR, the maximum resistance measured in a calibration test was approximately 1.3 kN, but the pull-out resistance reduced to an approximately constant value of 0.9 kN at less than 5 mm of displacement. Hence, a value of 0.9 kN was adopted as the force correction. For the Soils SW and M, the complete force-displacement curves are presented in Figure 11. These curves indicate that the measured noise is small compared to the force correction. The maximum resistance is mobilised rapidly and a sharp peak resistance was not observed. Hence, the force correction can easily be derived from the maximum resistance as measured in a calibration test. 6.2

Friction Factor Versus Overburden Stress

The maximum pull-out resistance was calculated by deducting the force correction from the maximum force recorded in a test. The friction factor, f, was then calculated using Equation 2 and with σo equated to the test pressure. The friction factors were then plotted against the test pressure (Figures 12a, 12b, and 12c for Soils PR, SW, and M, respectively). 6.2.1 Soil PR As evident from Figure 12a, the increase in the friction factor with a reduction in the overburden stress is very significant. Despite the fact that two strap grades are used in this test series, the test results are well approximated by a single curve. The exception is test PR-8a, which achieves a significantly lower friction factor. No explanation can be established for this discrepancy other than noting that this is a restart test. This data point was excluded in deducing the best-fit curve.

1.00

Force (kN)

Soil SW Soil M

0.00 0

5

10

15

Displacement at exit (mm) Figure 11.

376

Calibration of test results.


S 1998, VOL. 5, NO. 4

20


(a)

2.00

Friction factor

Soil PR 1.50

1.00

tanφ

Grade 30 strap Grade 20 Best fit

0.50

0.00 1.50

(b)

Friction factor

Soil SW 1.00 tanφ 0.50

Grade 30 strap Grade 20 Best fit

0.00 1.50

(c)

Friction factor

Soil M 1.00 tanφ

0.50 Grade 30 strap Grade 20 Best fit 0.00 0.00

Figure 12.

50.00 100.00 Overburden stress (kPa)

Friction factor versus overburden stress: (a) Soil PR; (b) Soil SW; (c) Soil M.


S 1998, VOL. 5, NO. 4

377


6.2.2 Soil SW As evident from Figure 12b, the test results are well approximated by a single curve despite the fact that two strap grades are used in this test series. The data point for 100 kPa, however, is slightly below the best-fit curve. This data point corresponds to a Grade 20 strap (lower stiffness) and higher strap tension. The higher strap tension developed due to the high applied pressure of 100 kPa. This condition led to a greater degree of progressive failure and, thus, a lower pull-out resistance when compared with the test data for Grade 30 or 20 straps, which were subjected to a lower reinforcement tension. 6.2.3 Soil M The test results for Soil M are also well approximated by a single curve (Figure 12c). All the tests except one were conducted using Grade 30 straps. The data point corresponding to the higher strength Grade 50 strap does not display any deviation from the best-fit curve. This occurred because the strap was subjected to high tension due to the high overburden stress used in this particular test and, thus, compensated for the higher stiffness of a Grade 50 strap. 6.3

Synthesis and Discussion

All three fill soils displayed a similar variation of the friction factor with the applied pressure. The friction factor, f, decreased with an increase in the applied pressure, but at a reducing rate. Note that, for both Soils SW and M, the data point for an overburden pressure of 15 kPa was located well below the corresponding best-fit curve. This is believed to be due to overestimation of the force correction for apparent cohesion and exit resistance. The most important observation is that at a low overburden stress, f > tanφ, where φ is the peak friction angle of the soil. Although the φ values at a low overburden stress can be higher than those reported in Table 1, the results reported by Juran and Christopher (1989) and Tatsuoka et al. (1986a, 1986b) indicated that the φ value at a normal stress of 15 kPa is unlikely to exceed 50_. Note that for δ < φ and α < 1, an assumed value of φ = 50_ cannot yield the high f values in Figures 12a to 12c. The observed high f value at a low test pressure is best analysed by comparing this observation with Equation 7 reproduced below: f = α (1 + [Δσ∕σo]) tan δ Noting that for α < 1 and δ < φ , the observation that f > tanφ can be explained by a very significant constrained dilatancy effect, thus, leading to a high value for the second term, (1 + [∆σ / σo ]) . The increase in the friction factor at low overburden stress can be represented by ∆f = f15 -- f100 , where f15 and f100 are the f values at an overburden stress of 15 and 100 kPa, respectively. Soil PR was the most dilatant material of the three and had the highest value of ∆f in excess of 1.6. Soil SW had the lowest dilatancy, which was consistent with its low ∆f value of approximately 0.65. As evident from Figures 12a and 12b, a single curve can be used to fit the test data covering both Grade 20 and 30 straps. This implies that the difference in the f value be-

378


S 1998, VOL. 5, NO. 4


tween Grade 20 and 30 straps is slight. However, the higher extensibility of Grade 20 straps would lead to a higher progressive failure. Hence, one might expect the Grade 20 strap to have a lower friction factor, even though the surface texture of the two strap grades was the same. This apparently unexpected observation can also be explained by the constrained dilatancy hypothesis. The higher reinforcement extensibility of a Grade 20 strap leads to higher shear strain and greater strain softening near the exit. But the higher shear strain may also lead to a higher normal stress, σn , acting locally on the strap, due to the constrained dilatancy effect, thus, partly compensating for the higher strain softening. Such a mechanism also provides a consistent explanation for the uncertain effect of strap grade on the observed Xp versus Rp trend (Figures 10a and 10b). At a high applied pressure, f appeared to asymptotically approach a minimum (threshold) value, and this value may be approximated by f100 . The second important observation was that the friction factor at f100 can be considerably lower than that given by the empirical correlation for the interface friction angle, δ, expressed as follows: tan δ = 0.7 tan φ

(9)

where δ is the peak interface friction angle measured using a direct shear test as an element property. This can be explained by progressive failure. The interface friction angle as given by Equation 9 is the peak interface parameter for an infinitesimal element. At a high applied pressure, the constrained dilatancy effect is negligible. Equating f to tanδ, given by Equation 9, implies that the peak interface strength can be mobilised simultaneously along the complete length of the reinforcement. This cannot be true if there is progressive failure along the interface. However, Equation 9 can better estimate f100 if the residual friction angle is used in lieu of the peak friction angle.

7

CONCLUSIONS

The pull-out resistance of polyester straps was investigated using large-scale pull-out testing. Three types of soil, obtained from active construction sites, were used in the investigation. The mobilisation of the pull-out resistance was observed to be ductile in nature. The test results unambiguously showed that, at low overburden stress, the friction factor as measured in laboratory pull-out testing was higher than tanφ. This can be consistently explained by the constrained dilatancy hypothesis and the textured surface of the polyester straps. For the test conditions used in this testing program, the dependency of the pull-out resistance on strap grade appeared to be slight. However, at an overburden stress of 100 kPa, the as-measured friction factor was considerably lower than tanδ. This implies that at a high overburden stress, the constrained dilatancy effect was small and the progressive failure mechanism dominated.

ACKNOWLEDGMENT This project was partially supported by Austress Freyssinet Pty Ltd. The opinions expressed in the current paper are, however, solely those of the author.


S 1998, VOL. 5, NO. 4

379


NOTATIONS Basic SI units are given in parentheses. dξ F f f15 f100 Lp p Rp w wopt Xp

= = = = = = = = = = =

α ∆f ∆σ

= = =

δ δres γ γd γd-mean ρd-max σo σn τ φ φres

= = = = = = = = = = =

infinitesimal element length along soil-reinforcement interface (m) pull-out resistance factor in Equation 2 (dimensionless) friction factor measured in large-scale pull-out box (dimensionless) friction factor at 15 kPa overburden pressure (dimensionless) friction factor at 100 kPa overburden pressure (dimensionless) length of reinforcement embedded in resistance zone (m) perimeter of reinforcement (m) pull-out resistance of reinforcement (N) water content (%) optimum water content (%) displacement required to mobilise peak pull-out resistance of reinforcement (m) scale effect correction factor (Equation 2) (dimensionless) f15 -- f100 (dimensionless) increase in normal stress acting directly on infinitesimal element due to constrained dilatancy effects (N/m2) peak interface friction angle of infinitesimal element (_) residual interface friction angle of infinitesimal element (_) bulk unit weight (N/m3) dry unit weight (N/m3) mean dry unit weight (N/m3) maximum dry density measured in Standard Proctor test (kg/m3) overburden stress in Equation 2 (N/m2) normal stress acting directly on infinitesimal element (N/m2) interface shear stress of infinitesimal element (N/m2) peak friction angle of soil (_) residual friction angle of soil (_)

REFERENCES ASTM D 3080 “Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions”, American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. BS 6906, “Methods of Test for Geotextiles: Part I, Determination of Tensile Properties Using a Wide-Width Strip”, British Standards Institution, London, UK.

380


S 1998, VOL. 5, NO. 4


BS 8006, “Strengthened/Reinforced Soils and Other Fills”, British Standards Institution, London, UK. Bergado, D.T. and Chai, J., 1994, “Pull-Out Force-Displacement Relationship of Extensible Grid Reinforcements”, Geotextiles and Geomembranes, Vol. 12, No. 4, pp. 395-316. Bergado, D.T., Lo, K.H., Chai, J.C., Shivashankar, R., Alfaro, M.C. and Anderson, L.R., 1992, “Pull-Out Testing Using Steel Grid Reinforcements Using Lower Quality Steel Backfill”, Journal of Geotechnical Engineering, Vol. 118, No. 7, pp. 1047-1063. Christopher, B.R., Gill, S.A., Giroud, J.P., Juran, I., Schlosser F., Mitchell, J.K. and Dunnicliff, J., 1989a, “Reinforced Soil Structures: Volume I. Design and Construction Guidelines”, Report No. FHWA-RD-89-043, Washington, DC, USA, November 1989, 287 p. Christopher, B.R., Gill, S.A., Giroud, J.P., Juran, I., Schlosser F., Mitchell, J.K. and Dunnicliff, J., 1989b, “Reinforced Soil Structures: Volume II. Summary of Research and System Information”, Report No. FHWA-RD-89-043, Washington, DC, USA, November 1989, 287 p. Fannin, R.J. and Raju, D.M., 1993, “On the Pullout Resistance of Geosynthetics”, Canadian Geotechnical Journal, Vol. 30, No. 3, June 1993, pp. 409-417. Farrag, K, Acar, Y.B. and Juran, I., 1993, “Pull-Out Resistance of Geogrid Reinforcement”, Geotextiles and Geomembranes, Vol. 11, No. 2, pp. 133-159. Jewell, R.A., Milligan G.W.E., Sarsby, R.W. and DuBois, D., 1985, “Interaction Between Reinforcement and Geogrids”, Polymer Grid Reinforcement, Thomas Telford, 1985, Proceedings of a conference held in London, UK, March 1984, pp. 18-30. Juran, I., Knochenmus, G., Acar, Y.B. and Arman, A., 1988, “Pull-Out Response of Geotextiles and Geogrids (Synthesis of Available Experimental Data)”, Geosynthetics for Soil Improvement, Holtz, R.D., Editor, Geotechnical Special Publication No. 18, proceedings of the symposium sponsored by the Geotechnical Engineering Division of the ASCE, Nashville, Tennessee, USA, May 1988, pp. 92-111. Juran, I. and Christopher, B., 1989, “Laboratory Model Study on Geosynthetic Reinforced Soil Walls”, Journal of Geotechnical Engineering, Vol. 115, No. 7, pp. 905-926. Lo, S-C.R., 1990b, “Determination of Design Parameters of a Mesh-Type Soil Reinforcement”, Geotechnical Testing Journal, Vol. 13, No. 4, pp. 343-350. Lo S-C.R., 1990a, “Discussion of ‘Scale and Other Factors Affecting the Results of Pull-Out Tests of Grids Buried in Sand’ ”, Geotechnique, Vol. 40, No. 3, pp. 519-521. Long, P.V., Bergado, D.T. and Balasubramanian, A.S., 1997 “Interaction Between Soil and Geotextile Reinforcement”, Ground Improvement, Ground Reinforcement and Ground Treatment: Developments 1987-1997, Schaefer, V.R., Editor, ASCE Geotechnical Special Publication No. 69, proceedings of the symposium held in Logan, Utah, USA, July 1997, pp. 560-578. Ochai, H., Otani, J., Hiyaschic, S. and Hirai, T., 1996, “The Pull-Out Resistance of Geogrids in Reinforced Soils”, Geotextiles and Geomembranes, Vol. 14, No. 1, pp. 19-42.


S 1998, VOL. 5, NO. 4

381


Tatsuoka, F., Sakamoto, M., Kawamura, T. and Fufushima, S., 1986a, “Strength and Deformation Characteristics of Sand in Plane Strain at Extremely Low Pressure”, Soils and Foundations, Vol. 26, No. 1, pp. 65-84. Tatsuoka, F., Goto, S. and Sakamoto, M., 1986b, “Effects of Some Factors on Strength and Deformation Characteristics of Sand at Low Pressure”, Soils and Foundations, Vol. 26, No. 1, pp. 105-114.

382


S 1998, VOL. 5, NO. 4

Errata

PULL-OUT RESISTANCE OF POLYESTER STRAPS AT LOW OVERBURDEN STRESS TECHNICAL PAPER FOR ERRATA: Lo, S.C.R., 1998, “Pull-Out Resistance of Polyester Straps at Low Overburden Stress”, Geosynthetics International, Vol. 5, No. 4, pp. 361-382. PUBLICATION: Geosynthetics International is published by the Industrial Fabrics Association International, 1801 County Road B West, Roseville, Minnesota 55113-4061, USA, Telephone: 1/651-222-2508, Telefax: 1/651-631-9334. Geosynthetics International is registered under ISSN 1072-6349. REFERENCE FOR ERRATA: Lo, S.C.R., 2000, “Errata for ‘Pull-Out Resistance of Polyester Straps at Low Overburden Stress’”, Geosynthetics International, Vol. 7, No. 1, p. 73.

The authors inadvertently left out one of the test descriptions in Table 2, p. 371, and incorrectly labeled Figure 12c, p. 377, in their technical paper, which appeared in Geosynthetics International, Vol. 5, No. 4. ERRATUM FOR SECTION:

4.3

Testing Program

In Table 2, p. 371 : Under the “Soil PR test series”, Test PR-6 should be added. The strap grade of PR-6 is 30 and the test pressure is 149 kPa. ERRATUM FOR SECTION:

6.2.1 Soil PR

In Figure 12c, p. 377 : The point labeled “Grade 20” should be labeled “Grade 50”.


S 2000, VOL. 7, NO. 1

73