Zornberg, J.G. (2007). “New Concepts in Geosynthetic-Reinforced Soil.” Keynote lecture, Proceedings of the Fifth Brazilian Symposium on Geosynthetics, Geossinteticos 2007, and of the Sixth Brazilian Congress on Environmental Geotechnics, REGEO `2007, Recife, Brazil, 18-21 June, pp. 1-26 (CD-ROM). New Concepts in Geosynthetic-Reinforced Soil

Jorge G. Zornberg, Ph.D., P.E. The University of Texas at Austin

ABSTRACT: Traditional soil reinforcing techniques involve the use of continuous geosynthetic inclusions such as geogrids and geotextiles. The acceptance of geosynthetics in reinforced soil construction has been triggered by a number of factors, including aesthetics, reliability, simple construction techniques, good seismic performance, and the ability to tolerate large deformations without structural distress. Following an overview of conventional reinforced soil applications, this paper focuses on recent advances in reinforced soil technology. Examples include advances in reinforced soil design for conventional loading (e.g. validation of analysis tools), advances in design for unconventional loading (e.g., reinforced bridge abutments), and advances in reinforcement materials (e.g., polymeric fiber reinforcements).

KEYWORDS: Soil Reinforcement, Shear Strength, Fiber-Reinforcement.

provide vertical grade separations at a lower cost 1 INTRODUCTION than traditional concrete walls. Reinforced wall systems involve the use of shotcrete facing Geosynthetic inclusions within a soil mass can protection or of facing elements such as precast provide a reinforcement function by developing or cast-in-place concrete panels. Alternatively, tensile forces which contribute to the stability of steepened reinforced slopes may eliminate the the geosynthetic-soil composite (a reinforced use of facing elements, thus saving material soil structure). Design and construction of stable costs and construction time in relation to vertical slopes and retaining structures within space reinforced walls. As indicated in Figure 1 a constrains are aspects of major economical reinforced soil system generally provides an significance in geotechnical engineering optimized alternative for the design of earth projects. For example, when geometry retaining structures. requirements dictate changes of elevation in a highway project, the engineer faces a variety of A reduced scale geotextile-reinforced slope distinct alternatives for designing the required model built using dry sand as backfill material. earth structures. Traditional solutions have been The maximum slope inclination of an either a concrete retaining wall or a unreinforced sand under its own weight is the conventional, relatively flat, unreinforced slope. angle of repose of the sand, which is well below Although simple to design, concrete wall the inclination of the slope face of the model. alternatives have generally led to elevated Horizontal geotextile reinforcements placed construction and material costs. On the other within the backfill provided stability to the steep hand, the construction of unreinforced sand slope. In fact, not only the reinforced slope embankments with flat slope angles dictated by model did not fail under its own weight, but its stability considerations is an alternative often failure only occurred after the unit weight of the precluded in projects where design is controlled backfill was increased 67 times by placing the by space constraints. model in a geotechnical centrifuge (Zornberg et al., 1998). Geosynthetics are particularly suitable for soil reinforcement. Geosynthetic products typically The use of inclusions to improve the mechanical used as reinforcement elements are nonwoven properties of soils dates to ancient times. geotextiles, woven geotextiles, geogrids, and However, it is only within the last quarter of geocells. Reinforced soil vertical walls generally century or so (Vidal, 1969) that analytical and

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experimental studies have led to the deformations without structural distress. The contemporary soil reinforcement techniques. design of reinforced soil slopes is based on the Soil reinforcement is now a highly attractive use of limit equilibrium methods to evaluate alternative for embankment and retaining wall both external (global) and internal stability of projects because of the economic benefits it the structure. The required tensile strength of offers in relation to conventional retaining the reinforcements is selected during design so structures. Moreover, its acceptance has also that the margins of safety, considering an been triggered by a number of technical factors, internal failure are adequate. Guidance in soil that include aesthetics, reliability, simple reinforcement design procedures is provided construction techniques, good seismic by Elias et al. (2001). performance, and the ability to tolerate large

Increasing right-of-way

a) Concrete retaining b) Reinforced wallc) Reinforced slope d) Unreinforced slope wall

Increasing construction cost

Figure 1. Reinforcement function of geosynthetics used to optimize the design of earth retaining structures.

deformations without structural distress. The 2 VALIDATION OF DESIGN TOOLS design of reinforced soil slopes is based on the use of limit equilibrium methods to evaluate 2.1 Overview both external (global) and internal stability. After adopting the shear strength properties of The use of inclusions to improve the mechanical the backfill material, the required tensile strength properties of soils dates to ancient times. of the reinforcements can be defined in the However, it is only within the last three decades design so that the margin of safety is adequate. or so (Vidal 1969) that analytical and experimental studies have led to the Geosynthetics are classified as extensible contemporary soil reinforcement techniques. reinforcements. Consequently, the soil strength Soil reinforcement is now a highly attractive may be expected to mobilize rapidly, reaching alternative for embankment and retaining wall its peak strength before the reinforcements projects because of the economic benefits it achieve their ultimate strength. This rationale offers in relation to conventional retaining has led to some recommendations towards the structures. Moreover, its acceptance has also adoption of the residual shear strength for the been triggered by a number of technical factors, design of geosynthetic-reinforced slopes. This is which include aesthetics, reliability, simple the case of commonly used design methods such construction techniques, good seismic as those proposed by Jewell (1991) and performance, and the ability to tolerate large Leshchinsky and Boedeker (1989). Several

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agencies have endorsed the use of residual shear review of current design criteria used by strength parameters in the design of reinforced different agencies for geosynthetic-reinforced soil structures, as summarized in Table 1. walls, geosynthetic-reinforced slopes, and Zornberg and Leshchinsky (2001) present a embankments over soft soils.

Table 1. Summary of Guidelines on Selection of Soil Shear Strength Parameters for Geosynthetic-Reinforced Soil Design

Method/Agency Shear Strength Reference Parameters Jewell’s Method Residual Jewell (1991) Leshchinsky and Boedeker’s method Residual Leshchinsky and Boedeker (1989) Queensland DOT, Australia Residual RTA (1997) New South Wells, Australia Residual QMRD (1997) Bureau National Sols-Routes (draft French Residual Gourc et al. (2001) Standard) Federal Highway Administration (FHWA), Peak Elias et al. (2001), AASHTO AASHTO 1996 National Concrete Masonry Association Peak NCMA (1997, 1998) GeoRio, Brazil Peak GeoRio (1989) Canadian Geotechnical Society Peak Canadian Geotechnical Society (1992) German Society of Soil Mechanics and Peak EBGEO (1997) Geotechnical Engineering Geotechnical Engineering Office, Hong Peak GCO (1989), GEO (1993) Kong Public Works Research Center, Japan Peak Public Works Research Center (2000) British Standards, United Kingdom Peak British Standard Institution (1995) Leshchinsky’s hybrid method Hybrid Leshchinsky (2001)

The use of the peak friction angle has been design guidance manuals recommend the use of common practice in the US for the design of the peak friction angle in the limit equilibrium geosynthetic-reinforced slopes. Guidance in soil analyses. Other agencies that have also endorsed reinforcement design procedures has been the use of peak shear strength parameters in the compiled by several federal agencies in the US, design of reinforced soil structures are including the American Association of State summarized in Table 1. Highway and Transportation Officials (AASHTO 1996), and the Federal Highway A hybrid approach was recently proposed by Administration (Elias et al. 2001). Design Leshchinsky (2000, 2001). Central to his guidance is also provided by the National approach is the use of a design procedure in Concrete Masonry Association (NCMA 1997), which peak soil shear strength properties would possibly the only industry manual of soil be used to locate the critical slip surface, while reinforcement practice. The above mentioned the residual soil shear strength properties would

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subsequently be used along the located slip surface to compute the reinforcement requirements. LVDT1 LVDT2

In order to address the controversial issue LP6 regarding selection of shear strength properties LP5 in reinforced soil design, this paper presents LP4 experimental evidence on failed reinforced H = 228 mm slopes. Specifically, the experimental LP3 information obtained from centrifuge modeling LP2 supports the use of peak shear strength LP1 parameters in the design of geosynthetic- reinforced soil structures. The perceived conservatism in design is also not supported by L = 203 mm the generally observed good performance of Figure 2. Typical centrifuge model. monitored reinforced soil structures. The number of reinforcement layers in the 2.2 Centrifuge Testing Program models ranged from six to eighteen, giving reinforcement spacing ranging from 37.5 mm Limit equilibrium analysis methods have been to 12.5 mm. All models used the same traditionally used to analyze the stability of reinforcement length of 203 mm. The use of a slopes with and without reinforcements. reasonably long reinforcement length was However, to date, limit equilibrium predictions deliberate, since this study focused on the of the performance of geosynthetic-reinforced evaluation of internal stability against breakage slopes have not been fully validated against of the geotextile reinforcements. In this way, monitored failures. This has led to a perceived external or compound failure surfaces were not overconservatism in their design. expected to develop during testing. As shown Consequently, an investigation was undertaken in the figure, the geotextile layers were to evaluate design assumptions for wrapped at the slope facing in all models. geosynthetic-reinforced slopes (Zornberg et al. Green colored sand was placed along the 1998a, 2000). The results of centrifuge tests Plexiglas wall at the level of each provide an excellent opportunity to examine reinforcement in order to identify the failure the validity of various assumptions typically surface. In addition, black colored sand made in the analysis and design of reinforced markers were placed at a regular horizontal soil slopes. This paper presents the aspects of spacing (25 mm) in order to monitor lateral that study aimed at evaluating the shear displacements within the backfill material. strength properties governing failure of reinforced soil slopes. The variables investigated in this study were selected so that they could be taken into All reinforced slope models in the account in a limit equilibrium framework. experimental testing program had the same Accordingly, the selected variables were: geometry and were built within the same strong box. A transparent Plexiglas plate was  Vertical spacing of the geotextile used on one side of the box to enable side view reinforcements: four different of the models during testing. The other walls of reinforcement spacings were adopted; the box were aluminum plates lined with  soil shear strength parameters: the same Teflon to minimize side friction. The overall sand at two different relative densities was dimensions of the geotextile-reinforced slope used; and models are as shown in Figure 2 for a model  ultimate tensile strength of the with nine reinforcement layers. Displacement reinforcements: two geotextiles with transducers are also indicated in the figure.

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different ultimate tensile strength were single residual shear strength for large strain selected. conditions. Figure 4 shows the increase in peak friction angle with increasing relative density Of particular relevance, for the purpose of the at a confining pressure of 100 kPa. Of issues addressed in this paper, is the fact that particular interest are the friction angles that the same sand placed at two different obtained at relative densities of 55% and 75%, relative densities was used as backfill material which correspond to the relative density of the for the centrifuge models. The backfill material backfill material in the models. The estimated at these two relative densities has different triaxial compression friction angles (tc) at peak shear strength values but the same these relative densities are 35° and 37.5°, residual shear strength. respectively. Although the tests did not achieve strain values large enough to guarantee a The model slopes were built using Monterey critical state condition, the friction angles at No. 30 sand, which is a clean, uniformly large strains appear to converge to a residual graded sand classified as SP in the Unified Soil value (r) of approximately 32.5°. This value Classification System (Zornberg et al. 1998b). agrees with the critical state friction angle for The particles are rounded to subrounded, Monterey No. 0 sand obtained by Riemer consisting predominantly of quartz with a (1992). As the residual friction angle is mainly smaller amount of feldspars and other a function of mineralogy (Bolton 1986), minerals. The average particle size for the Monterey No. 0 and Monterey No. 30 sands material is 0.4 mm, the coefficient of should show similar r values. The effect of uniformity is 1.3, and the coefficient of confining pressure on the frictional strength of curvature is about 1.1. The maximum and the sand was also evaluated. The results minimum void ratios of the sand are 0.83 and showed that the friction angle of Monterey 0.53, respectively. To obtain the target dry No. 30 decreases only slightly with increasing densities in the model slopes, the sand was confinement. The fact that the friction angle of pluviated through air at controlled this sand does not exhibit normal stress combinations of sand discharge rate and dependency avoids additional complications in discharge height. The unit weights for the the interpretation of the centrifuge model tests. Monterey No. 30 sand at the target relative 3 densities of 55% and 75% are 15.64 kN/m and Scale requirement for the reinforcing material 3 16.21 kN/m , respectively. establish that the reinforcement tensile strength in the models be reduced by N. That is, an Two series of triaxial tests were performed to Nth-scale reinforced slope model should be evaluate the friction angle for the Monterey built using a planar reinforcement having 1/N No. 30 sand as a function of relative density the strength of the prototype reinforcement and of confining pressure. The tests were elements (Zornberg et al. 1998a). Two types of performed using a modified form of the nonwoven interfacing fabrics, having mass per automated triaxial testing system developed by unit area of 24.5 g/m2 and 28 g/m2, were Li et al. (1988). The specimens had nominal selected as reinforcement. Unconfined ultimate dimensions of 70 mm in diameter and 150 mm tensile strength values, measured from wide- in height and were prepared by dry tamping. width strip tensile tests ASTM D4595, were Figure 3 shows the stress strain response 0.063 kN/m and 0.119 kN/m for the weaker obtained from the series of tests conducted to and stronger geotextiles, respectively. evaluate the behavior of Monterey No. 30 sand Confined tensile strength values, obtained from as a function of relative density. All tests backcalculation of failure in the centrifuge shown in the figure were conducted using a slope models, were 0.123 kN/m and 0.183 confining pressure of 100 kPa. As can be kN/m for the weaker and stronger geotextiles, observed in the figure, while the sand shows a respectively (Zornberg et al. 1998b). Confined different peak shear strength for different tensile strength values were used for estimating relative densities, the shear stress tends to a

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the factor of safety of the models analyzed in program is presented by Zornberg et al. this study under increasing g-levels. (1998a). The centrifuge tests can be grouped into three test series (B, D, or S). Accordingly, 350 each reinforced slope model in this study was D =83.3% r named using a letter that identifies the test D =74% r series, followed by the number of 300 D =68% r reinforcement layers in the model. Each test series aimed at investigating the effect of one D =57.5% r variable, as follows: 250 D =52.7% r

D =37%  Baseline, B-series: Performed to r investigate the effect of the reinforcement 200 vertical spacing.  Denser soil, D-series: Performed to

150 investigate the effect of the soil shear strength on the stability of geosynthetic- reinforced slopes. The models in this series

100 were built with a denser backfill sand but with the same reinforcement type as in the B-series. 50  Stronger geotextile, S-series: Performed to investigate the effect of the reinforcement  =100 kPa  tensile strength on the performance of 0 reinforced slopes. The models in this series 0 2 4 6 8 10 12 14 16 18 20 were built using reinforcements with a Axial strain (%) higher tensile strength than in the B-series

Figure 3. Stress strain behavior of Monterey No. 30 sand but with the same backfill density as in that pluviated at different relative densities and tested in series. triaxial compression under the same confinement The history of centrifugal acceleration during

45 centrifuge testing of one of the models is indicated in Figure 5. In this particular test, the acceleration was increased until sudden failure 40 occurred after approximately 50 min of testing when the acceleration imparted to the model 35 was 76.5 times the acceleration of gravity. Settlements at the crest of the slope, monitored 30 by LVDTs, proved to be invaluable to Confining stress: 100 kPa accurately identify the moment of failure. Peak Friction (deg) Angle 25 Figure 6 shows the increasing settlements at 20 40 60 80 100 the top of a reinforced slope model during Relative Density (%) centrifuge testing. The sudden increase in the monitored settlements indicates the moment of Figure 4. Friction angle for Monterey No. 30 sand obtained from triaxial testing at different relative failure when the reinforced active wedge slid densities. along the failure surface. Figure 7 shows a typical failure surface as developed in the 2.3 Typical Centrifuge Test Results centrifuge models. As can be seen, the failure surface is well defined and goes through the The models were subjected to a progressively toe of the reinforced slope. increasing centrifugal acceleration until failure occurred. A detailed description of the characteristics of the centrifuge testing

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retrieved from the top of the model. All 80 retrieved geotextiles show clear tears at the 70 location of the failure surface. The pattern 60 Failure 50 observed from the retrieved geotextiles shows

40 that internal failure occurred when the tensile

30

g-level (N) g-level strength on the reinforcements was achieved. 20 The geotextile layers located towards the base 10 of the slope model also showed breakage of the 0 geotextile overlaps, which clearly contributed 0 102030405060 time (min) to the stability of the slope. No evidence of pullout was observed, even on the short Figure 5. G-level (N) versus time during centrifuge testing. overlapping layers.

. 40

35

30

25

20

15

10 LVDT1

5 LVDT2 Failure

Vertical displacement (mm) (mm) displacement Vertical 0 0 1020304050607080 g-level (N) Figure 8. Geotextile reinforcements retrieved after Figure 6. Settlements at the crest of a reinforced slope testing. model.

2.4 Effect of Backfill Shear Strength on the Experimental Results

The criteria for characterizing reinforcements as extensible or inextensible has been established by comparing the horizontal strain in an element of reinforced backfill soil subjected to a given load, to the strain required to develop an active plastic state in an element of the same soil without reinforcement (Bonaparte and Schmertmann 1987). Accordingly, reinforcements have been Figure 7. Failed geotextile-reinforced slope model. typically classified as:

Following the test, each model was carefully  extensible, if the tensile strain at failure in disassembled in order to examine the tears in the reinforcement exceeds the horizontal the geotextile layers. Figure 8 shows the extension required to develop an active geotextiles retrieved after centrifuge testing of plastic state in the soil; or as a model reinforced with eighteen geotextile  inextensible, if the tensile strain at failure layers. The geotextile at the top left corner of in the reinforcement is significantly less the figure is the reinforcement layer retrieved than the horizontal extension required to from the base of the model. The geotextile at develop an active plastic state in the soil. the bottom right corner is the reinforcement

The geotextiles used to reinforce the centrifuge in the D-series failed at higher g-levels than model slopes are extensible reinforcements. models in the B-series built with the same The effect of reinforcement spacing on the reinforcement spacing and reinforcement type. stability of the reinforced slope models, as Since the backfill soil in models from the D- indicated by the measured g-level at failure Nf, and B-series have the same residual soil shear is shown in Figure 9. The number of strength, the higher g-level at failure in the reinforcement layers n in the figure includes D-series models is due to the higher peak soil the total number of model geotextiles shear strength in this test series. intersected by the failure surface (i.e. primary reinforcements and overlaps intersected by the Analysis of the data presented in this figure failure surface). The overlaps intersected by emphasizes that the use of a single residual the failure surface developed tensile forces and shear strength value, common to the two eventually failed by breakage and not by backfill materials used in the test series, can pullout. The figure shows that a well-defined not explain the experimental results. Instead, linear relationship can be established between the experimental results can be explained by the number of reinforcement layers and the g- acknowledging that the stability models level at failure. As the fitted lines for each test constructed with the same reinforcement layout series passes through the origin, the results in and the same sand backfill, but placed at each test series can be characterized by a single different densities, is governed by different n/ Nf ratio. shear strength values. Indeed, limit equilibrium analyses (Zornberg et al. 1998b) indicated that 25 the shear strength value that should be used in the analysis of these slope failures is the plain B18 strain peak shear strength of the backfill.

20 The experimental results indicate that the B 12 stability of structures with extensible reinforcements is governed by the peak shear D12 15 strength and not by the residual shear strength of the backfill soil. A plausible explanation of these experimental results is that, although the

B 9 soil shear strength may have been fully 10 S9 mobilized along certain active failure planes within the reinforced soil mass, shear

B6 D6 displacements have not taken place along these S6 failure surfaces. That is, although the soil may 5 have reached active state due to large horizontal strains because of the extensible nature of the reinforcements, large shear 0 displacements (and drop from peak to residual 0 1020304050607080 soil shear strength) only take place along the G-level at Failure (Nf) failure surface during final sliding of the active Figure 9. G-level at failure for the centrifuge models. reinforced wedge (Zornberg et al. 1998b).

Models in the B- and D-series were reinforced An additional way of evaluating these using the same geotextile reinforcement, but experimental results is by using dimensionless using sand backfill placed at two different coefficients, which have been used in order to relative densities (55 and 75%). As mentioned, develop design charts for geosynthetic- the Monterey sand at these two relative reinforced soil slopes (Schmertmann et al. densities has the same soil residual friction 1987, Leshchinsky and Boedeker 1989, Jewell angle (32.5°) but different peak friction angles 1991). The validity of the proposed (35° and 37.5°). As shown in Figure 9, models

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normalization can be investigated from the provide sound experimental evidence centrifuge results of this study. For a reinforced supporting the use of charts based on slope model that failed at an acceleration equal normalized coefficients for preliminary design to Nf times the acceleration of gravity, a of geosynthetic-reinforced slopes. If failure of dimensionless coefficient K can be estimated reinforced soil slopes were governed by the as follows: residual soil shear strength, the results of all  2  1 centrifuge tests should have defined a single K = n T ult .   . (1) line. However, as can be observed in the   2   H  N f figure, different normalized coefficients are obtained for different soil densities. This where n is the number of reinforcements, Tult is confirms that the normalization should be the reinforcement tensile strength, H is the based on the peak shear strength and not on the slope height, Nf is the g-level at failure from residual shear strength of the backfill material. the centrifuge test, and  is the sand unit weight. The value of n used in Equation 1 7 includes the number of overlaps that were B18 intersected by the failure surface in the centrifuge slope models in addition to the 6 number of primary reinforcement layers. The B12 coefficient K is a function of the shear strength 5 of the soil and of the slope inclination. [i.e. K = S9 K(,)]. All centrifuge slope models were built D12 with the same slope inclination . 4 KB = KS Consequently, validation of the suggested 1 normalization requires that a single coefficient B9 3 55% Relative KD K(,) be obtained for all models built with the Density S6 1 same backfill. If the soil shear strength governing failure of the models is the residual 2 B6 strength, a single coefficient K(,) should be D6 obtained for all models. On the other hand, if 75% Relative Density the soil shear strength governing failure is the 1 peak shear strength, a single coefficient should be obtained for those models built with sand 0 placed at the same relative density. 0 1020304050607080 G-level at Failure (N ) f Figure 10 shows the centrifuge results in terms Figure 10. Normalized Reinforcement Tension 2 Summation (RTS) values from centrifuge test results. of (n Tult) (2 /  H ) versus the g-level at failure

Nf . The results in the figure show that a linear relationship can be established for those 2.5 Final Remarks on Validation of Design models built with sand placed at the same Tools relative density. As inferred from Equation 1, The selection of the backfill shear strength the slope of the fitted line corresponds to the properties in the design of geosynthetic- dimensionless RTS coefficient K = K(,). reinforced soil structures is an issue over which The results obtained using the centrifuge design guidelines disagree. The main debate models from the B- and S-series, built using has been over whether the peak or the residual Monterey sand placed at 55% relative density, shear strength of the backfill material should define a normalized coefficient K(,) = KB = be adopted for design. The use of residual KS = 0.084. Similarly, centrifuge results from shear strength values in the design of the D-series models, built using Monterey sand geosynthetic reinforced slopes while still using at 75% relative density, define a normalized peak shear strength in the design of coefficient K(,) = KD = 0.062. These results unreinforced embankments could lead to

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illogical comparisons of alternatives for 3 GEOSYNTHETIC-REINFORCED embankment design. For example, an BRIDGE ABUTMENTSF unreinforced slope that satisfies stability criteria based on a factor of safety calculated 3.1 Overview using peak strength, would become unacceptable if reinforced using inclusions of The technology of geosynthetic-reinforced soil small (or negligible, for the purposes of this (GRS) systems has been used extensively in example) tensile strength because stability transportation systems to support the self- would be evaluated in this case using residual weight of the backfill soil, roadway structures, soil shear strength values. The main purpose of and traffic loads. The increasing use and this investigation was to provide experimental acceptance of soil reinforcement has been evidence addressing this currently unsettled triggered by a number of factors, including cost issue. savings, aesthetics, simple and fast construction techniques, good seismic The experimental results presented herein performance, and the ability to tolerate large indicate that the soil shear strength governing differential settlement without structural the stability of geosynthetic-reinforced soil distress. A comparatively new use of this slopes is the peak shear strength. A centrifuge technology is the use of GRS systems as an experimental testing program was undertaken integral structural component of bridge which indicated that reinforced slopes abutments and piers. Use of a reinforced soil constructed with the same reinforcement layout system to directly support both the bridge (e.g. and the same backfill sand, but using different using a shallow foundation) and the sand densities failed at different centrifuge approaching roadway structure has the accelerations. That is, nominally identical potential of significantly reducing construction models built with backfill material having the costs, decreasing construction time, and same residual shear strength but different peak smoothing the ride for vehicular traffic by shear strength did not have the same factor of eliminating the “bump at the bridge” caused by safety. Since the residual shear strength of the differential settlements between bridge sand backfill is independent of the relative foundations and approaching roadway density, these results indicate that the soil shear structures. strength governing stability is the peak shear strength of the backfill material. The most prominent GRS abutment for bridge support in the U.S. is the recently-opened-to- Several design guidance manuals have traffic Founders/Meadows Parkway bridge, implicitly recommended the selection of the which crosses I-25 approximately 20 miles peak shear strength for the design of reinforced south of downtown Denver, Colorado (Figure soil slopes. Considering the current debate over 11). Designed and constructed by the Colorado the selection of the soil shear strength in design Department of Transportation (CDOT), this is and the experimental results presented herein, the first major bridge in the United States to be design manuals should explicitly endorse built on footings supported by a geosynthetic- selection of peak shear strength values for the reinforced system, eliminating the use of design of reinforced soil structures. This traditional deep foundations (piles) altogether. approach would not only be consistent with the Phased construction of the almost 9-m high, observed experimental centrifuge results, but horseshoe-shaped abutments, located on each also with the US practice of using peak shear side of the highway, began July 1998 and was strength in the design of unreinforced slopes. completed twelve months later. Significant previous research by FHWA and CDOT on GRS bridge abutments, which has demonstrated their excellent performance and high load-carrying capacity, led to the construction of this unique structure.

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Figure 11. View of the Founders/Meadows GRS bridge abutments near Denver, Colorado.

The performance of bridge structures includes preloaded and prestressed bridge piers supported by GRS abutments has not been (Tatsuoka et al. 1997, Uchimura et al. 1998) tested under actual service conditions to merit and geosynthetic-reinforced wall systems with acceptance without reservation in highway continuous rigid facing for railway construction. Consequently, the infrastructure (Kanazawa et al. 1994, Tateyama Founders/Meadows structure was considered et al. 1994). European experience includes experimental and comprehensive material vertically loaded, full-scale tests on testing, instrumentation, and monitoring geosynthetic reinforced walls constructed in programs were incorporated into the France (Gotteland et al. 1997) and Germany construction operations. Design procedures, (Brau and Floss 2000). Finally, Won et al. material characterization programs, and (1996) reported the use of three terraced monitoring results from the preliminary (Phase geogrid-reinforced walls with segmental block I) instrumentation program are discussed by facing to directly support end spans for a major Abu-Hejleh et al. (2000). Large-size direct bridge in Australia. shear and triaxial tests were conducted to determine representative shear strength The experience in the U.S. regarding properties and constitutive relations of the geosynthetic-reinforced bridge abutments for gravelly backfill used for construction. Three highway infrastructure includes full-scale sections of the GRS system were instrumented demonstration tests conducted by the Federal to provide information on the structure Highway Administration (FHWA) (e.g. Adams movements, soil stresses, geogrid strains, and 1997, 2000) and by CDOT (e.g. Ketchart and moisture content during construction and after Wu 1997). In the CDOT demonstration project, opening the structure to traffic. the GRS abutment was constructed with roadbase backfill reinforced with layers of a 3.2 Past experiences in GRS bridge woven polypropylene geotextile placed at a abutments spacing of 0.2 m. Dry-stacked hollow-cored concrete blocks were used as facing. A vertical Although the Founders/Meadows structure is a surcharge of 232 kPa was applied to the 7.6 m pioneer project in the U.S. involving high abutment structure. The measured permanent GRS bridge abutments for highway immediate maximum vertical and lateral infrastructure, significant efforts have been displacements were 27.1 mm and 14.3 mm, undertaken in Japan, Europe and Australia respectively. The maximum vertical and lateral regarding implementation of such systems in creep displacements after a sustained vertical transportation projects. Japanese experience surcharge pressure of 232 kPa, applied during

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70 days, were 18.3 mm and 14.3 mm, completed by CDOT in July of 1999, replaced respectively. The excellent performance and a deteriorated two-span bridge structure. In this high loading capacity demonstrated by these project, both the bridge and the approaching geosynthetic-reinforced soil abutments with roadway structures are supported by a system segmental block facing convinced CDOT of geosynthetic-reinforced segmental retaining design engineers to select GRS walls to walls. Figure 12 shows a picture of one of the support the bridge abutment at the segmental retaining wall systems, located at Founders/Meadows structure. the east side of the bridge. This figure shows the bridge superstructure supported by the 3.3 Description of the GRS bridge abutment “front MSE wall,” which extends around a 90- degree curve into a “lower MSE wall” The Founders/Meadows bridge is located 20 supporting the “wing wall” and a second tier, miles south of Denver, Colorado, near Castle “upper MSE wall”. Rock. The bridge carries Colorado State Highway 86, Founders/Meadows Parkway, over U.S. Interstate 25. This structure,

Girder Wing Wall

Instrumentation Box Upper MSE Wall

Front MSE Wall Lower MSE Wall

Photo 12. View of the Southeast side of the completed Founders/Meadows bridge abutment.

Each span of the new bridge is 34.5 m long and abutment wall and two wing walls, resting on 34.5 m wide, with 20 side-by-side prestressed the spread foundation, confine the reinforced box girders. The new bridge is 13 m longer and backfill soil behind the bridge abutment and 25 m wider than the previous structure, support the bridge approach slab. The bridge is accommodating six traffic lanes and sidewalks supported by central pier columns along the on both sides of the bridge. A typical middle of the structure, which in turn are monitored cross-section through the “front supported by a spread footing founded on MSE wall” and “abutment wall” transmits the bedrock at the median of U.S. Interstate 25. load through abutment walls to a shallow strip footing placed directly on the top of a geogrid- When compared to typical systems involving reinforced segmental retaining wall. The the use of deep foundations to support bridge centerline of the bridge abutment wall and structures, the use of geosynthetic-reinforced edge of the foundation are located 3.1 m and systems to support both the bridge and the 1.35 m, respectively, from the facing of the approaching roadway structures has the front MSE wall. A short reinforced concrete potential to alleviate the “bump at the bridge”

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problem caused by differential settlements design of the GRS walls. To evaluate the between the bridge abutment and approaching suitability of these design parameters, roadway. In addition, this approach also allows conventional direct shear tests and large size for construction in stages and comparatively direct shear and triaxial tests were conducted. smaller construction working areas. Several of In the conventional tests, the 35% gravel the common causes for development of bridge portion was removed from the specimens, but bumps were addressed in the design of the in the large-size triaxial and direct shear tests, Founders/Meadows structure. The main cause the backfill soil specimens included the gravel of uneven settlements in typical systems is the portion. The results of conventional direct use of different foundation types. That is, while shear tests and large size direct shear and the approaching roadway structure is typically triaxial tests indicate that assuming zero constructed on compacted backfill soil cohesion in the design procedure and removing (reinforced or not), the bridge abutment is the gravel portion from the test specimens lead typically supported on stronger soils by deep to significant underestimation of the actual foundations. The roadway approach shear strength of the backfill. embankment and the bridge footing were integrated at the Founders/Meadows structure The geogrid reinforcements used in this project with an extended reinforced soil zone in order were manufactured by the Tensar Corporation. to minimize uneven settlements between the Three types of geogrid reinforcements were bridge abutment and approaching roadway. A used: UX 6 below the footing, and UX 3 and second cause of differential settlements can be UX 2 behind the abutment wall. The long- attributed to erosion of the fill material around term-design-strength (LTDS) of these the abutment wall induced by surface water reinforcements is 27 kN/m, 11 kN/m, and 6.8 runoff. Several measures were implemented in kN/m, respectively. CDOT specifications this project to prevent that surface water, as imposed a global reduction factor of 5.82 to well as groundwater, reach the reinforced soil determine the long-term design strength mass and the bedrock at the base of the fill (LTDS) of the geogrid reinforcements from (e.g. placement of impervious membranes with their ultimate strength. This global reduction collector pipes). Finally, a third potential cause factor accounts for reinforcement tensile of differential settlements is the thermally strength losses over the design life period due induced movements, i.e., expansion and to creep, durability, and installation damage. It contraction of bridge girders strongly attached also includes a factor of safety to account for to the abutment wall (integral abutment). A uncertainties. compressible 75 mm low-density expanded polystyrene sheet was placed between the 3.4 Performance reinforced backfill and the abutment walls. It was expected that this system would The instrumentation program was conducted in accommodate the thermally induced two phases (Phases I and II), which movements of the bridge superstructure correspond, respectively to the construction of without affecting the retained backfill. two phases of the GRS bridge abutment structure. A pilot instrumentation plan was The backfill soil used in this project includes conducted during construction of the Phase I fractions of gravel (35%), sand (54.4%), and structure in order to obtain information that fine-grained soil (10.6%). The liquid limit and will tailor the design of a more comprehensive plasticity index for the fine fraction of the monitoring program to be implemented during backfill are 25% and 4 %, respectively. The Phase II. The Phase I instrumentation program backfill soil classifies as SW-SM per ASTM included survey targets, pressure cells, 2487, and as A-1-B (0) per AASHTO M 145. jointmeters, and inclinometer. The more The backfill met the construction requirements comprehensive Phase II instrumentation for CDOT Class 1 backfill. A friction angle of program included monitoring using survey 34o and zero cohesion were assumed in the targets, digital road profiler, pressure cells,

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strain gauges, moisture gauges, and (ii) Locations B and C along the center and temperature gauges. A view of the interior edge of the abutment instrumentation plan for Phase II is shown in foundation. Information collected at Figure 13. The figure shows the four critical these locations is relevant for the design locations that were instrumented in Phase II: of the reinforcement elements. (iii) Location D, behind the bridge (i) Location A, close to the facing. Data foundation, and horizontal plane at the collected at this location is particularly base of the fill. Data measured at these useful for guiding the structural design locations is useful to estimate the of the facing and of the connection external forces acting behind and below between facing and reinforcements. the reinforced soil mass.

Bridge Deck Concrete Approach Slab Concrete Roadway

Girder 19 Two Gages 18 17

16

15 29 28 Bridge Foundation 14 27 26 13 25 24 12 23 22 Two 11 21 Gages 20 10 19 18 9 17 16 8 15 14 7 13

Front GRS Walll 12 6 11 10 5 9 8 4 Geogrid Layer # 7 6 3 5 4 2 3 2 1 1

Bedrock

Location A Location B Location C Location D

Strain Gage Pressure Cell Survey Point Moisture Gage Temperature Gage

Figure 13. Instrumentation plan Fiof Phase 9 I II structure. i L S i 800 (Ph II)

A comprehensive discussion of the  The measured response from both the instrumentation results, the collection and pressure cells and strain gauges correlates analysis of which is under progress, is beyond well with the applied loads during the the scope of this paper. Results of the construction stages. preliminary Phase I instrumentation program  The maximum geogrid strains experienced have been reported by Abu-Hejleh et al. during construction are comparatively very (2000). Some of the relevant findings obtained small (approximately 0.45 %). based on the information collected so far are  Horizontal earth pressures collected at the the following: facing and of the reinforcement maximum tensile strains are well below design values.

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 Most of the straining of the geogrid problem or any structural damage, and post- reinforcements occurred during construction movements became negligible construction of the wall and not during after an in-service period of 1 year. placement of the bridge surcharge load. This can be explained by the effect of compaction operations and presence of 4 ADVANCES IN FIBER-REINFORCED slacks in the geogrid reinforcements. Strain SOIL DESIGN gauge monitoring results collected so far suggest that approximately 50% of the total 4.1 Overview recorded strains occurred during placement and compaction of a few lifts of soil above Fiber reinforcement has become a promising the geogrid layers (e.g. approximately 2 m solution to the stabilization of thin soil veneers of soil or 40 kPa). The maximum measured and localized repair of failed slopes. Randomly front wall outward displacement induced distributed fibers can maintain strength by wall construction (before placement of isotropy and avoid the existence of the the bridge superstructure) was 12 mm, potential planes of weakness that can develop which corresponds to 0.20 % of the wall parallel to continuous planar reinforcement height. elements. The design of fiber-reinforced soil slopes has typically been performed using  The maximum outward displacement induced by placement of the bridge composite approaches, where the fiber- superstructure was additional 10 mm, reinforced soil is considered a single which corresponds to 0.17% of the wall homogenized material. Accordingly, fiber- height. The maximum settlement of the reinforced soil design has required non- bridge footing due to placement of the conventional laboratory testing of composite bridge superstructure was 13 mm. fiber-reinforced soil specimens which has discouraged implementation of fiber-  The maximum outward displacements induced after opening the structure to reinforcement in engineering practice.

traffic and until June 2000 (18 months) was Several composite models have been proposed 13 mm. These movements correspond to to explain the behavior of randomly distributed 0.22 % of the wall height. The measured fibers within a soil mass (Maher and Gray, settlement of the leveling pad supporting 1990, Michalowski and Zhao, 1996, Ranjan et the front wall facing was approximately 5 al., 1996). The mechanistic models proposed mm. However, it is important to emphasize by Gray and Ohashi (1983) and Maher and that these movements took place only Gray (1990) quantify the “equivalent shear during the initial 12 months of service strength” of the fiber-reinforced composite as a (until January 2000). Lateral and vertical function of the thickness of the shear band that movements have been negligible from develops during failure. Information needed to January to June 2000. characterize shear band development for these  Elevation profiling and surveying results models is, however, difficult to quantify show no signs of development of the (Shewbridge and Sitar, 1990). Common “bump at the bridge” problem. findings from the various testing programs implemented to investigate composite models Overall, the performance of the include: (i) randomly distributed fibers provide Founders/Meadows bridge structure, based on strength isotropy in a soil composite; (ii) fiber the monitored behavior recorded so far, inclusions increase the “equivalent” shear showed excellent short- and long-term strength within a reinforced soil mass; and (iii) performance. Specifically, the monitored the “equivalent” strength typically shows a movements were significantly smaller than bilinear behavior, which was experimentally those expected in design or allowed by observed by testing of comparatively weak performance requirements, there were no signs fibers under a wide range of confining stresses. for development of the “bump at the bridge”

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A discrete approach for the design of fiber- Specifically, the magnitude of the fiber- reinforced soil slopes was recently proposed to induced distributed tension is defined as a characterize the contribution of randomly function of properties of the individual fibers. distributed fibers to stability (Zornberg, 2002). In this way, as in analysis involving planar In this approach, fiber-reinforced soil is reinforcements, limit equilibrium analysis of characterized as a two-component (soil and fiber-reinforced soil can explicitly account for fibers) material. Fibers are treated as discrete tensile forces. elements that contribute to stability by mobilizing tensile stresses along the shear The interface shear strength of individual fibers plane. Consequently, independent testing of can be expressed as: f = c  c  c  tan  (4) soil specimens and of fiber specimens, but not f i,c i, n,ave of fiber-reinforced soil specimens, can be used where c and  are the cohesive and frictional to characterize fiber-reinforced soil components of the soil shear strength and n,ave performance. is the average normal stress acting on the

fibers. The interaction coefficients, ci,c and ci,, This paper initially reviews the main concepts commonly used in soil reinforcement literature of the discrete approach and subsequently for continuous planar reinforcement, is adopted validates the framework for design purposes. herein to relate the interface shear strength to the shear strength of the soil. The interaction

coefficients are defined as: 4.2 Discrete frame work for fiber a (5) c = reinforcement i,c c tan (6) c = i, tan The volumetric fiber content, , used in the where a is the adhesive component of the proposed discrete framework is defined as: interface shear strength between soil and the

V f (1)  = polymeric fiber, tan is the skin-frictional V component. where Vf is the volume of fibers and V is the control volume of fiber-reinforced soil. The pullout resistance of a fiber of length lf should be estimated over the shortest side of The gravimetric fiber content, w, typically the two portions of a fiber intercepted by the used in construction specifications, is defined failure plane. The length of the shortest portion as: of a fiber intercepted by the failure plane varies W f (2)  w = from zero to lf /2. Statistically, the average W s embedment length of randomly distributed where W is the weight of fibers and W is the f s fibers, l , can be analytically defined by: dry weight of soil. e,ave l f (7) le,ave = 4 The dry unit weight of the fiber-reinforced soil where lf is total length of the fibers. composite, d , is defined as: W W f s (3) The average pullout resistance can be  d = V quantified along the average embedment The contribution of fibers to stability leads to length, le,ave , of all individual fibers crossing a an increased shear strength of the soil control surface A. The ratio between the “homogenized” composite reinforced mass. total cross sectional area of the fibers Af and However, the reinforcing fibers actually work the control surface A is assumed to be defined in tension and not in shear. A major objective by the volumetric fiber content . That is: of the discrete framework is to explicitly Af  = quantify the fiber-induced distributed tension, A t, which is the tensile force per unit area induced in a soil mass by randomly distributed When failure is governed by the pullout of the fibers. fibers, the fiber-induced distributed tension, tp, is defined as the average of the tensile forces

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inside the fibers over the control area A. tension t, and the shear strength of the Consequently, tp can be estimated as: unreinforced soil, S: (9) (15) t p =     ci,c  c  ci,  tan  n,ave  S eq = S   t c   n tan   t where  is the aspect ratio defined as: where  is an empirical coefficient that l (10)  = f accounts for the orientation of fiber and the d f efficiency of the mixing of fibers.  is equal to where df is the equivalent diameter of the fiber. 1, if the fibers are randomly distributed and

When failure is governed by the yielding of the working with 100% efficiency, otherwise  fibers, the distributed tension, t , is determined should be smaller than 1. t from the tensile strength of the fiber: Depending on whether the mode of failure is t =    (11) t f ,ult fiber pullout or yielding, the equivalent shear where f,ult is the ultimate tensile strength of strength can be derived by combining (9) or the individual fibers. (11) with (15). It should be noted that the average normal stress acting on the fibers, The fiber-induced distributed tension t to be  , does not necessarily equal the normal used in the discrete approach to account for the n,ave stress on the shear plane  . For randomly tensile contribution of the fibers in limit n equilibrium analysis is: distributed fibers, n,ave could be represented by the octahedral stress component. However, a t = mint ,t  (12) p t sensitivity evaluation undertaken using typical The critical normal stress, n,crit , which defines ranges of shear strength parameters show that the change in the governing failure mode, is  can be approximated by  without the normal stress at which failure occurs n,ave n introducing significant error. simultaneously by pullout and tensile breakage of the fibers. That is, the following condition Accordingly, the following expressions can be holds at the critical normal stress: used to define the equivalent shear strength t  t (13) t p when failure is governed by fiber pullout: An analytical expression for the critical normal (16) stress can be obtained as follows: S eq, p = ceq, p  tan eq, p  n    c  c f ,ult i,c (14) (17)  n,crit  ceq, p = 1      ci,c  c   ci,  tan tan  = 1       c  tan  (18)  eq, p  i,  As in analyses involving planar inclusions, the orientation of the fiber-induced distributed Equivalently, the following expressions can be tension should also be identified or assumed. obtained to define the equivalent shear strength Specifically, the fiber-induced distributed when failure is governed by tensile breakage of tension can be assumed to act: a) along the the fibers: failure surface so that the discrete fiber- S = c  tan   induced tensile contribution can be directly eq,t eq,t eq,t n (19) c = c     “added” to the shear strength contribution of eq,t f ,ult (20) tan  = tan the soil in a limit equilibrium analysis; b) eq,t (21) horizontally, which would be consistent with design assumptions for reinforced soil The above expressions yield a bilinear shear structures using planar reinforcements; and c) strength envelope, which is shown in Figure in a direction somewhere between the initial 14. fiber orientation (which is random) and the orientation of the failure plane.

This equivalent shear strength of fiber- reinforced specimens can be defined as a function of the fiber-induced distributed

REGEO ‘2007 - 17 -

cohesion of 6.1 kPa and friction angle of 34.3°, S Se =S+ t while the cohesion and friction angle of CL S soil were 12.0 kPa and 31.0° respectively.

tan Table 3 Summary of fiber properties 1 SP tests CL tests t Linear density (denier) 1000 & 360 2610 Fiber content (%) 0.2 & 0.4 0.2 & 0.4 c Length of fibers (mm) 25 & 51 25 & 51 Type of fiber fibrillated & fibrillated n,cri n tape

Figure 14 Representation of the equivalent shear strength according to the discrete approach The governing failure mode for the polymeric fibers used in this investigation is pullout because of the comparatively high tensile 4.2 Experimental validation strength and short length of the fibers. Accordingly, the triaxial testing program A triaxial compression testing program on conducted in this study focuses only on the fiber-reinforced soil was implemented to first portion of the bilinear strength envelope validate the proposed discrete framework. Both shown in Figure 14. cohesive and granular soils were used in the testing program, and the soil properties were Figure 15 shows the stress-strain behavior of summarized in Table 2. SP soil specimens reinforced with 360 denier

Table 2 Summary of soil properties fibers, and placed at gravimetric fiber contents Soil type Soil 1 Soil 2 of 0, 0.2 and 0.4 %. Specimens were tested USCS SP CL under confining pressure of 70 kPa. The peak classification deviator stress increases approximately linearly LL % - 49 with increasing fiber content, which is PL % - 24 consistent with the discrete framework (see IP % - 25 equation (9)). The post-peak shear strength loss % Fines 1.4 82.6 is smaller in the reinforced specimens than in the unreinforced specimens. However, the initial portions of the stress-strain curves of the The tests were conducted using commercially reinforced and unreinforced specimens are available polypropylene fibers, and the approximately similar. Accordingly, the soil properties of fibers were summarized in Table appears to take most of the applied load at 3. A series of tensile test were performed in small strain levels, while the load resisted by general accordance with ASTM D2256-97 to the fibers is more substantial at higher strain evaluate the ultimate tensile strength of fibers. level. The larger strain corresponding to the The average tensile strength of the fibers was peak deviator stress displayed by the fiber- approximately 425,000 kPa. reinforced specimens suggests that fibers

increase the ductility of the reinforced soil The triaxial testing program involved specimen. These findings are confirmed in consolidated drained (CD) tests for SP soils Figure 16, which shows the test results and consolidated undrained (CU) tests for CL obtained under higher confining stress (140 soils. The specimens have a diameter of 71 mm kPa). and a minimum length-to-diameter ratio of 2. The CU tests were performed in general accordance with ASTM D4767, and the specimens were back pressure saturated and the pore water pressure was measured. The unreinforced tests of SP soil yielded an effective shear strength envelope defined by

REGEO ‘2007 - 18 -

500 a similar trend for the case of tests conducted 450 w=0.4% under higher confining pressures. 400 350 350 300 w=0.2% l f=50 mm 250 300

200 250 w=0% 150 l f=25 mm Deviator (kPa) stress 200 100 unreinforced 50 150 0

0 5 10 15 20 25 (kPa)Deviator stress 100 Axial strain (%) 50 Figure 15. Stress-strain behavior of specimens prepared using w =0, 0.2 and 0.4% with lf =25 mm fibers (360 0 denier), 70 kPa, Soil 1 0 5 10 15 20 25 Axial strain (%) 1000 900 w=0.4% Figure 17 Stress-strain behavior of specimen prepared 800 using w=0.2 %, with lf=25 mm and 50 mm fibers (1000 700 denier), =70 kPa, Soil 1  =0.2% 600 600 w l =50 mm 500 500 f 400 w=0% l f=25 mm 300 400

Deviator stress (kPa) stress Deviator 200 unreinforced 300 100

0 200 0 5 10 15 20 25 Deviator stress (kPa) Axial strain (%) 100 Figure 16 Stress-strain behavior of specimens prepared using w =0, 0.2 and 0.4% with lf =25 mm fibers (360 0 0 5 10 15 20 25 denier), 140 kPa, Soil 1 Axial strain (%) The effect of fiber length on the stress-strain Figure 18 Stress-strain behavior of specimen prepared using w=0.2 %, with lf=25 mm and 50 mm fibers (1000 behavior is shown in Figure 17. The specimens denier), =140 kPa, Soil 1 were prepared using fibers with a different fiber type (1000 denier) than that used in the Figure 19 compares the stress-strain behavior tests shown in Figures 15 and 16. The of both unreinforced and fiber-reinforced specimens were prepared using the same specimen using soil 2. The reinforced gravimetric fiber content, but with varying specimen were prepared at w=0.2%, using 2- fiber length. The specimens reinforced with inch long 2610 denier fibers. Both specimens longer (50 mm) fibers displayed higher shear were compacted at optimum moisture content strength. The peak deviator stress increases to 90% of the maximum dry density achieved linearly with increasing aspect ratio, which is in the standard Proctor test as specified in also consistent with the trend indicated by ASTM D 698, and tested under confining equation (9). The strain corresponding to the pressure =98 kPa. Due to the undrained test peak strength increases with increasing fiber condition, the effective confining stress length. When the governing failure mode is changes with the excess pore water pressure pullout, the fiber-induced distributed tension induced in the process of shearing. The peak reaches its peak when the pullout resistance is shear strength was selected in terms of the fully mobilized. For longer fibers, it usually maximum value of (’/’). The increment of requires a larger interface shear deformation to deviator stress due to fiber addition is not as fully mobilize the interface strength. obvious as in the case of SP sand. However, Consequently, the macroscopic axial strain at the pore water pressure generated during peak stress should be larger for specimen shearing is larger for reinforced specimen than reinforced with longer fibers. Figure 18 shows for unreinforced specimen (see Figure 20). Consequently the effective confining stress

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inside the reinforced specimen is smaller than and 0.4% gravimetric fiber contents. As the that inside the unreinforced specimen. The fiber content increases, the pore water pressure fiber-reinforced specimen achieved equal or generated during undrained shearing also higher peak deviator stress than the increases. unreinforced specimen under a lower effective confining stress. This shows that the addition 140 of fibers increases the shear strength of the 120 =0.4% reinforced specimen. Since positive water w 100 pressure is associated with the tendency of w=0.2% volume shrinkage, this observation shows that 80 fiber reinforcement restrains the dilatancy of 60 the reinforced soil. Other researchers (Michalowski and Cermak, 2003, Consoli et (kPa) stress Deviator 40 al., 1998) reported that fiber-reinforced 20 specimens displayed smaller volume dilatation 0 than unreinforced specimen in consolidated 0 5 10 15 20 drained (CD) test. This observation confirms Axial strain (%) their findings in a different test condition. Figure 21 Stress-strain behavior of specimens prepared using w=0.2, 0.4%, with lf=25 mm fibers (2610 denier), 100 =116 kPa, Soil 2 w=0.2% 120  =0% w =0.4% 80 w 100

w=0.2% 60 80

60 40

Deviator stress (kPa) stress Deviator 40 20 20 Pore water pressure (kPa) pressure water Pore

0 0 0 5 10 15 20 0 5 10 15 20 Axial strain (%) Figure 19 Stress-strain behavior of specimens prepared -20 Axial strain (%) using w=0, 0.2 %, with lf=50 mm fibers (2610 denier), =98 kPa, Soil 2 Figure 22 Excess pore water pressure of specimens

prepared using w =0.2, 0.4 %, with lf=25 mm fibers 120 (2610 denier), =116kPa, Soil 2

100 w=0.2% Equations (16) through (18) were used to 80 predict the equivalent shear strength for fiber- w=0%

60 reinforced specimens. Interaction coefficients

(ci,c and ci,) of 0.8 are assumed in the analyses 40 conducted in this study. The interface shear 20

Pore water pressure (kPa) pressure water Pore strength obtained from pullout test results

0 conducted on woven geotextiles was 0 5 10 15 20 considered representative of the interface shear -20 strength on individual fibers. For practical Axial strain (%) Figure 20 Excess pore water pressure of specimens purposes, interaction coefficients can be prepared using w=0, 0.2 %, with lf=50 mm fibers (2610 selected from values reported in the literature denier), =98kPa, Soil 2 for continuous planar reinforcements. This is

because pullout tests conducted using a variety Similar observation can be made from Figures of soils and planar geosynthetics have been 21 and 22, which shows the stress-strain reported to render interaction coefficient values behavior and the pore water pressure evolution falling within a narrow range (Koutsourais et obtained using 25-mm fibers placed at 0.2%

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al., 1998, Michalowski and Cermak, 2003).  26, which shows the results obtained from Soil is assumed to be 1.0 for randomly distributed 2 using 25 mm and 50 mm-long fibers and fibers. Table 4 summarized the values of placed at w =0.4%. parameters used in the analyses. 400 Exp. data, 0% fibers Stren. envelope, 0% fibers (best fit) Table 4 Summary of parameters used in the prediction Exp. data, 0.2% fibers (fibr.) Exp. data, 0.2% fibers (tape) Stren. envelope, 0.2% fibers (predicted)  ° c ci,c ci, 300 Exp. data, 0.4% fibers (fibr.) Exp. data, 0.4% fibers (tape) (kPa) Stren. envelope, 0.4% fibers (predicted) Soil 1 1.0 34.3 6.1 0.8 0.8

Soil 2 1.0 31.0 12.0 0.8 0.8 200

(kPa)  The effect of fiber content on shear strength is shown in Figure 23, which compares the 100 experimental data and predicted shear strength envelopes obtained from Soil 1 using 25 mm 0 fibers with linear density of 360 denier placed 0 100 200 300 400 at fiber contents of 0.0%, 0.2%, and 0.4%. The ' (kPa) Figure 23 Comparison between predicted and experimental results show a clear increase in experimental shear strength results for specimens equivalent shear strength with increasing fiber reinforced at w =0, 0.2%, 0.4% with 25 mm-long fibers content. No major influence of fibrillation is (360 denier), Soil 1 perceived in the results of the testing program. 100 The shear strength envelope for the Exp. data, 0% fibers Stren. envelope, 0% fibers(best fit) unreinforced specimens was defined by fitting Exp. data, 0.2% fibers 80 Stren. envelope, 0.2% fibers(predicted) the experimental data. However, the shear Exp. data, 0.4% fibers strength envelopes shown in the figure for the Stren. envelope, 0.4% fibers(predicted) reinforced specimens were predicted 60

analytically using the proposed discrete (kPa)  framework. A very good agreement is 40 observed between experimental data points and predicted shear strength envelopes. As 20 predicted by the discrete framework, the distributed fiber-induced tension increases 0 0 20 40 60 80 100 linearly with the volumetric fiber content. ' (kPa)  Similar observation can be made in Figure 24, Figure 24 Comparison between predicted and which shows the results obtained from Soil 2 experimental shear strength results for specimens using 50- mm-long fibers with linear density of reinforced at w=0, 0.2%, 0.4% with 50 mm-long fibers (2610 denier), Soil 2 2610 denier. Additional insight into the validity of the The effect of fiber aspect ratio on shear proposed discrete approach can be obtained by strength is shown in Figure 25, which comparing the results obtained for specimens compares the experimental and predicted shear reinforced with 50 mm-long fibers placed at a strength envelopes of specimens of Soil 1 fiber content of 0.2% with those obtained for placed at w=0.2%, with 25 and 50 mm-long specimens reinforced with 25 mm-long fibers fibers. As predicted by the discrete framework, placed at a fiber content of 0.4%. That is increasing the fiber length increases the pullout specimens with a constant value of (w· As resistance of individual fibers, and results in a inferred from inspection of equation (9) the higher fiber-induced distributed tension. fiber-induced distributed tension is directly Consequently, for the same fiber content, proportional to both the fiber content and the specimens reinforced with longer fibers will fiber aspect ratio. Consequently, the predicted have higher equivalent shear strength. This equivalent shear strength parameters for the trend agrees well with the experimental data. above combinations of fiber length and fiber Similar observation can be made from Figure

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content are the same. Figures 27 and 28 comparatively high aspect ratios (i.e. combine these experimental results. comparatively long fibers) and for

400 comparatively high fiber contents. The fiber Exp. data 0% fibers Stren. envelope, 0% fibers (best fit) content or fiber length at which the validity of Exp. data, 25mm (tape) Exp. data, 25mm (fibr) these relationships is compromised should be 300 Stren. envelope, 25mm (predicted) Exp. data 50mm (tape) further evaluated. Nonetheless, good mixing Exp. data 50mm (fibr) Stren. envelope, 50mm (predicted) was achieved for the fiber contents and fiber lengths considered in this investigation, which 200 (kPa)

 were selected based on values typically used in geotechnical projects.

100 400 Experimental data, 0% fibers Stren. envelope, 0% fibers (best fit) Exp. data, 0.2% fibers (fibr.), 50 mm 0 Exp. data, 0.2% fibers (tape), 50 mm Exp. data, 0.4% fibers (fibr.), 25 mm 0 100 200 300 400 300 Exp. data, 0.4% fibers (tape), 25 mm Stren. envelope, (predicted) ' (kPa) Figure 25 Comparison between predicted and 200 experimental shear strength results for specimens (kPa)  reinforced at w =0.2%, with 25 mm-long and 50 mm-long fibers (1000 denier), Soil 1

100 100 Exp. data, 0% fibers Stren. envelope, 0% fibers (best fit) Exp. data, 25mm fibers 80 Stren. envelope, 25mm fibers(predicted) 0 Exp. data, 50mm fibers 0 100 200 300 400 Stren. envelope,25mm fibers(predicted) ' (kPa)

60 Figure 27 Consolidated shear strength results for specimen reinforced with 50 mm-long fibers (1000 (kPa)

 denier) placed at w =0.2% and 25 mm fibers placed at 40 w =0.4%, Soil 1

100 20 Exp. data, 0% fibers Stren. envelope, 0% fibers (best fit)

80 Exp. data, 0.2% fibers, 50 mm Exp. data, 0.4% fibers, 25mm 0 0 20406080100 Stren. envelope (predicted) ' (kPa) 60

Figure 26 Comparison between predicted and (kPai) experimental shear strength results for specimens  40 reinforced at w =0.4%, with 25 mm-long and 50 mm-long fibers (2610 denier), Soil 2 20 The good agreement between experimental 0 results and predicted values provides additional 0 20406080100 evidence of the suitability of the proposed '(kPa) discrete approach. From the practical Figure 28 Consolidated shear strength results for standpoint, it should be noted that using 50 specimen reinforced with 50 mm-long fibers (2610 denier) placed at w=0.2% and 25 mm fibers placed at w mm-long fibers placed at a fiber content of =0.4%, Soil 2 0.2% corresponds to half the reinforcement material than using 25 mm-long fibers placed Figure 29 shows the stress-strain behavior of at a fiber content of 0.4%. That is, for the same specimen reinforced with 50 mm fibers placed target equivalent shear strength the first at w =0.2% and 25 mm fibers placed at w combination leads to half the material costs =0.4%. While the discrete approach was than the second one. It is anticipated, though, developed only to predict the shear strength that difficulty in achieving good fiber mixing response, the results in the figure show that may compromise the validity of the fiber-reinforced specimens prepared using a relationships developed herein for constant value display similar stress-strain

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behavior. This similar response is observed for  The peak shear strength increases with both fibrillated and tape fibers, suggesting that increasing aspect ratio. The strain at peak the fibrillation procedure does not have a deviator stress increases with increasing significant impact on the mechanical response fiber aspect ratio. of fiber-reinforced soil. The experimental  As predicted by the discrete framework, the results suggest that the proportionality of shear experimental results confirmed that the strength with the fiber content and fiber aspect fiber-induced distributed tension increases ratio predicted by the discrete framework can linearly with fiber content and fiber aspect be extrapolated to the entire stress-strain ratio when failure is characterized by response of fiber-reinforced specimens. pullout of individual fibers.  Experimental results conducted using 350 specimens with a constant (w·) value 300 show not only the same shear strength but

250 also display a similar stress-strain behavior.  If good mixing can be achieved, fibers with 200 comparatively high aspect ratio can lead to 150 0% fibers lower fiber contents while reaching the 100 0.4% fibers(tape), 25mm same target equivalent shear strength, Deviator stress (kPa) 0.2% fibers(tape), 50mm 50 0.4% fibers(fibr.), 25mm resulting in savings of reinforcement 0.2% fibers(fibr.), 50mm material. 0 0 5 10 15 20 25  Overall, for both sand and clay specimens, Axial strain (%) the discrete approach was shown to predict

Figure 29 Comparison between stress-strain behavior for accurately the shear strength obtained specimen reinforced with 50mm fibers (1000 denier) experimentally using specimens reinforced placed at w=0.2% and 25 mm fibers placed at w =0.4%, with polymeric fibers tested under =70 kPa confining stresses typical of slope stabilization projects. 4.3 Remarks on Fiber Reinforced Soil

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