Fiber reinforcement effectiveness in two different sand specimens

Abstract Fiber Reinforced Soils (FRS) are mixtures of discrete fibers with the soil to create a composite with improved mechanical properties compared to unreinforced material that depends on several soil and fiber properties. Therefore, comparative studies are needed to better understand their influence on FRS mechanical response. This paper analyzes the results of a comprehensive triaxial testing program performed on specimens of two different sands at the same relative density focusing on how the grain size distribution affects the composite behavior in terms of shear strength and dilatancy. It is shown that the grain size curve's uniformity coefficient (Cu) is one of the critical variables controlling FRS's dilatancy. Dune sand specimens (Cu = 1.79) presented dilatancy even for confining stresses as high as 300 kPa. The shear gains due to reinforcement were controlled by fiber length (L) and percentage (Pf), and size and shape of soil particles. River sand specimens with L = 51 mm and 1% fiber addition (dry mass) presented increments of 47.7 kPa in soil cohesion and a 5.2o increase in the soil friction angle compared to unreinforced material.


Introduction
The use of fiber Reinforced Soils (FRS) dates from ancient times.Vegetable fibers of jute and bamboo, among other species, were and are still used.However, Vidal (1966) conceived a soil reinforcement method using metallic strips recognized as the debut of the FRS modern use.FRS are mixtures of discrete fibers or strips with the soil to create a composite with improved mechanical properties compared to unreinforced material.The emergence of plastics offered newly manufactured durable fibers and reinforcement geosynthetics, such as geogrids, as an option to substitute metallic strips.FRS use can improve the mechanical behavior of soil in different applications, such as composing landfill cover layers, where their use could prevent superficial cracking due to wetting/drying cycles and differential waste mass settlements, which can lead to greenhouse gases emissions, embankments, earth dams, and other earthworks (Daniel & Benson, 1990;Daniel & Wu, 1993;Broderick & Daniel, 1990;Shackelford, 2014;Damasceno et al., 2019;Zhang et al., 2022).
Fiber length or aspect ratio (the relationship between the fiber length and its diameter/width), stiffness, fiber content, soil friction angle, and the coupled effects that occur in the soil grain/fiber interfaces are among the main parameters affecting the FRS mechanical behavior (Maher & Gray, 1990;Gao & Zhao, 2013;Michalowski, 2008;Li et al., 2020).Fiber orientation is also a critical factor interfering with the mechanical behavior of fiber-reinforced soils.Wang et al. (2017) present results of several triaxial tests with jute fibers disposed at different orientations.It is shown that vertical fibers had a negligible effect on composite shear strength.Horizontal fibers are most beneficial to the increase of peak deviator stress, with randomly oriented fibers also producing encouraging results.However, the laboratory moist tamping technique has presented a growing interest when using compacted specimens.This technique offers good control of specimen density, prevents fiber segregation, and produces a soil-fiber fabric that resembles that of FRS compacted in the field, although leading to the sub-horizontal orientation of fibers (Diambra et al., 2010).
Besides the early cited characteristics of fibers, some soil properties also play a paramount role in the overall FRS performance.Considering the universe of nonplastic coarse soils, the density index (I D ) is recognized as the main parameter controlling the mechanical behavior of coarse soils.Variations in friction angle between 6-10 o are observed when The benefits associated with fiber reinforcement include but are not restricted to shear strength gains, higher ductility, smaller post-peak strength losses, and minored cracks appearance and propagation (Gray & Ohashi, 1983;Loehr et al., 2005;Choobbasti et al., 2019;Mandolini et al., 2019;Gao et al., 2020).Furthermore, fiber reinforcement is reported to increase the liquefaction and post-liquefaction shear strength of sand (Jain et al., 2023;Rasouli & Fatahi, 2022).
In this paper, compacted specimens from two different sands were submitted to a comprehensive triaxial testing program to evaluate the effects of fiber length, grain size curve parameters, and size, roughness, and shape of solid particles on the reinforcement effectiveness, measured in terms of the observed increments in the shear strength parameters, and FRS dilatancy.

Materials and methods
Table 1 summarizes the main characteristics of the employed sand, which were determined following the Brazilian standards ABNT NBR 6458 (ABNT, 2016a), ABNT NBR 7181 (ABNT, 2016b), ABNT NBR 12004 (ABNT, 1990), andABNT NBR 12051 (ABNT, 1991).d xx is the sieve equivalent diameter for a given percentage of the particles passing.Cc is the GSC curvature coefficient, and e max and e min are the maximum and minimum void ratios, respectively.Gs is the specific gravity of particles and ϕ pk and ϕ ls are the unreinforced soil friction angles for peak and large strain condition, respectively (approximating the friction angle at critical state conditions).As observed, dune sand presents a more uniform grain size curve and smaller particles.Additional details are provided in Conceição (2021) and Pinto (2021).
Figure 1 illustrates the visual aspect of the river and dune solid particles.The larger size and less uniformity of the river sand grains than dune sand are easily noted, besides the subangular aspect of their particles.
FRS specimens used polypropylene fibers with lengths (L) of 12.5 mm, 25 mm, and 51 mm.As common properties, according to the manufacturer Viapol™, fiber diameter of D = 0.51 mm, specific gravity of G sf = 0.91, fiber stiffness modulus of E f = 5.0 GPa, and tensile strength of 500 MPa are cited.The adopted fiber contents (P f , dry mass) were 0.5% and 1%.The experimental program considered fibers as part of the solid particles, calculating the composite's G s value for each P f .Figure 2 illustrates the visual aspect of the employed fibers.The specimen molding procedure used the moist tamping technique (Diambra et al., 2010).
Figure 3 illustrates the molding preparation steps.A vacuum pump provided an internal air pressure of about -15 kPa to preserve specimen integrity after mold removal.After molding, the specimen underwent vertical upward water flow until the permeability coefficient (k) stabilized.k values served as an indication of the molding process quality since small variations in molding conditions (especially in the void ratio) have a noticeable impact on k.
The experimental program used specimens with the same I D (60%).Triaxial tests adopted the back pressure technique (Skempton's B parameter, B > 0.95) to saturate the specimens, which were then hydrostatically consolidated and

Results and analysis
Figures 4 and 5 illustrate some triaxial tests results in terms of deviator stress and volumetric strain curves for the performed tests.The presented results refer to tests performed with P f = 0.5% and 1%, and confining stresses (σ c ) of 50 and 200 kPa.The results are coherent with many authors who cite the increase in composite cohesion, friction angle, and ductility, as well as the decrease in the after-peak shear strength reduction as fiber reinforcement effects (Ranjan et al., 1994;Diambra et al., 2010;Diambra et al., 2013;Gao & Diambra, 2021;Feuerharmel, 2000;Santiago, 2011;Michalowski & Čermák, 2003;Choobbasti et al., 2019;Li et al., 2020).
The fiber-reinforced sand specimens increased their shear strength with both fiber length and percentage, as reported by many other authors (Choobbasti et al., 2019;Li et al., 2020;Jishnu et al., 2020).Comparing pure soil and reinforced specimens with P f = 1% and L = 51 mm, the composite shear strengths are approximately double that obtained for pure soil (see Figure 5).The cohesion was the most sensitive shear strength parameter to the fiber reinforcement, reaching values as high as 47.7 kPa for river sand specimens (see Table 2, P f = 1% and L = 51 mm).For both sand, the fiber length was more effective in reinforcement than the fiber content since samples with P f = 0.5% and L = 25 mm showed better resistance results than samples with P f = 1% and L = 12.5 mm (Table 2).The observed behavior is the opposite of that reported by Fang et al. (2020), indicating that fiber-reinforcement effectiveness is dependent not only on P f and L, but on a combination of fiber and soil characteristics.
Comparing the shear strength results of the two different sand composites, as expected, river sand specimens always presented higher peak and residual shear strength values.This results from its large and subangular particles and the less uniform grain size curve than dune sand.
As expected, specimens dilated more for lower confining stresses.However, dune sand specimens presented a dilation of about 2% even in the tests performed with σ c = 200 kPa and higher, contrary to the river sand specimens.Different authors have reported a contradictory influence of fibers on composite dilation (Aguilar, 2015;Diambra et al., 2013;Festugato, 2008;Michalowski & Čermák, 2003;Rasouli & Fatahi, 2022).
Table 2 summarizes the shear strength parameters obtained considering all performed tests.For all the specimens, the failure criterion adopted was the maximum deviator stress.This corresponded to the peak stress in most cases, but in the cases of P f = 1% and L = 51 mm specimens, the maximum strength occurred at 20% of axial deformation.As observed, the dune sand friction angle varied from 33.6 o    to 41.8 o and cohesion changed from 0 to 23.9 kPa from nonreinforced soil to composites with P f = 1% and L = 51 mm.In contrast, variations from 36.5 o to 41.7 o and 0 to 47.7 kPa were observed for river sand specimens under the same conditions.Although a slightly smaller variation is kept in the friction angle of the river sand specimens, the cohesion increment was remarkably higher, and the final shear strength values of such composites are very promising.
Figure 6 presents the increments in q pk as a function of P f and σ c .As observed, fiber reinforcement was more effective in the case of the river sand specimens.The authors believe the subangular shape and the larger size of the solid particles played an essential role in this case.
Figure 7 illustrates how the fiber length influences the stiffness and compressibility of the tested specimens.As observed (Figure 7a), increasing fiber length becomes samples more ductile in both cases (dune and river sands), and the peak stress occurs for higher axial strains, mainly in the case of fibers with L = 51 mm.However, volumetric behavior was much more complex and dependent on the grain size distribution.For lower confining stresses, the fiber tends to increase the soil dilatancy, no matter the soil tested in this study.For higher values of confining stress, river sand specimens, fibers become more effective in reducing dilatancy.However, this tendency is not observed in the case of the dune sand samples.The rounded shape and the smaller size of the dune specimens reduce the fiber reinforcement action not only in terms of shear strength but also when preventing soil volume increases.It also seems that the grain size curve uniformity prevails over particle size and shape, influencing the soil dilation since different authors (Michalowski &Čermák, 2003 andGhadr et al., 2022) point to higher dilation in soils with coarser and angular grains.
Figure 8 illustrates how the mean dilatancy (-Δε v / Δε a ) before peak stress influences the soil shear strength in terms of the normalized difference between peak (q pk ) and large strain (q ls ) deviator stress.In this case, N ϕ is given by Equation 1.As observed, river sand (RS) specimens presented an appreciable amount of tests with negative dilatancy (compression) or dilatancy values inferior to 0.1.This is coherent with the data shown in Figure 7b.Although data scattering, it is clear that dune sand specimens (DS) require higher dilatancy for the same gain in shear strength.However, for dilatancy values higher than 0.1, DS samples are more  responsive regarding shear strength gains due to dilatancy than RS specimens.In fact, only tests performed with L = 25mm (see Figure 8b) for RS specimens captured shear strength gains due to dilatancy.Non-reinforced and samples with L = 12.5 mm presented values of normalized deviator stress differences that are less sensitive to dilatancy in both soils.
It is impossible to differentiate the behavior obtained for P f = 0.5% and 1% (Figure 8a).The more ductile behavior of the reinforced samples with L = 51 mm (Figure 7a) reduced the dilatancy values presented in Figure 8b.

Conclusions
Although fiber-reinforced soils are an up-andcoming alternative in earthworks, their use requires a deep knowledge of the interactions between the solid particles and the reinforcement elements and how the properties of each phase interfere with the overall composite mechanical performance.This paper used the results of a comprehensive triaxial testing campaign performed in two different sand reinforced with the same type, length, and percentage of fibers.Samples differed mainly in grain shape and grain size curve characteristics, and tests employed composites with the same relative density.As expected, river sand specimens formed by subangular particles with less uniform grain size curves  than dune sand presented higher peak and residual shear strength values.Furthermore, more effective reinforcement effects were also observed for river sand specimens under the same testing conditions.Concerning the stiffness and volumetric behavior, fiber addition increased ductility in composites of both sand, which passed to present peak strength for higher axial values.At least for river sand specimens, composites tended to reduce dilation as the reinforcement increased.For dune sand specimens, this effect was much less noticeable.Composite dilatancy was much less pronounced in river dune specimens, mainly for higher P f values.Dune sand specimens required higher dilatancy values for the same shear strength increments than river sand composites.However, dilatancy was more effective in increasing DS shear strength for dilatancy values higher than 0.1.

Figure 3 .
Figure 3. a) end of the molding process and b) specimen aspect after mold removal (about -15 kPa air pressure applied by vacuum pump).

Figure 7 .
Figure 7. Effect of fiber length on axial and volumetric strains at failure for P f = 1% specimens.a) axial strain behavior and b) volumetric strain behavior.

Figure 8 .
Figure 8. Dilatancy effect in increasing peak stress compared to residual values.a) comparing composites with different fiber percentage and b) comparing composites with fibers of different lengths.

Table 1 .
Main characteristics of the employed sand.

Table 2 .
Shear strength parameters for different fiber lengths and contents.
Axial strain at the end of the tests ϵ vf Volumetric strains at the end of the tests σ c Confining stress ϕ ls Composite friction angle for large strain conditions ϕ peak Composite friction angle for peak stress