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Article

Mechanical Behavior of Fiber-Reinforced Soils under Undrained Triaxial Loading Conditions

by
Evangelos D. Evangelou
,
Ioannis N. Markou
*,
Sofia E. Verykaki
and
Konstantinos E. Bantralexis
Soil Mechanics and Foundation Engineering Laboratory, Department of Civil Engineering, Democritus University of Thrace, University Campus, Kimmeria, 67100 Xanthi, Greece
*
Author to whom correspondence should be addressed.
Geotechnics 2023, 3(3), 874-893; https://doi.org/10.3390/geotechnics3030047
Submission received: 20 July 2023 / Revised: 28 August 2023 / Accepted: 31 August 2023 / Published: 5 September 2023
Browse Figures
Versions Notes

Abstract

:
The design of fiber-reinforced soil structures, such as embankments and pavements, can be carried out using the results of unconsolidated, undrained triaxial compression tests conducted on specimens at their “as-compacted” water content and analyzed in terms of total stresses. The effects of soil and fiber type on the mechanical behavior of fiber-reinforced soils have not been methodically or adequately examined in the past under these conditions, and the effects of fiber length and content on the shear strength parameters of fiber-reinforced soils need further experimental documentation. Accordingly, five soils ranging from “excellent” to “poor” materials for use in earthwork structures were tested in the present study, in combination with five types of polypropylene fibers having lengths ranging from 9 to 50 mm. Unconsolidated undrained triaxial compression tests were conducted on specimens at their “as-compacted” water content, with fiber contents ranging from 0.5 to 2% by weight of dry soil. Fiber reinforcement reduces the stiffness and increases the deformability of the soil. The fiber-reinforced soils exhibit a more ductile behavior in comparison with the unreinforced soils. A Mohr–Coulomb type linear failure criterion satisfactorily describes the shear strength behavior of fiber-reinforced soils in total stress terms. The cohesion values of the fiber-reinforced soils range between 61 kPa and 301 kPa and increase up to seven times in comparison with the cohesion values of the unreinforced soils. The variations of the angle of internal friction of soils due to fiber reinforcement are generally limited to ±25%. The cohesion improvement due to fiber reinforcement is increased with increasing fiber content and fiber length up to 30 mm and is inversely proportional to the fine-grained fraction and the cohesion of the unreinforced soil.

1. Introduction

Soil reinforcement with geogrids, geotextiles, metal strips, fibers, etc., is an efficient and trustworthy technique for improving the mechanical behavior of soil in several applications, including retaining structures, embankments, foundations, slopes and pavements. Reinforcing the soil with flexible, discrete fibers is not a new technique in civil engineering. Houses have been built for many centuries with clay bricks reinforced with straw [1,2]. However, as the fiber inclusions bring several technical, economic and environmental benefits, a great deal of interest has recently emerged worldwide regarding the potential applications of fibers within the soils and other similar materials, such as coal ashes and mine tailings [3]. Although natural fibers, mainly from different plants, are used in countries where they are in abundance, synthetic polymer fibers are preferred because they are standardized industrial products exhibiting better mechanical behavior and durability than natural fibers. The use of recycled fibers produced from waste materials is gaining ground in civil engineering structures because it is an economical and environmentally friendly solution. The documentation of the effectiveness of fibers for soil reinforcement has been the objective of several research efforts based on UU triaxial compression testing and this is summarized in Table 1.
The design of fiber-reinforced soil structures can be carried out by adopting the “composite approach” in which the fiber-reinforced soil structure is analyzed in a traditional way, considering the engineering properties of fiber-reinforced soil as a homogeneous material [3]. It is based on the fact that the inclusion of fibers contributes to stability due to an increase in the shear strength of the homogenized composite reinforced soil mass, although the reinforcing fibers actually work in tension and not in shear. The contribution of the fibers is typically quantified by an equivalent cohesion intercept and the angle of internal friction of the soil [3]. The fiber-reinforced soils in applications such as embankments and pavements are usually unsaturated both at the construction and operation stages. Significant research work has been carried out on the behavior of unsaturated soils (e.g., [30,31,32,33]) and the unsaturated shear strength of unreinforced soils (e.g., [34,35]) and the unsaturated soil mechanics principles were applied successfully in the design and construction of a capillary barrier system used as a slope protective measure [36]. However, the measurement of the shear strength of unsaturated soils is costly and time-consuming and requires special laboratory equipment [34,35]. It is therefore more practical for the design of structures such as embankments and pavements to investigate the mechanical behavior of fiber-reinforced soils by conducting unconsolidated undrained (UU) triaxial compression tests on specimens at their “as-compacted” water content and to analyze the obtained results in terms of total stresses.
As shown in Table 1, Hoare [4] studied the mechanical behavior of fiber-reinforced sandy gravel with polypropylene and nylon tapes and found that the addition of fibers leads to an increase in the angle of internal friction, φ, and failure strain, εf, and to a decrease in the initial modulus of elasticity, Ei. From the UU triaxial compression tests conducted on sands reinforced with natural or synthetic fibers, mostly monofilament (Table 1), it was generally found that the strength parameters (cohesion, c, and friction angle, φ) increased and the deformability was enhanced with fiber addition [5,6,8,10,12,15,16,22,23,28]. In cohesive soils, the effect of fiber addition is mostly similar. In most cases, the cohesion and the deformability parameters increase [7,13,14,17,20,21,24] but the friction angle presents a not systematic behavior as it decreases [17], is slightly affected [7,14] or increases [11,13,20,21] after the addition of fibers.
The results of the literature review presented in Table 1 also indicate that different soils, ranging from sandy gravel to clays, were investigated in the preceding research efforts in combination with a wide variety of synthetic and natural fibers with lengths, Lf, between 2 mm and 100 mm. Monofilament fibers of circular cross-section were used in the majority of investigations, whereas a smaller number of tests were conducted with tape, fibrillated, mesh and crimped fibers, and with fibers of triangular or Y-shaped cross-section. Fiber contents, wf, ranging from 0.09% to 3% by weight of dry soil were used in specimen preparation and the UU triaxial compression tests were conducted with confining pressures, σ3, ranging from 21 kPa to 700 kPa. However, it is observed that the effects of soil and fiber type on the mechanical behavior of fiber-reinforced soils have not been methodically or adequately examined in the past as only one or a limited number of soil or fiber types were used in each investigation. Although the fiber length and content have been investigated more extensively in previous research efforts (Table 1), their effect on the shear strength parameters of fiber-reinforced soil is ambiguous, possibly due to differences in the tested materials and, as a result, it needs further experimental documentation.
Based on the abovementioned information, the study reported herein aims to experimentally investigate the mechanical behavior of fiber-reinforced soils at their “as-compacted” water content for the design of structures such as embankments and pavements. Accordingly, the specific objectives of this study are as follows:
(a)
The presentation of the results of 61 UU triaxial compression test series conducted on five types of soil reinforced with synthetic fibers of five different types, which serve to enrich and supplement the available information on the behavior and the design parameters of fiber-reinforced soils under undrained loading conditions.
(b)
The documentation of the effect of soil composition and fiber type, length and content on the strength and deformability parameters of fiber-reinforced soils.
(c)
The quantification of the improvement in the strength and deformability of soils with fiber reinforcement.

2. Materials and Experimental Procedures

As mentioned above, the study of the effect of soil type on the mechanical behavior of unsaturated fiber-reinforced soils was a basic objective of the present research effort. Consequently, soils of controlled composition and properties, but differing in quality with respect to their use in embankments and pavements, were tested. These soils were produced by mixing a poorly graded sand with negligible fine-grained fraction and a lean clay, by weight, using the proportions shown in Table 2. The sand and lean clay are classified as SP and CL, respectively, according to the Unified Soil Classification System (USCS) [37] and as A-1-b and A-7-6 type, respectively, according to the AASHTO (American Association of State Highway and Transportation Officials) M 145 specification [38]. The mixing proportions were selected in order to produce four composite soils (CS1-CS4) that belong to different categories in accordance with the AASHTO M 145 specification [38]. The gradations and the values of Atterberg limits (liquid limit, LL, and plastic limit, PL) of all soils are shown in Figure 1 and Table 2, respectively. From the AASHTO group symbols shown in Table 2, it is evident that the original SP soil and the four composite soils tested in this laboratory investigation cover a wide range of soil materials that can be used in earthwork structures with SP, CS1 and CS2 characterized as “excellent to good” soils and CS3 and CS4 characterized as “fair to poor” soils for that purpose [38]. According to the AASHTO M 57 specification [39], SP and CS1 soils are suitable materials for the construction of embankments and subgrades, whereas CS2, CS3 and CS4 soils may be used with special attention given to the design and construction of embankments. The shear strength and deformability parameters summarized in Table 2, were obtained by conducting UU triaxial compression tests on soil specimens under confining pressures equal to 50, 100, 200 and 400 kPa. The specimens were prepared by compacting the soils, either in dry condition (SP soil) or with the optimum water content (CS1-CS4 soils), so as to obtain the maximum dry unit weight determined by the compaction test conducted in accordance with the ASTM Standard D 698 [40]. The dry unit weight of the unreinforced soil specimens prepared for triaxial compression testing ranges from 16.54 kN/m3 to 19.12 kN/m3, whereas their water content ranges from 10.69% to 17.42%.
This study also aims to investigate the effect of fiber type on the mechanical behavior of unsaturated fiber-reinforced soils. For that purpose, the abovementioned soils were reinforced with polypropylene fibers of five different types having densities equal to 905 kg/m3 and melting points at 165 °C. More precisely, monofilament fibers of circular cross-section, with two tapes of different width and hollow and fibrillated fibers, with dimensions and relevant properties presented in Table 3, were used for soil reinforcement. These fibers are designated as M, T1, T2, H and F, respectively, and their images are presented in Figure 2. Monofilament (M) and tape 1 (T1) fibers of lengths (Lf) ranging from 9 mm to 50 mm (Table 3) were mixed manually with soils at contents (wf) equal to 0.5%, 1.0%, 1.5% and 2.0%, by weight of dry soil, in order to investigate the effect of fiber length and content on the mechanical behavior of fiber-reinforced soils. As shown in Table 1, the values of fiber length and content used in the present study sufficiently cover the range of values used in the experimental investigation of the mechanical behavior of fiber-reinforced soils.
The cylindrical specimens prepared for triaxial compression testing had a diameter of 50 mm and a height of 110 mm. The specimens of fiber-reinforced SP soil were prepared in dry conditions. The total amount of uniform soil–fiber mixture for each specimen was divided into five equal parts and each part was compacted using a special hand-operated tamper into the rubber membrane that had been placed earlier in the three-part split mold. Extreme care was taken in order to achieve a constant value of the maximum dry unit weight by continuously checking the height of each compacted layer. The specimens of fiber-reinforced CS1-CS4 soils were prepared with the optimum water content. A homogeneous dry soil–fiber mixture was initially attained with manual mixing, then the optimum water content was added and manual mixing continued until the moisture was evenly distributed within the sample. The total amount of uniform wet soil–fiber mixture for each specimen was divided into two equal parts and the compaction was conducted using the equipment shown in Figure 3. The wet soil–fiber mixture was placed in two layers into the cylindrical mold (consisting of the base plate, the 3-part split mold and the extension collar shown in Figure 3) of internal diameter equal to 50 mm, with each layer compacted by blows of a 28.74 N rammer of a diameter slightly smaller than 50 mm, dropped from a distance of 11 cm. After the compaction of the first layer, its surface was scarified before the placement of the second layer with the tool shown in Figure 3 in order to enhance the specimen homogeneity. During the compaction process, the height of each layer was measured continuously in order to produce a uniform specimen with the required maximum dry unit weight. At the end of the compaction process, the base plate and the extension collar were removed and the specimen was extruded from the mold using a hydraulic sample extruder. The quality of the compacted specimens was assured by comparing their compaction characteristics with those obtained by the standard compaction test [40] and reported in a preceding publication [41]. The comparison presented in Figure 4 confirms the good quality of the specimens for triaxial compression testing as the deviation of their water contents (ranging from 10.85% to 19.56%) is generally limited to ±5% from the optimum water contents and their dry unit weight values (ranging from 15.33 kN/m3 to 18.71 kN/m3) were practically equal to the values of the maximum dry unit weight resulting from the compaction test.
Consolidated undrained (CU) and/or consolidated drained (CD) triaxial compression tests are normally conducted on saturated specimens to obtain the shear strength of soils in terms of effective stresses. However, the fiber-reinforced soils in applications such as embankments and pavements are usually not saturated both at the construction and operation stages. The measurement of pore water pressures and the determination of effective stresses are not practicable when conventional testing methods are applied to unsaturated specimens. Therefore, the approach followed in the present study to effectively simulate these conditions was to conduct unconsolidated undrained (UU) triaxial compression tests on the unreinforced and fiber-reinforced soil specimens at their “as-compacted” water contents and to analyze the obtained results in terms of total stresses. The UU triaxial compression tests were performed in accordance with the ASTM Standard D 2850-15 [42] and the specimens were tested under confining pressures of 50, 100, 200 and 400 kPa, at an axial strain rate equal to 0.715 mm/min (0.65%/min). The selected axial strain rate is the average of the recommended ASTM Standard D 2850-15 strain rate values, ranging from 0.3 to 1%/min, and is considered appropriate for all soils tested in this research effort. The tests were completed when either the maximum deviator stress was obtained or the axial strain reached the limit of 15%, as set by the ASTM Standard D 2850-15.
An excessive number of triaxial compression test series results, from testing all possible combinations of soils with fiber types, lengths and contents, were incorporated in the present research effort. However, a total of 61 triaxial compression test series, summarized in Table 4, each comprising four tests conducted under the confining pressures of 50, 100, 200 and 400 kPa, were sufficient for the purposes of the present study. This considerable reduction was accomplished (a) by testing all soils reinforced with wf = 1.0% of fibers having length equal to 30 mm for fibrillated fibers and 18 mm for all the other fiber types for the investigation of the effect of soil and fiber type on the mechanical behavior of fiber-reinforced soils, and (b) by investigating the effect of fiber length and content for the three intermediate soils (CS1, CS2 and CS3) reinforced with the most frequently used monofilament (M) and tape (T1) fibers. The fiber content was set equal to 0.5% by weight of dry soil in the investigation of the effect of fiber length, whereas the fiber length was kept equal to 18 mm in the investigation of the effect of fiber content on the mechanical behavior of fiber-reinforced soils. These constant values of fiber length and content were selected because they are representative of the values regularly used in fiber-reinforced soil research (Table 1).

3. Stress–Strain Relationship

As typically shown in Figure 5, two basic types of stress–strain curves were observed in this research effort, depending on the composition of fiber-reinforced soils. More specifically, the stress–strain curves of soils reinforced with low contents of fibers of small length (9 mm) more often exhibit a strain-softening behavior, i.e., an initial practically linear part followed by an extended plastic failure zone with a peak value of deviator stress defining the failure point in these cases and a significant or negligible deviator stress decrease after the peak value (Figure 5a). As the fiber length and content increase, the stress–strain curves generally demonstrate a strain-hardening behavior, i.e., an initial linear part followed by a second part not presenting a peak value of deviator stress (Figure 5b). In these cases, failure is defined at the axial strain limit of 15% set by the ASTM Standard D 2850-15 [42]. The fiber type does not have a clear effect on the shape of the stress–strain curves with the two abovementioned types appearing equally in the tested cases. On the contrary, the soil type has an effect on the shape of the stress–strain curves as the type shown typically in Figure 5a prevails in the SP, CS3 and CS4 soils and the type shown typically in Figure 5b prevails in the intermediate CS1 and CS2 soils.
The deformability of the fiber-reinforced soils is expressed herein in terms of the initial modulus of elasticity, Εi, the secant modulus of elasticity, E50, and the failure deformation, εf, chosen because they are practical design parameters for geotechnical engineering projects. The initial modulus of elasticity, Ei, is the gradient of the tangent to the initial linear part of the stress–strain curve. The secant modulus of elasticity, E50, is the gradient of the chord connecting the beginning of the stress–strain curve with the point where the deviator stress is equal to 50% of its maximum value. The failure deformation, εf, is the axial strain corresponding to the maximum value of the deviator stress. The deformability parameters of all the fiber-reinforced soils tested exhibit a wide range of values and are not consistently affected by the factors examined in the present study. The failure deformation values range from 3.52% to 15.00% and the values of the initial and the secant modulus of elasticity range from 6.2 MPa to 89.0 MPa and from 6.1 MPa to 86.7 MPa, respectively. From the comparison of the values of the two moduli of elasticity presented in Figure 6, it is observed that the initial modulus of elasticity, Ei, is either equal to or, in most cases, greater than the secant modulus of elasticity, E50. This observation indicates that the stiffness of the fiber-reinforced soil is generally superior in the initial part of the stress–strain curve but it can also remain invariable up to the point where the deviator stress is equal to 50% of its maximum value.
The assessment of fiber reinforcement effect on the deformability is quantified herein using the ratios of the initial modulus of elasticity, Eir, the secant modulus of elasticity, E50r, and the failure deformation, εfr, of the fiber-reinforced soils to the initial modulus of elasticity, Eiu, the secant modulus of elasticity, E50u, and the failure deformation, εfu, of the unreinforced soils, respectively. The results obtained are presented in Figure 7 with respect to the soil type (CL soil content), since it is one of the most significant parameters examined in the present study. As shown in Figure 7, the values of the Eir/Eiu and E50r/E50u ratios are generally lower than 1.0, whereas the values of the εfr/εfu ratio are generally greater than 1.0 and reach values approximately equal to 6.0, indicating that fiber reinforcement results in ductile behavior by decreasing the stiffness and increasing the deformability of the soil. These observations are in complete agreement with the failure deformation and in partial agreement with the moduli of elasticity with the observations of other researchers summarized in Table 1. More specifically, all researchers agree that fiber reinforcement leads to an increase in soil failure deformation but they have reported that the moduli of elasticity of soil can increase or decrease due to fiber reinforcement (Table 1). This ambiguity in the effect of fiber reinforcement on the moduli of elasticity of soil resulting from the available literature can possibly be attributed to differences in the tested materials and/or the testing conditions.
The typical failure modes of fiber-reinforced soil specimens are presented in Figure 8. As shown in Figure 8a, shear failure occurred in some cases, mostly in specimens tested under the confining pressure of 50 kPa. The failure mode of the majority of the fiber-reinforced soil specimens was plastic with intense bulging at the specimen mid-height (Figure 8b). This failure mode confirms that the fiber-reinforced soil generally exhibits a ductile behavior, as also reported by Hoare [4], Al-Refeai [6] and Ayothiraman et al. [26].

4. Shear Strength

The results of UU triaxial compression tests are also used in the present study to quantify the shear strength of fiber-reinforced soils at their “as-compacted” water content and to obtain dependable design parameters for geotechnical engineering projects. As typically shown in Figure 9, the shear strength of soils increased substantially with fiber addition and linear failure envelopes (Kf-lines) were obtained for all fiber-reinforced soils subjected to UU testing (total stresses). The efficiency of the linear failure envelopes to best fit the experimental data and, as a result, to successfully represent the shear strength of fiber-reinforced soils, is strongly supported by the high values obtained for the coefficient of determination, R2, ranging from 0.965 to 1. This finding is in good agreement with those of the greater part of the research efforts summarized in Table 1, as linear failure envelopes were also obtained by Al-Refeai [6], Singh and Bagra [12], Maheshwari et al. [13], Wu et al. [14], Muni et al. [15], Noorzad and Zarinkolaei [16], Botero et al. [17], Tanegonbadi et al. [23], Xu et al. [19] and Vafaei et al. [28] after conducting the same type of tests on various fiber-reinforced soils. Accordingly, it can be stated with confidence that the shear strength of the fiber-reinforced soils can be depicted satisfactorily by a Mohr–Coulomb type linear failure criterion and expressed in terms of an angle of internal friction, φ, and a cohesion, c, (total stresses). The cohesion of the fiber-reinforced soils ranges between 61 kPa and 301 kPa in the study reported herein, while their angle of internal friction ranges between 10° and 46.5°.
The effect of fiber length and content on the shear strength parameters was investigated for the three intermediate soils (CS1, CS2 and CS3), reinforced with the most frequently used monofilament (M) and tape (T1) fibers, and the results obtained are shown in Figure 10 and Figure 11, respectively. As shown in Figure 10a,b, the increase in fiber length leads to minor variations in the angle of internal friction, φ, of fiber-reinforced soils, limited to ±20% with respect to the corresponding values of the angle of internal friction of the unreinforced soils. These variations are higher in the T1 fiber compared to those observed in the M fiber. On the contrary, the fiber length has a measurable effect on the cohesion, c, of fiber-reinforced soils. The results shown in Figure 10c,d indicate that the increase in fiber length up to the value of 30 mm leads to a significant increase in the cohesion of reinforced soils reaching 125% in comparison with the corresponding cohesion values of the unreinforced soils. This observation is consistent with the optimum fiber lengths reported by other researchers which, as shown in Table 1, range generally between 10 mm and 30 mm.
The results shown in Figure 11a,b indicate that the increase in fiber content results in an increase in the angle of internal friction, φ, reaching 40% for the soils reinforced with M fiber and in variations of the angle φ limited to ±20% for the soils reinforced with T1 fiber, with respect to the corresponding values of the angle φ of the unreinforced soils. As shown in Figure 11c,d, the increase in fiber content is more effective in the cohesion, c, of fiber-reinforced soils regardless of the fiber type used. More specifically, the increase in fiber content leads to an increase in the fiber-reinforced soil cohesion of up to seven times in comparison with the corresponding cohesion values of the unreinforced soils. The largest cohesion increases observed in the CS1 soil were reduced substantially in the CS2 and CS3 soils, indicating that the effect of fiber content on soil cohesion is stronger with decreasing CL soil content. This observation will be discussed more comprehensively in the subsequent paragraphs. As shown in Table 1, the effect of fiber content has been investigated extensively in the past with some researchers reporting optimum fiber contents ranging widely from 0.2% to 2.0% by weight of dry soil. However, an optimum fiber content is not obtained based on the results of the present study in agreement with the greater part of the research efforts summarized in Table 1. It must be stated that fiber contents higher than 2.0% by weight of dry soil were not used in the research reported herein due to the difficulty in producing homogeneous soil–fiber mixtures for specimen preparation.
The effect of soil type, expressed using the CL soil content (Table 2), on the angle of internal friction, φr, and the cohesion, cr, of soils reinforced with wf = 1% of fibers is shown in Figure 12 and Figure 13, respectively, in comparison with the values of the angle of internal friction, φu, and the cohesion, cu, obtained for the unreinforced soils. The fiber length used in this investigation was equal to 30 mm for fibrillated fibers and 18 mm for all the other fiber types. The shear strength improvement in soils due to fiber reinforcement is also quantified in Figure 12 and Figure 13 in terms of improvement ratios, i.e., the ratios of the values obtained for φr and cr of the fiber-reinforced soils to the corresponding values for φu and cu of the unreinforced soils, respectively. It is observed that the soil type plays an important role in the shear strength of reinforced soil regardless of the type of fiber used. More specifically, the angle of internal friction of the fiber-reinforced and the unreinforced soil decreases with increasing fine-grained fraction (CL soil content) of the soil (Figure 12). The values of the φr and φu angles are comparable, resulting in minor variations of the φr/φu ratio for all soil and fiber types tested. As shown in Figure 13, the cohesion values of fiber-reinforced soils are greater than those of the unreinforced soils and, in some cases, they present an upward trend with increasing CL soil content. However, the differences between the cr and cu values and, as a result, the values of the cr/cu ratio decrease with increasing CL soil content. This observation indicates that fiber reinforcement becomes less effective in cohesion improvement as the fine-grained fraction of soil increases.
Presented in Figure 14 is the effect of soil and fiber type on the shear strength improvement in soils due to fiber reinforcement. As shown in Figure 14a, the values of φr/φu ratio range from 0.75 to 1.25 and are not consistently affected by the soil or the fiber type used. Consequently, fiber reinforcement leads to variations of the angle of internal friction of soil limited to ±25% regardless of the soil and fiber used. The significant contribution of fiber reinforcement to the improvement in soil cohesion is presented in Figure 14b,c. It is observed that fiber reinforcement gives cohesion values ranging between 84 kPa and 124 kPa to the non-cohesive SP soil and results in cr/cu ratio values ranging from 4.3 to 3.0, from 2.7 to 1.9, from 2.0 to 1.2 and from 1.5 to 1.2 in the cohesive CS1, CS2, CS3 and CS4 soils, respectively. Accordingly, the cohesion improvement induced by fiber reinforcement is affected substantially by the soil type and composition and is inversely proportional to the fine-grained fraction and the cohesion of the unreinforced soil. As also shown in Figure 14b,c, the monofilament (M) and tape 1 (T1) fibers generally gave better results regarding soil cohesion improvement in comparison with the other fiber types tested in the present study.
The reinforcement effect of randomly oriented discrete fibers incorporated into the soil mass is attributed to their mechanical interaction with the soil grains through surface friction and interlocking [12]. These mechanisms result in stress transfer from the soil to the fibers and the mobilization of the tensile strength of fibers. Thus, fiber reinforcement works as a frictional and tension resistance element [12]. The results presented and the observations made in the preceding paragraphs can be explained based on these reinforcement mechanisms. The cohesion improvement due to fiber reinforcement can be attributed to the increase in the confining pressure caused by the development of tension in the fibers [7]. The cohesion improvement increase with increasing fiber content is attributed to the increase in the number of tension resistance elements in the soil, and the better performance of M and T1 fibers regarding soil cohesion improvement can be attributed to their superior interlocking with the soil grains in comparison with the other fiber types tested in the present study. The cohesion improvement increase with increasing fiber length up to 30 mm can be anticipated because the tensile force in the fiber is proportionate to its length, when friction is mobilized fully along the length of the fiber [6]. The influence of fibers with lengths greater than 30 mm on the cohesion increase is generally less effective, probably because (a) the number of fibers decreases significantly [23] and/or (b) the fibers of such lengths cannot efficiently interlock the soil grains and, as a result, the fiber-reinforced soil does not act as a uniform composite material [7]. The interfacial peak and residual strength obtained from single fiber pull-out tests decreases with decreasing dry density and with the increasing water content of soil [16]. Consequently, the increasing optimum water content used in the compaction and/or the decreasing dry unit weight attained after the compaction of CS1-CS4 soil specimens [41] are probably responsible for the observed reduction in cohesion improvement with increasing fine-grained fraction of soil.

5. Conclusions

Based on the results obtained and the observations made during this experimental investigation, and within the limitations of the range of parameters investigated, the following conclusions may be advanced:
  • The stress–strain curves of soils reinforced with low contents of fibers of small length (9 mm) more often exhibit a strain-softening behavior. As the fiber length and content increase, the stress–strain behavior of fiber-reinforced soils becomes strain-hardening.
  • The deformability parameters of fiber-reinforced soils exhibit a wide range of values and are not consistently affected by the factors examined in the present study. The failure deformation values range from 3.52% to 15.00% and the values of the initial and the secant modulus of elasticity range from 6.2 MPa to 89.0 MPa and from 6.1 MPa to 86.7 MPa, respectively.
  • Fiber reinforcement reduces the stiffness and increases the deformability of the soil. The fiber-reinforced soil exhibits a more ductile behavior in comparison with the unreinforced soil.
  • The stiffness of the fiber-reinforced soil is generally superior in the initial part of the stress–strain curve but, in several cases, it remains invariable up to the point where the deviator stress is equal to 50% of its maximum value.
  • A Mohr–Coulomb type linear failure criterion satisfactorily describes the shear strength behavior of fiber-reinforced soils, in total stress terms, as obtained through UU triaxial compression tests. The cohesion values of the fiber-reinforced soils obtained in the present study range between 61 kPa and 301 kPa and the values of their angle of internal friction range between 10° and 46.5°.
  • The angle of internal friction of fiber-reinforced soils is not significantly affected by the factors examined in the present study. Although increases in the angle of internal friction reaching 40% were observed in some cases, the variations of the angle of internal friction of soils due to fiber reinforcement are generally limited to ±25%.
  • Fiber reinforcement contributes to the shear strength improvement in soils by adding cohesion ranging between 84 kPa and 124 kPa to the clean sand and by increasing the cohesion of cohesive soils up to seven times. The cohesion improvement due to fiber reinforcement is increased with increasing fiber content and fiber length up to 30 mm, is increased when monofilament (M) and tape 1 (T1) fibers are used and is inversely proportional to the fine-grained fraction and the cohesion of the unreinforced soil.

Author Contributions

Conceptualization, I.N.M.; methodology, I.N.M. and E.D.E.; validation, I.N.M. and E.D.E.; formal analysis, E.D.E., S.E.V. and K.E.B.; investigation, E.D.E., S.E.V. and K.E.B.; resources, I.N.M.; writing—original draft preparation, E.D.E.; writing—review and editing, I.N.M.; visualization, E.D.E.; supervision, I.N.M.; project administration, I.N.M. and E.D.E. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The data presented in this study are available in the article.

Acknowledgments

Thanks are expressed to the company, Thrace Nonwovens and Geosynthetics S.A., for supplying the fibers and to the company, KEBE S.A. (Northern Greece Ceramics), for supplying the clay used in the present study.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Figure 1. Grain size distributions of soils.
Figure 1. Grain size distributions of soils.
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Figure 2. Images of (a) monofilament, (b) tape, (c) hollow and (d) fibrillated fibers.
Figure 2. Images of (a) monofilament, (b) tape, (c) hollow and (d) fibrillated fibers.
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Figure 3. Image of the specimen compaction equipment.
Figure 3. Image of the specimen compaction equipment.
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Figure 4. Comparison of the compaction characteristics of specimens for triaxial compression testing (TXUU) with those resulting from the compaction test (Proctor), (a) optimum water content, wopt, and (b) maximum dry unit weight, γdmax.
Figure 4. Comparison of the compaction characteristics of specimens for triaxial compression testing (TXUU) with those resulting from the compaction test (Proctor), (a) optimum water content, wopt, and (b) maximum dry unit weight, γdmax.
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Figure 5. Typical stress–strain curves of fiber-reinforced soils, (a) strain-softening behavior and (b) strain-hardening behavior.
Figure 5. Typical stress–strain curves of fiber-reinforced soils, (a) strain-softening behavior and (b) strain-hardening behavior.
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Figure 6. Comparison between the initial and the secant modulus of elasticity.
Figure 6. Comparison between the initial and the secant modulus of elasticity.
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Figure 7. Variation of the improvement ratios of fiber-reinforced soil deformability as a function of soil composition, (a) Eir/Eiu ratio, (b) E50r/E50u ratio and (c) εfr/εfu ratio.
Figure 7. Variation of the improvement ratios of fiber-reinforced soil deformability as a function of soil composition, (a) Eir/Eiu ratio, (b) E50r/E50u ratio and (c) εfr/εfu ratio.
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Figure 8. Forms of fiber-reinforced soil specimens after UU triaxial compression testing, (a) shear failure mode and (b) plastic failure mode.
Figure 8. Forms of fiber-reinforced soil specimens after UU triaxial compression testing, (a) shear failure mode and (b) plastic failure mode.
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Figure 9. Typical failure envelopes of fiber-reinforced soil.
Figure 9. Typical failure envelopes of fiber-reinforced soil.
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Figure 10. Effect of fiber length on the shear strength parameters of fiber-reinforced soils, (a,b) angle of internal friction and (c,d) cohesion.
Figure 10. Effect of fiber length on the shear strength parameters of fiber-reinforced soils, (a,b) angle of internal friction and (c,d) cohesion.
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Figure 11. Effect of fiber content on the shear strength parameters of fiber-reinforced soils, (a,b) angle of internal friction and (c,d) cohesion.
Figure 11. Effect of fiber content on the shear strength parameters of fiber-reinforced soils, (a,b) angle of internal friction and (c,d) cohesion.
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Figure 12. Effect of soil type on the angle of internal friction of fiber-reinforced soils, (a) monofilament fiber, (b) tape 1 fiber, (c) tape 2 fiber, (d) hollow fiber and (e) fibrillated fiber.
Figure 12. Effect of soil type on the angle of internal friction of fiber-reinforced soils, (a) monofilament fiber, (b) tape 1 fiber, (c) tape 2 fiber, (d) hollow fiber and (e) fibrillated fiber.
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Figure 13. Effect of soil type on the cohesion of fiber-reinforced soils, (a) monofilament fiber, (b) tape 1 fiber, (c) tape 2 fiber, (d) hollow fiber and (e) fibrillated fiber.
Figure 13. Effect of soil type on the cohesion of fiber-reinforced soils, (a) monofilament fiber, (b) tape 1 fiber, (c) tape 2 fiber, (d) hollow fiber and (e) fibrillated fiber.
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Figure 14. Effect of soil and fiber type on the shear strength improvement in fiber-reinforced soils, (a) φr/φu ratio, (b) cr/cu ratio and (c) cohesion of fiber-reinforced sand.
Figure 14. Effect of soil and fiber type on the shear strength improvement in fiber-reinforced soils, (a) φr/φu ratio, (b) cr/cu ratio and (c) cohesion of fiber-reinforced sand.
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Table 1. Summary of literature review.
Table 1. Summary of literature review.
Ref.Soil
Type		Fiber
Type		Lf (opt)
(mm)		wf (opt)
(%)		σ3 (kPa)Failure EnvelopeCohesionFriction AngleFailure StrainModulus of Elasticity
[4]sandy gravelpp, nylon tape660.09–0.25---iiEi: d
[5]sandreed, glass mf13, 380.21–2.0049–392biiii
[6]sandpp mf/mesh, glass mf2–100 (75)0.5049–294l, b-iiE50: d, i
[7]clay, CLsisal leaves mf10–25 (20)0.25–1.00 (0.75)69–207-imi-nsii
[8]sandpp mf/fibr/tape511.0021–138--i, d--
[9]clay, CL
silt, ML
sand, SM		coir mfAr: 50–1000.75–3.040---iEi: i
[10]sandcoir mf10–300.50–2.50 (1.5–2.0)50–150-id, iiEi: i
[11]claypp mf120.30, 06050–200-di-i
[12]silty sandjute mf300.25–1.0050–150lii-i
[13]clay, CHpolyester mf-tr120.25–1.50 (0.50)50–150lii--
[14]silty claysisal mf5–15 (10)0.50–1.50100–400limi--
[15]silty sandarecanut mf20, (30)0.25-(1.00)50–200lii-mi-i
[16]sand, SPpp mf6–180.25–1.0050–400liiii
[17]silt, MHPET mf-cr500.10–1.0062–186lmid-Ei: d
[18,19]clay, CLhemp mf400.50–1.50 (1.25)-b--iE50: d
[20]silt, MLbasalt mf6-(24)1.0–2.0 (1.50)100–400-increase in major pr. stress at failure--
[21]claypp, basalt mf120.25–1.00300–500-ii--
[22]sandpp mf Ysection3–18 (12)0.10–0.30 (0.20)100–700-id-Ei: i
[23]sand, SPPET mf, pp tape5–15 (10) 150.25–1.0050–200liiiE50: i
[24,25]loessbasalt mf6–18 (12)0.30–1.00 (0.60)50–200lii-mi-Ei: i
[26,27]silt, SM clay, CLhuman hair mf20–502.0025, 75---iEi, E50: i
[28]sand, SPhemp mf6–140.30–0.9050–200liiiE50: i
[29]red claycoir mf10–40 (30)0.10–0.40 (0.30)50–200----i, d
Legend: mf: monofilament fibers, fibr: fibrillated fibers, tr: fibers of triangular cross-section, cr: crimped fibers, Ei: initial modulus of elasticity, E50: secant modulus of elasticity, Ar: aspect ratio. l: linear, b: bilinear, i: increase, d: decrease, mi: minimal influence, ns: not systematic effect.
Table 2. Soil characteristics, classification and mechanical properties.
Table 2. Soil characteristics, classification and mechanical properties.
Soil
Designation		Mixing Proportions (%)
SP-CL		Atterberg Limits
LL-PL		Soil Classification
USCS (AASHTO)		Unconsolidated Undrained Triaxial Compression Test Results
φ (ο)c (kPa)εf (%)Ei (MPa)E50 (MPa)
SP100–0-SP (A-1-b)42.204.6–7.924.5–96.117.1–71.7
CL *0–10046–21CL (A-7-6)-----
CS185–1526–17SC (A-2-4)36.937.12.5–5.039.9–107.631.3–102.9
CS270–3029–17SC (A-2-6)30.154.22.6–12.414.5–91.714.3–88.4
CS350–5037–19SC (A-6)19.070.14.4–12.030.2–56.127.9–33.2
CS425–7545–20CL (A-7-6)12.9109.96.9–13.716.6–47.714.1–22.8
* Soil used only for the production of the composite soils.
Table 3. Fiber characteristics.
Table 3. Fiber characteristics.
Fiber TypeDesignationDiameter/Thickness (μm)Width (mm)Length
(mm)		Tensile Stress at
Failure (N/mm2)		Elongation at Failure (%)
MonofilamentM35-9, 18, 30, 5057020.2
Tape 1T1431.139, 18, 30, 5054123.3
Tape 2T2382.781855627.0
HollowH45-1851354.2
FibrillatedF422.783041612.1
Table 4. Triaxial compression testing program.
Table 4. Triaxial compression testing program.
Soil TypeFiber TypeFiber Content
wf (%)		Fiber Length
Lf (mm)		Examined Parameter
SP, CS1, CS2, CS3, CS4M, T1, T2, H, F1.018 or 30 *Soil type, Fiber type
CS1, CS2, CS3M, T10.59, 18, 30, 50Fiber length
CS1, CS2, CS3M, T11.5, 2.018Fiber content
* Fibrillated fibers.
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Evangelou, E.D.; Markou, I.N.; Verykaki, S.E.; Bantralexis, K.E. Mechanical Behavior of Fiber-Reinforced Soils under Undrained Triaxial Loading Conditions. Geotechnics 2023, 3, 874-893. https://doi.org/10.3390/geotechnics3030047

AMA Style

Evangelou ED, Markou IN, Verykaki SE, Bantralexis KE. Mechanical Behavior of Fiber-Reinforced Soils under Undrained Triaxial Loading Conditions. Geotechnics. 2023; 3(3):874-893. https://doi.org/10.3390/geotechnics3030047

Chicago/Turabian Style

Evangelou, Evangelos D., Ioannis N. Markou, Sofia E. Verykaki, and Konstantinos E. Bantralexis. 2023. "Mechanical Behavior of Fiber-Reinforced Soils under Undrained Triaxial Loading Conditions" Geotechnics 3, no. 3: 874-893. https://doi.org/10.3390/geotechnics3030047

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