Drained and Undrained Behavior of Fiber-Reinforced Sand by Cheng-Wei Chen

Transcription

1 Drained and Undrained Behavior of Fiber-Reinforced Sand by Cheng-Wei Chen Cheng-Wei Chen University of Missouri Columbia Graduate Research Assistant Department of Civil and Environmental Engineering E2509 Lafferre Hall Columbia, MO Telephone: (573) Fax: (573) Submitted October 12, 2006 Word Count: 2290 words plus 2750 word equivalents for tables and figures (5040 total words)

2 Cneng-Wei Chen 2 Drained and Undrained Behavior of Fiber-Reinforced Sand by Cheng-Wei Chen ABSTRACT A series of CU and CD type triaxial compression tests were performed on comparable unreinforced and fiber-reinforced specimens of Ottawa Sands to evaluate the effective stressstrain-pore pressure-volume change behavior of fiber-reinforced soils. The results show that fibers increase the cohesion (c ) and effective friction angle ( ) for Ottawa Sands. The c and determined for the reinforced specimens increases with strains. Reinforced loose specimens tend to have a higher friction angle, but lower cohesion intercept than the reinforced medium-dense specimens. In addition, the inclusion of fibers with loose specimens has a significant effect in increasing effective friction angle than with medium-dense specimens. In CU tests, the loose reinforced specimens exhibited lower pore pressures than unreinforced specimens. In CD tests, the loose and medium-dense reinforced specimens showed more dilation than unreinforced specimens at moderate and larger strains. These are in agreement with the response observed in undrained tests. For Ottawa sands, the fiber resistance is mobilized at small strains in both undrained and drained conditions. However, the mobilized shear resistances in drained tests occur sooner than in undrained tests.

3 Cneng-Wei Chen 3 INTRODUCTION The behavior of fiber-reinforced soils has been studied by several investigators over the last two decades. Fiber-reinforced soil is becoming a viable soil improvement method for geotechnical engineering problems. Fiber-reinforced soils are currently being used or considered include stabilization of shallow slope failures (1), construction of new embankments with marginal soils, reduction of shrinkage cracking in compacted clay liners (2), and mechanical stabilization of roadway subgrades (3). PREVIOUS WORK Fiber-reinforced soil is a mixture of soil and synthetic fibers. Synthetic fibers can be made of different materials, shapes and lengths. Polypropylene and polyester are the most common materials used to manufacture fibers. Fibers can be flat or round, and continuous or discrete. Discrete fibers are manufactured in several lengths, ranging from 0.5 in to 3 in, and in different types such as monofilament, fibrillated, tape, and mesh. Significant fundamental research has been performed over the last few decades to evaluate basic shear strength properties and deformation characteristics of fiber-reinforced soils. Previous work has clearly shown that an increase in fiber content increased the shear strength of the soils. Most investigators found that shear strength increased in direct proportion to fiber content or area ratio (3, 5, 6, 7, 8). However, (9) observed that increase in strength was not proportional to the reinforcement concentration. Some of the previous research has shown that inclusion of fibers increased both the cohesion intercept and angle of internal friction values as compare to values for unreinforced soil (10, 11, 1). However, (4, 5, 7, 8) found that inclusion of fibers did not significantly affect the angle of internal friction of the unreinforced soils, but rather that fiber-reinforced specimens exhibited bi-linear failure envelopes as a result of the existence of a critical confining stress below which the fibers tended to slip or pull-out. (12) observed an increase in the angle of internal friction but a decrease in the cohesion intercept. (6) found that an increase in fiber content only increased the cohesion intercept whereas the angle of internal friction remained unchanged from that of the unreinforced soil. Inclusion of fibers was generally found to increase the peak and post-peak strength, as well as the strain at failure. Furthermore, inclusion of fibers has been found to not noticeably affect the initial stiffness of the unreinforced specimens. However, some investigators have reported an increase in the initial stiffness of specimens with increasing fiber content (11), whereas others have shown a decrease in initial stiffness with increasing fiber content (12,13). It is shown by many researchers that inclusion of fibers increases the shear strength under different loading conditions. Most of pervious work in this area has concentrated on the behavior of fiber-reinforced granular (i.e. sand) and undrained behavior of clays under total stress conditions. The laboratory work was mainly utilizing the simply direct shear tests. The data from most investigators lacks evaluation of the load transfer mechanics in terms of effective stress. Additional tests of fiberreinforced sand are needed to confirm the reinforcement response with different loading conditions in terms of effective stress measurements. TESTING MATERIALS AND PROGRAM The soil used in triaxial testing program was Ottawa sand (Grade F-75), which is well known laboratory-tested sand. The particles have a mean diameter, D 50 of 0.18 mm, a uniformity coefficient, U c of 1.7, a minimum void ratio, e min of 0.46, a maximum void ratio, e max

4 Cneng-Wei Chen 4 of 0.77, and a specific gravity of 2.65, respectively. The soil classifies as poorly graded sands (SP) according to the Unified Soil Classification System. The fibers utilized in the specimens are commercially available 2-inch (50-mm) long fibrillated polypropylene fibers of 3600 denier. The specific gravity of the fibers is 0.91 gr/cm 3 (14). The ultimate tensile strength (15) and modulus of elasticity (16) of the fiber are 45 ksi, and 700 ksi, respectively. An undercompaction process (17) was selected to produce homogeneous samples using Ottawa sand for a parametric study in a laboratory-testing program. Unreinforced and fiberreinforced Ottawa sand specimens were prepared and mixed to the nominal 10 percent water content as loose state and 3 percent water content as medium-dense state, which nominal relatively density were equal to 10 percent (e 0 = 0.74) and 55 percent (e 0 = 0.60), respectively. The soil was also allowed to hydrate overnight prior to compaction. Decided how many lifts of compacting and calculated the desired thickness of each layers according to the undercompaction process suggested. All specimens were backpressure saturated at effective consolidation stresses of 2.5 psi using the dry mounting method as specified in ASTM D4767 (18). Skempton s pore pressure coefficient B (18) was measured during saturation. All specimens were allowed to saturate until measured B-values were reached at least 0.96 before consolidation and shear. Approximately 5 days were required to bring the B-value of the Ottawa sand specimens to The strain rate used to shear all conventional triaxial compression and extension specimens was 10 percent per hour (deformation rate of 0.49-inch per hour) to eliminate concern over strain rate when compared to drained and undrained test results. Most specimens were sheared up to a maximum axial strain of 30 percent to permit evaluation of the post-peak stressstrain behavior. A summary of testing program undertaken to evaluate the stress-strain behavior of unreinforced and fiber-reinforced specimens in term of effective stresses is shown in Table 1. A total of sixteen consolidated-undrained triaxial compression tests with pore pressure measurements ( CU tests) were performed to evaluate the stress-strain-pore pressure generation behavior of fiber-reinforced specimens under undrained loading conditions. A total of sixteen consolidated-drained triaxial compression tests (CD tests) were also performed for specimens compacted at loose and medium-dense state to evaluate the stress-strain-volume change behavior of fiber-reinforced specimens under drained loading conditions. All tests were performed on 2.5-inch diameter by nominal 4.9-inch tall specimens. Specimens isotropically consolidated to the target effective stress of 5, 20, 40, and 60-psi. STRESS-STRAIN-PORE PRESSURE-VOLUME CHANGE RESPONSE Typical deviatoric stress versus triaxial shear strain behavior from CU and CD tests for unreinforced and reinforced specimens is shown in Figure 1 and 2. Loose fiber-reinforced specimens show a strain-hardening type of behavior whereas medium-dense reinforced specimens exhibit a noticeable peak stress at large strains of 20 percent. Figure 1 shows that stress-strain behavior of medium-dense reinforced specimen begins to deviate at 5 percent stain under undrained condition. However, Figure 2 shows that the considerable strength is gained by the inclusion of fibers at 1 percent strain of medium-dense reinforced specimen under drained condition. Change in pore pressure versus triaxial shear strain observed in tests for both unreinforced and reinforced Ottawa sand specimens are shown in Figure 3. Loose unreinforced specimen exhibits the lower initial increase in pore pressure than reinforced specimen at 1

5 Cneng-Wei Chen 5 percent strain, slightly decrease in a range of 1 percent to 2 percent and increase again slowly with addition strains. In contrast, the loose fiber-reinforced specimens show the initial increases in pore pressure at very small strain, decrease with additional strains, and tend to level at large strains. Both medium-dense unreinforced and reinforced specimens show the initial increases in pore pressure followed by significant decreases and absolute value of pore pressures equal or less than zero before 10 percent strains. It is noticed that medium-dense reinforced specimens tend to have higher initial increases in pore pressure than unreinforced specimens and keep relative higher pore pressures when compared to the unreinforced specimens at given strains before absolute pore pressures equal or less than zero. When the readings of pore pressure transducer measured less than the atmosphere pressure, cavitation is taken place. Pore pressure transducers cannot measure negative pressure accurately. Therefore, the measure values can not represent the real readings in the soil when the absolute value of pore pressures is equal or less than zero. The typical volumetric strain versus triaxial shear strain response from CD tests for the unreinforced and reinforced Ottawa sand specimens are shown in Figure 4 for the samples compacted to loose and medium-dense state. The unreinforced specimens exhibit volumetric strain response typical of loose and medium-dense behavior, with volume compressing at small strains and then keeping constant at large strains for loose specimen whereas with initial volume decreasing followed by significant dilation up to large strains. The loose fiber-reinforced specimens show that less volume compressing than the unreinforced specimen consolidated to 20-psi or higher effective confining stresses. Conversely, medium-dense specimens exhibit less dilation at low shear strains at the range of 2 percent to 5 percent, but more dilation at moderate and large strains than observed on unreinforced specimens. Therefore, it indicates that the medium-dense sand exhibit the lower pore pressure to maintain the zero volume change in undrained loading condition at moderate to large strains, which is similar to loose sand behavior. The volumetric strain versus triaxial shear strain behavior inspect on the fiber-reinforced specimens under drained tests is in agreement with the pore pressure versus triaxial shear strain response tested at undrained condition. The causes for the unusual pore pressure responses observed in the fiber-reinforced specimens are not clear. (20) assumed that the fibers create an internal confining stress (due to tension developed in the fibers) that, when added to the applied total stresses and actual pore pressures generated in the fiber-reinforced soil, the fibers produces additional effective stress to prevent volume change in undrained tests. However, the results presented above show that fiberreinforced Ottawa sand require lower pore pressure to maintain the zero volume change in undrained loading conditions for both loose and medium-dense state, which are different observation with (20) for fiber-reinforced silty clay specimens. The inclusion of fibers generates a negative internal confining stress and produces negative effective stress to maintain zero volume change in undrained tests. FAILURE ENVELOPES FOR TRIAXIAL COMPRESSION TEST Failure envelopes were determined from the peak deviator stress (PDS) and peak effective stress ratio (PSR) failure criteria for CU tests. Values of the Mohr-Coulomb strength parameters, effective cohesion intercept,, and effective internal friction angle,, for the unreinforced Ottawa sand specimens from CU tests and CD tests are listed in Tables 2 and 3, respectively. The results indicate that the strength of unreinforced specimens under undrained loading can be represented by no cohesion intercept, and an effective friction angle of 29 and 34, for loose state and medium-dense specimens, respectively. The shear strength parameters determined from PRS failure criteria show a slightly greater than the results from the PDS failure

6 Cneng-Wei Chen 6 criteria. Furthermore, the shear strength parameters determined from CD tests show a greater value than the results from the CU tests, which are presented in Table 3. Table 2 and 3 also present the strength parameters for the fiber-reinforced Ottawa sand specimens from CU tests and CD tests. It can be seen that inclusion of fibers has a pronounce effect both on the effective cohesion intercept and on the measured effective friction angle. Reinforced specimens compacted at loose state tend to have a higher friction angle, but lower cohesion intercept than specimens compacted at medium-dense state. In addition, the inclusion of fibers with loose specimens has a significant effect in increasing effective friction angle than with medium-dense specimens, which is shown in Table 3. Peak deviator stress and peak effective stress ratio for the fiber-reinforced specimens under undrained and drained loading occurred at very large strain. Since such large strain are seldom tolerable, the data were also analyzed for limiting strains of 5, 15, and 25 percent strain. For these analyses, the PDS and PSR failure criteria were taken to be the maximum values measured at strains close or equal to the limiting strains. Figure 5 and 6 show the Cambridge stress path diagrams and failure envelopes for the chosen limiting strains from CU tests and CD tests on unreinforced and reinforced loose specimens. The failure envelopes of unreinforced specimens do not show a significant difference at established limiting strains for both loose and medium-dense state. In contrast, the shear strength parameters calculated from reinforced specimens increase with chosen limiting strains in terms of effective cohesion intercept and effective friction angle. The results of Mohr-Coulomb strength parameters for the unreinforced and reinforced specimens at the limiting strains from CU and CD tests are summarized in Table 4 and 5, respectively. In general, the strength parameters measured from CU tests are greater than those from CD tests for loose reinforced specimens, whereas the effective friction measured from CU tests are less than those from CD tests. Furthermore, reinforced specimens compacted at loose state show a significant increase in the effective friction angle from CU and CD tests. The opposite was observed for specimens compacted at medium-dense state, a significant increase in the effective cohesion intercept. CONCLUSIONS The results of the triaxial compression tests performed on loose and medium-dense Ottawa sand show that inclusion of fibers can improve the strength of soils under undrained and drained loading conditions. Shear strength parameters of effective cohesion intercept and effective friction angle increase significantly in the CU and CD tests, due to the addition of fibers. The angle of internal friction under drained loading was slightly greater than for those under undrained loading for both unreinforced and reinforced specimens. It is noted the reinforcing fibers alter the pore pressure response of specimens tested under undrained loading conditions and the volume change response of specimens tested under drained loading condition. However, the response in Ottawa sand is totally different from the response in silty clay (20). It was shown that fiber reinforced specimens must deform before developing and increase in shear strength due to the inclusion of fibers. Under undrained conditions, deformations can be high for most structures. However, drained specimens mobilized the shear fiber resistance at very low strain, which can be tolerable for must structures. As a result, more strains are needed to mobilize the fiber shear strain for specimens consolidated at high effective stresses.

7 Cneng-Wei Chen 7 REFERENCES 1. Gregory, G.H., and D.S. Chil. Stabilization of Earth Slopes with Fiber Reinforcement. Proceedings of the Sixth International Conference on Geosynthetics, March 25-29, Atlanta, Georgia, 1998, pp Rifai, S.M. Impact of Polypropylene Fibers on Dessication Cracking and Hydraulic Conductivity of Compacted Clay Liners. Dissertation submitted in partial fulfillment for the requirements of the Doctoral Degree, Wayne State University, Detroit, Michigan, Santoni, R.L., J.S. Tingle, and S.L. Webster. Engineering Properties of Sand-Fiber Mixtures for Road Construction, Journal of Geotechnical and Environmental Engineering, ASCE, Vol. 127, No. 3, 2001, pp Gray, D.H., and H. Ohashi. Mechanics of Fiber Reinforcement in Sand. Journal of the Geotechnical Engineering Division, ASCE, Vol. 109, No. 3, 1983, pp Ranjan G., R.M. Vasan, and H.D. Charan. Probability Analysis of Randomly Distributed Fiber-reinforced Soil. Journal of the Geotechnical Engineering Division, ASCE, Vol. 122, No. 6, 1996, pp Bauer, G., and A. Oancea. Soils Reinforced with Discrete Synthetic Fibers. Geosynthetics 99 Specifying Geosynthetics and Developing Design Detail, IFAI, Boston, Massachusetts, 1999, pp Maher, M.H., and D.H. Gray. Static Response of Sands Reinforced with Randomly Distributed Fibers. Journal of the Geotechnical Engineering Division, ASCE, Vol. 116, No. 11, 1990, pp Gray, D.H., and T. Al-Refeai. Behavior of Fabric- versus Fiber-reinforced Sand. Journal of the Geotechnical Engineering Division, ASCE, Vol. 112, No. 8, 1986, pp Shewbridge, S.E., and N. Sitar. Deformation Characteristics of Reinforced Soil in Direct Shear. Journal of the Geotechnical Engineering Division, ASCE, Vol. 115, No. 8, 1989, pp Kumar, R., V.K. Kanaujia, and D. Chandra. Engineering Behaviour of Fibre-Reinforced Pond Ash and Silty Sand, Geosynthetics International, Vol. 6, No. 6, 1999, pp Nataraj, M.S., and K.L. McManis. Strength and Deformation Properties of Soils Reinforced with Fibrillated Fibers," Geosynthetics International, Vol. 4, No. 1, 1997, pp Consoli, N.C., P.D.M. Prietto, and L.A. Ulbrich. Influence of Fiber and Cement Addition on Behavior of Sandy Soil. Journal of the Geotechnical Engineering Division, ASCE, Vol. 124, No.12, 1998, pp Michalowski R.L., and J. Cermak. Triaxial Compression of Sand Reinforced With fibers, Journal of the Geotechnical Engineering Division, ASCE, Vol. 192, No. 2, 2003, pp ASTM. D792. Standard test methods for density and specific gravity (relative density) of plastics by displacement. Annual Book of ASTM Standards, Vol , Philadelphia. 15. ASTM. D2256. Standard test method for tensile properties of yarns by the single-strand method. Annual Book of ASTM Standards, Vol , Philadelphia. 16. ASTM. D2101. Standard test methods for tensile properties of single man-made textile fibers taken from yarns and tows. Annual Book of ASTM Standards, Vol , Philadelphia. 17. Ladd, R. S. Preparing Test Specimens Using Undercompaction Geotechnical Testing Journal, Vol. 1, No. 1,1978, pp

8 Cneng-Wei Chen ASTM D4767, Standard test method for consolidated-undrained triaxial compression test on cohesive soils, Annual Book of ASTM Standards, Vol , Philadelphia. 19. Skempton, A.W. The Pore Pressure Coefficient A and B, Geotechnique, Vol. 4, 1954, pp Romero, R.J. Development of a Constitutive Model for Fiber-Reinforced Soils. Dissertation submitted in partial fulfillment for the requirements of the Doctoral Degree, University of Missouri-Columbia, 2003.

9 Cneng-Wei Chen 9 List of Tables TABLE 1 Summary of Triaxial Tests Performed to Evaluate the Stress-Strain Behavior of Unreinforced and Reinforced Ottawa Sand Specimens TABLE 2 Mohr-Coulomb Strength Parameters, and, Measured for Unreinforced and Reinforced Ottawa Sand Specimens from CU Tests TABLE 3 Mohr-Coulomb Strength Parameters, and, Measured for Unreinforced and Reinforced Ottawa Sand Specimens from CD Tests TABLE 4 Mohr-Coulomb Strength Parameters, and, from CU Tests on Unreinforced and Reinforced Ottawa Sand Specimens When Strength Is Taken as Peak Stress Experienced at Limiting Strains of 5, 15, 25 Percent TABLE 5 Mohr-Coulomb Strength Parameters, and, from CD Tests on Unreinforced and Reinforced Ottawa Sand Specimens When Strength Is Taken as Peak Stress Experienced at Limiting Strains of 5, 15, 25 Percent List of Figures FIGURE 1 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CU tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). FIGURE 2 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CD tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). FIGURE 3 Change in pore pressure ( u) versus triaxial shear strain ( q ) curves from CU tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). FIGURE 4 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CD tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). FIGURE 5 Cambridge stress paths and failure envelopes for limiting strains of 5, 15, and 25 percent strain from CU tests on Ottawa sand specimens compacted at loose state ( e 0 = 0.74): a) 0.0 percent fiber content, and b) 0.4 percent fiber content. FIGURE 6 Cambridge stress paths and failure envelopes for limiting strains of 5, 15, and 25 percent strain from CD tests on Ottawa sand specimens compacted at loose state ( e 0 = 0.74): a) 0.0 percent fiber content, and b) 0.4 percent fiber content.

10 Cneng-Wei Chen 10 TABLE 1 Summary of Triaxial Tests Performed to Evaluate the Stress-Strain Behavior of Unreinforced and Reinforced Ottawa Sand Specimens Type of Triaxial Testing CU CD Fiber Content (%) Effective Confining Stress Loose Specimens (e 0 =0.74) Dense Specimens (e 0 =0.60) 5 psi 20 psi 40 psi 60 psi 5 psi 20 psi 40 psi 60 psi

11 Cneng-Wei Chen 11 TABLE 2 Mohr-Coulomb Strength Parameters, and, Measured for Unreinforced and Reinforced Ottawa Sand Specimens from CU Tests Initial Void Ratio 0.0% Fiber Content 0.4% Fiber Content Peak PSD Peak PSR Peak PSD/PSR a - - a a Data not available.

12 Cneng-Wei Chen 12 TABLE 3 Mohr-Coulomb Strength Parameters, and, Measured for Unreinforced and Reinforced Ottawa Sand Specimens from CD Tests Initial Void Ratio 0.0% Fiber Content 0.4% Fiber Content Peak PSD Peak PSD

13 Cneng-Wei Chen 13 TABLE 4 Mohr-Coulomb Strength Parameters, and, from CU Tests on Unreinforced and Reinforced Ottawa Sand Specimens When Strength Is Taken as Peak Stress Experienced at Limiting Strains of 5, 15, 25 Percent Initial Void Ratio 0.0% Fiber content 0.4% Fiber content 5% Strain 15% Strain 25% Strain 5% Strain 15% Strain 25% Strain a - - a - - a - - a a - - a - - a - - a a Data not available.

14 Cneng-Wei Chen 14 TABLE 5 Mohr-Coulomb Strength Parameters, and, from CD Tests on Unreinforced and Reinforced Ottawa Sand Specimens When Strength Is Taken as Peak Stress Experienced at Limiting Strains of 5, 15, 25 Percent Initial Void Ratio 0.0% Fiber content 0.4% Fiber content 5% Strain 15% Strain 25% Strain 5% Strain 15% Strain 25% Strain

15 Cneng-Wei Chen 15 a) Loose state (e 0 = 0.74) b) Medium-dense state (e 0 = 0.60) FIGURE 1 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CU tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). *: start point of suspicious measurement.

16 Cneng-Wei Chen 16 a) Loose state (e 0 = 0.74) b) Medium-dense state (e 0 = 0.60) FIGURE 2 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CD tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60).

17 Cneng-Wei Chen 17 a) Loose state (e 0 = 0.74) b) Medium-dense state (e 0 = 0.60) FIGURE 3 Change in pore pressure ( u) versus triaxial shear strain ( q ) curves from CU tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60). *: start point of suspicious measurement.

18 Cneng-Wei Chen 18 a) Loose state (e 0 = 0.74) b) Medium-dense state (e 0 = 0.60) FIGURE 4 Deviatoric stress ( q) versus triaxial shear strain ( q ) curves from CD tests for Ottawa sand specimens consolidated to 20-psi effective stress and compacted at: a) loose state (e 0 = 0.74), and b) medium-dense state (e 0 = 0.60).

19 Cneng-Wei Chen 19 a) 0.0 percent fiber content b) 0.4 percent fiber content FIGURE 5 Cambridge stress paths and failure envelopes for limiting strains of 5, 15, and 25 percent strain from CU tests on Ottawa sand specimens compacted at loose state (e 0 = 0.74): a) 0.0 percent fiber content, and b) 0.4 percent fiber content.

20 Cneng-Wei Chen 20 a) 0.0 percent fiber content b) 0.4 percent fiber content FIGURE 6 Cambridge stress paths and failure envelopes for limiting strains of 5, 15, and 25 percent strain from CD tests on Ottawa sand specimens compacted at loose state (e 0 = 0.74): a) 0.0 percent fiber content, and b) 0.4 percent fiber content.