Effect of confining pressure on shear resistance of ultra-high-performance fiber reinforced concrete

This study aims to investigate the effect of confining pressure on the shear resistance of UHPFRCs reinforced with different types of fiber: 1.5 vol.-% of the short smooth (SS, l/d = 13/0.2) fiber and the long smooth (LS, l/d = 30/0.3) were investigated.

Journal of Science and Technology in Civil Engineering NUCE 2020 14 (2): 108–115 EFFECT OF CONFINING PRESSURE ON SHEAR RESISTANCE OF ULTRA-HIGH-PERFORMANCE FIBER REINFORCED CONCRETE Ngo Tri Thuonga,∗ a Department of Civil Engineering, Thuyloi University, 175 Tay Son street, Dong Da district, Hanoi, Vietnam Article history: Received 08/03/2020, Revised 27/03/2020, Accepted 31/03/2020 Abstract Effect of confining pressure on the shear resistance of ultra-high-performance fiber-reinforced concrete (UHPFRCs), containing 1.5% volume content (1.5 vol.-%) of short smooth steel fiber (SS, l = 13, d = 0.2 mm) and long smooth steel fiber (LS, l = 30, d = 0.3 mm), was investigated using a new shear test method Three levels of confining pressure were generated and maintained to the longitudinal axis of the specimen prior shear loading was applied The test results exhibited that the shear strength of UHPFRCs was obviously sensitive to the confining pressure: the higher confining pressure produced higher shear strength UHPFRC reinforced with 1.5 vol.-% long smooth steel fiber exhibited higher shear resistance than those reinforced with short smooth steel fiber, regardless of confining pressure levels The confined shear strength could be expressed as an empirical function of unconfined shear strength, confining pressure, and tensile strength of UHPFRCs Keywords: UHPFRCs, shear resistance; confining pressure effect; smooth fiber https://doi.org/10.31814/stce.nuce2020-14(2)-10 c 2020 National University of Civil Engineering Introduction Ultra-high-performance fiber reinforced concrete (UHPFRCs) has been exhibited very high compressive strength, tensile strength, shear strength, strain capacity, and energy absorption capacity [1– 8] It is, therefore, expected to apply widely into the civil infrastructures to enhance their shear resistance subjected to extreme loads, such as impact and blast loads [3–6, 8, 9] However, the application of UHPFRCs to civil infrastructures is still very limited owing to its complex characters, such as fiber reinforcement parameter dependence as well as confining pressure dependence Several methods have been applied to investigate the confining pressure shear dependence of normal concrete (NC) as well as fiber reinforced concrete (FRC) including push-off specimens [10–13], punch-through specimens (PTS) [14–17], and Iosipescu specimens [18, 19]) However, these methods cannot indicate the unique strain-hardening response (accompanied by the formation of multiple microcracks) of UHPFRCs under tension, owing to using the pre-crack on the specimen to govern the shear crack path Ngo et al [2] have proposed a new shear test method to investigate the shear resistance of UHPFRCs capable of measuring the shear-related hardening response of UHPFRCs, accompanied with multiple microcracks This method, later, has developed by Ngo et al [4] to investigate the confining shear dependence of UHPFRCs However, they have just investigated with 1.5 vol.-% of medium smooth steel fiber (MS, l/d = 19/0.2) ∗ Corresponding author E-mail address: trithuong@tlu.edu.vn (Thuong, N T.) 108 UHPFRCs However, they have just investigated with 1.5 vol.-% of medium smooth steel fiber (MS, l/d=19/0.2) This study aims to investigate the effect of confining pressure on the shear resistance of UHPFRCs reinforced with different types of fiber: 1.5 vol.-% of the Thuong, N T / Journal of Science and Technology in Civil Engineering short smooth (SS, l/d=13/0.2) fiber and the long smooth (LS, l/d=30/0.3) were Thisinvestigated study aims to investigate the effect of confining pressure on the shear resistance of UHPFRCs reinforced with different types of fiber: 1.5 vol.-% of the short smooth (SS, l/d = 13/0.2) fiber and the long smooth (LS, l/d = 30/0.3) were investigated Experimental program Experimental Fig 1program shows an experimental program designed for investigating the effect of pressure on the shear resistance of for UHPFRCs: six series of specimens werepressure Fig.confining shows an experimental program designed investigating the effect of confining cast and tested In the notation of the series, the two first letters designate the on the shear resistance of UHPFRCs: six series of specimens were cast and tested In thefiber notation of types for letters short smooth fiber “LS” for(“SS” long smooth while theand next twofor long the series, the(“SS” two first designate theand fiber types for shortfiber) smooth fiber “LS” smooth characters fiber) whilerepresent the next two confining for 2.0 MPa the characters confining represent pressure the level (“02” pressure for 2.0 level MPa (“02” confining confining pressure) pressure) Fiber types Confining pressure Short smooth fiber Shear resistance of UHPFRCs MPa 02 MPa Long smooth fiber 04 MPa (2) (1) Notation SS-00 SS-02 SS-04 LS-00 LS-02 LS-04 Effect of fiber types Effect of confining pressure on shear resistance Figure Experimentalprogram program Fig 1.1.Experimental 2.1 Material and specimen preparation 2.1 MaterialThe andcomposition specimen preparation and compressive strength of ultra-high-performance concrete (UHPC) matrix are provided in Table 1, while the properties of smooth steel fibers are matrix The composition and compressive strength of ultra-high-performance concrete (UHPC) are provided in Table 1, while the properties of smooth steel fibers are listed in Table The detail of mixing and curing procedure could be found in2[2, 20] A Hobart 20-L capacity type mixer with a controllable rotation speed was used to mix the UHPC mixture Silica fume and silica sand were first dry-mix for before silica powder and cement (Type I) was added and mix about more Water and superplasticizer were then gradually added as the dry compositions show well-distribution After the mortar showed suitable workability and viscosity, the fiber distributed by hand and mixed about for uniform fiber distribution Table The composition of UHPC matrix by weight ratio Cement (Type I) Silica fume Silica sand Silica powder Super-plasticizer Water Compressive strength 0.25 1.10 0.30 0.067 0.2 180 MPa The mixture was poured into molds with no vibration and stored in room temperature for 48 hours before demolding and curing in water at 90 ± 2◦C for days All specimens were tested at the age of 28 days 109 Thuong, N T / Journal of Science and Technology in Civil Engineering Table Properties of smooth steel fibers Fiber types, 1.5 vol.-% Diameter, d f (mm) Length, l f (mm) Density, ρ (g/cc) Tensile strength, σu (MPa) Elastic modulus, E (GPa) Short smooth steel fiber - SS 0.2 13 7.90 2580 200 Long smooth steel fiber - LS 0.3 30 7.90 2580 200 2.2 Test setup and procedure Fig shows the shear test setup with a confining pressure frame A high strength aluminum frame was designed to apply and maintain a compressive load along the longitudinal axis of the specimen The shear specimen was placed into the confining pressure frame and the rotating screw at the end of the frame wasJournal tightened to generate theincompressive in2019 the longitudinal axis of the specimen of Science and Technology Civil Engineeringload NUCE ISSN 1859-2996 The pre-stressed level was measured by an indicator system and a load cell installing coaxial with the longitudinal axis the the specimen Three 2, and MPa) pre-stressed cell of inside UTM, while the levels vertical(0, displacement of the of middle region of were the used in this study Details specimen of the test methods and testing procedures can be found elsewhere [21] was measured by two linear variable displacement transducers (LDVTs) Rotation screw Load cell Specimen Confining frame LDVTs Supporting blocks Load cell indicator Fig Shear test setup with confining frame Figure Shear test setup with confining frame Results The shear testFig setup was the installed in a universal curves testingofmachine shear load was shows shear stress-versus-strain UHPFRCs.(UTM) The shearThe stress applied to the (t) specimen by upwards movement of the lower element of the UTM at a was calculated using Eq (1), while shear strain (g) was calculated using Eq (2) constant speed of mm/min The applied load was measured by a load cell inside the UTM, while the vertical P t =region of the specimen was measured by two linear variable displacement displacement of the middle 2bd (1) transducers (LDVTs) g= Results d a (2) Where b is the specimen width (mm), P is the applied load (kN), d is the depth of Fig shows the shear stress-versus-strain curves of UHPFRCs The shear stress (τ) was calculated the specimen (mm), a is shear span (mm) and d is the vertical displacement in the using Eq (1), middle while shear strain (γ) was calculated using Eq (2): part of the specimen.t is the peak value of the shear stress-versus-strain max Pthe area under shear stress-versus-strain curve; gmax is the shear strain at tmax; and Tsp is τ= curve up to tmax The tmax, gmax, and Tsp were2bd averaged and summarized in Table 110 As can be seen in Figs 3a and 3b, all specimens featured shear-related hardening responses at shear strengths >18 MPa, although their shear resistances differed according to the confining pressure (sl) level Higher sl levels produced higher tmax and gmax in the UHPFRCs Specifically, the UHPFRCs reinforced with 1.5 vol.-% of (1) Thuong, N T / Journal of Science and Technology in Civil Engineering δ (2) a where b is the specimen width (mm), P is the applied load (kN), d is the depth of the specimen (mm), a is shear span (mm) and δ is the vertical displacement in the middle part of the specimen τmax is the peak value of the shear stress-versus-strain curve; γmax is the shear strain at τmax and Tsp is the area under shear stress-versus-strain curve up to τmax The τmax , γmax , and T sp were averaged and summarized in Table γ= Table Test results Confining pressure, σl (MPa) Shear strength, τmax (MPa) Shear strain at peak stress, γmax (%) Shear peak toughness, T sp (MPa) SP1 SP2 SP3 SP4 SP5 SP6 Average Standard deviation 0 0 0 18.30 18.88 17.88 18.13 17.78 17.88 18.10 0.4 0.054 0.046 0.055 0.054 0.049 0.055 0.052 0.004 0.75 0.67 0.66 0.81 0.70 0.80 0.73 0.07 02-SS SP1 SP2 SP3 SP4 SP5 Average Standard deviation 2 2 2 23.87 25.93 24.34 24.85 25.52 24.90 0.8 0.053 0.057 0.053 0.052 0.058 0.055 0.003 1.07 1.17 1.04 1.03 1.18 1.10 0.07 04-SS SP1 SP2 SP3 SP4 SP5 Average Standard deviation 4 4 4 31.94 30.45 32.80 31.09 29.80 31.20 1.2 0.054 0.064 0.061 0.060 0.067 0.061 0.005 1.44 1.61 1.60 1.53 1.59 1.55 0.07 00-LS SP1 SP2 SP3 SP4 SP5 SP6 Average Standard deviation 0 0 0 22.19 24.25 23.22 24.25 23.58 22.23 23.30 0.9 0.067 0.065 0.061 0.068 0.062 0.070 0.066 0.004 1.06 1.09 0.98 1.19 1.01 1.17 1.08 0.08 02-LS SP1 SP2 SP3 SP4 SP5 SP6 Average Standard deviation 2 2 2 31.84 33.76 31.42 33.06 32.50 31.96 32.42 0.9 0.072 0.071 0.064 0.094 0.066 0.061 0.071 0.012 1.54 1.23 1.36 1.05 0.91 1.29 1.23 0.22 04-LS SP1 SP2 SP3 SP4 SP5 SP6 Average Standard deviation 4 4 4 36.20 37.00 35.72 38.75 37.27 37.35 37.00 1.1 0.088 0.091 0.105 0.059 0.085 0.080 0.085 0.015 2.35 2.31 1.20 1.42 1.27 1.99 1.76 0.52 Test series Spec 00-SS 111 Journal of Science and Technology in Civil Engineering NUCE 2019 ISSN 1859-2996 Journal of Science and Technology in Engineering NUCE 2019 ISSN 1859-2996 Thuong, N T.shear / Journal of Civil Science and Technology in2019 Civil Engineering Journal ofwith Science and Technology in Civil Engineering NUCE ISSN 1859-2996 accompanied two major cracks The typical failure of UHPFRC specimen is shown in Fig 3(c): all specimens failed with multiple cracks on the front and back sides of the40specimen, accompanied with two major shear 40 flexural-shear accompanied with two major shear cracks accompanied with two major shear cracks cracks LS-0 MPa SS-0 MPa 40 40 30 MPa SS-0SS-0 MPa SS-4 MPa SS-2SS-2 MPaMPa 30 30 SS-4SS-4 MPaMPa 20 LS-2 MPa LS-4 MPa LS-0LS-0 MPaMPa LS-2LS-2 MPaMPa LS-4LS-4 MPaMPa 30 30 20 20 20 20 20 10 10 10 10 30 Shear stress (MPa) Shear Shear stressstress (MPa)(MPa) SS-2 MPa Shear stress (MPa) Shear stress (MPa) Shear stress (MPa) 40 40 10 10 0 0.05 0.1 0.05to peak 0.1 0.1 g Shear 0.05 strain up stress, 0.15 Shear strain to peak stress, Shear strain up up to peak stress, g g 0 00 0.150.15 0 UHPFRC withwith 1.5 vol.% SS SSSS a) UHPFRC with 1.5 vol.% a) UHPFRC vol.% a) (a) UHPFRC with 1.51.5 vol.% SS 0.05 0.1 0.15 0.1 stress,0.15 0.050.05 0.1peak Shear strain up to g 0.15 Shear strain uppeak to peak stress, Shear strain up to stress, g g (b) UHPFRC with 1.5 vol.% UHPFRC with 1.5 vol.% b) UHPFRC with 1.5 vol.% LS LS b) b) UHPFRC with 1.5 vol.% LSLS LS-00 LS-00 LS-00 LS-00LS-00 LS-00 c) Failure of shear specimens (front back side) c) Failure of shear specimens (front andand back side) (c) of Failure of shear specimens (front and back c) Failure shear specimens (front andside) back side) Fig Shear stress-versus-strain curves of UHPFRCs at different confining pressure Fig Shear stress-versus-strain curves of UHPFRCs at different confining pressure Figure Shear stress-versus-strain curvesofofUHPFRCs UHPFRCs at different confining pressure pressure Fig Shear stress-versus-strain curves at different confining Discussions Discussions 3.4.3 Discussions Discussions Fig 4Fig expressed the effects of confining pressure on the shear resistance of UHPFRCs The shear expressed effects confining pressure shear resistance Fig expressed thethe effects of of confining pressure on on thethe shear resistance of of strength and shear strain capacity were strongly dependent on the confining pressure level The τmax The shear strength strain capacity were strongly dependent on of UHPFRCs The shear strength andand shear strain capacity strongly dependent Fig expressed the effects ofshear confining pressure the resistance ofUHPFRCs UHPFRC reinforced with 1.5 vol.-% SS fiber increased from were 18.1 toon 24.9 andshear 31.2 MPa ason the the confining pressure level The tmax of UHPFRC reinforced with 1.5 vol.-% SS fiber the confining pressure level The of UHPFRC reinforced with 1.5 vol.-% SS fiber confining pressure (σl ) strength increased from tto and 4strain MPa, while those ofwere UHPFRC reinforced with 1.5 max UHPFRCs The shear and shear capacity strongly dependent on vol.-% LS fiber are 23.3, 32.4 and 37.0 MPa The results were well-matched with previous experimenincreased from 18.1 andand 31.2 MPa as as thethe confining pressure (sl()sincreased increased from 18.1to to24.9 24.9 31.2 MPa confining pressure ) increased l the confining pressure level Theshear tmaxstrain of UHPFRC reinforced with 1.5 vol.-% SS fiber tal results reported by [4, 22] The capacity slightly increased as the confining pressure from to and MPa, while those of UHPFRC reinforced with 1.5 vol.-% LS fiber from to and MPa, while those of UHPFRC reinforced with 1.5 vol.-% LS fiber increased The γmax of UHPFRC containing 1.5 vol.-% SS fiber increased from 0.052 to 0.055 and increased from 18.1 to 24.9 and 31.2 MPa as2.0 the confining pressure (sprevious l) increased are andand37.0 The results with previous are23.3, 23.3,32.4 37.0MPa MPa Thefrom results were with 0.061 when the32.4 confining pressure increased to were andwell-matched 4.0well-matched MPa, while those values of LS fromexperimental 0fiber towere and results MPa, while those of The UHPFRC reinforced with 1.5 vol.-% LSasfiber 0.066, 0.071, and 0.085 Consequently, Tshear alsostrain increased as confining pressure increased spshear results reported by [4,22] capacity slightly increased as experimental reported by [4,22] The strain capacity slightly increased owing to the increase of τmax and γmax , as shown in Fig 4(c) are the 23.3, 32.4 pressure and 37.0 MPa.TheThe The results were well-matched with previous confining increased gmaxgmax of UHPFRC containing 1.5 vol.-% SS fiber the confining pressure increased of UHPFRC containing vol.-% fiber Among the investigated fiber reinforcement, the UHPFRC reinforced with1.5 higher fiberSS aspect increased 0.052 to to 0.055 and[4,22] 0.061 the confining pressure increased from 0 as increased from 0.052 0.055 and 0.061 when the confining pressure increased from experimental results reported by The shear strain slightly increased ratio (l/d) from produced higher shear resistance in when terms of shear strength,capacity shear strain capacity, and shear peak toughness, regardless the confining pressure level, as can be seen in Fig The shear resistance to to 2.02.0 andand 4.04.0 MPa, while those values LS fiber were 0.066, 0.071, 0.085 MPa, while those values LS fiber were 0.066, 0.071, and 0.085 the confining pressure increased The gmaxofofof UHPFRC containing 1.5and vol.-% SS fiber of UHPFRC reinforced with the long smooth steel fiber (LS, l/d = 30/0.3 = 100) are higher than Consequently, TspTalso increased as confining pressure increased owing to the increase Consequently, also increased as confining pressure increased owing to the increase increased from 0.052spto 0.055 and 0.061 when the confining pressure increased from of of tmax andand gmaxgmax , as, as shown in in Fig 4c.4c tmax shown Fig 112 to 2.0 and 4.0 MPa, while those values of LS fiber were 0.066, 0.071, and 0.085 Among fiber reinforcement, thethe UHPFRC reinforced with Among theinvestigated investigated fiber reinforcement, UHPFRC reinforced with Consequently, Tsp the also increased as confining pressure increased owing to the increase higher (l/d) produced higher shear resistance in in terms of of shear higherfiber fiberaspect aspectratio ratio (l/d) produced higher shear resistance terms shear of tmax and gmax, as shown in Fig 4c S S with the long smooth steel fiber (LS, l/d=30/0.3 = 100) are higher than those of short with the long smooth steel fiber (LS, l/d=30/0.3 = 100) are higher20than those of short smooth steel fiber (SS, l/d=13/0.2= 65), while those of medium smooth steel fiber smooth steel fiber (SS, l/d=13/0.2= 65), while those of medium smooth steel fiber (MS, l/d=19/0.2 = 95) were in the middle according to Ngo et al.[23].A similar trend (MS, l/d=19/0.2 = 95) were in the middle according to Ngo et al.[23].A similar trend 15 waswas experimentally by Tran et al [5] for tensile resistance and agree with -1 the experimentally by Tran et al [5] for tensile resistance and agree with the2 Confining pressure (MPa) theoretical equation proposed by Wille et al [24]: the resistance of UHPFRC is theoretical equation proposed by Wille et al [24]: the resistance of UHPFRC is Thuong, N T / Journal of Science and Technology in Civil Engineering proportional to the aspect ratio (l/d) of of fiber reinforcement proportional to the aspect ratio (l/d) fiber reinforcement a) Shear strength 0.10.1 SS SS 30 30 0.09 0.09 0.08 0.08 25 25 20 20 15 15 -1 -1 0 1 2 3 Confining pressure (MPa) Confining pressure (MPa) (a)a)Shear strength a) Shear strength Shear strength 0.05 -1 Confining pressure (MPa) b) Shear strain capacity SSSS LSLS Journal of Science and Technology in Civil Engineering SS LS NUCE 2019 Shear strain capacity Shear strain capacity Shear strength (MPa) Shear strength (MPa) 35 35 LS LS Shear peak toughness (MPa) 40 40 0.06 ISSN 1.5 experimental results [4] The shear failure in this study was governed 0.07 tensile failure along the shear plane, which was demonstrated by both the 0.07 experimental analysis results [21] Therefore, the confined shear strength 0.06 0.06 proposed as a function of tensile strength (st) and confining pressure (sl) 0.5 0.05 0.05 and -1in Fig and -1 0their 5 (4) -1 relationship 22 33 4is plotted 55 Confining pressure (MPa) Confining pressure (MPa) Confining pressure (MPa) tShear =strain t max + 1.863 s ls t (b)b)Shear strain capacity b) Shear capacity conf strain capacity (c)c)Shear peaktoughness toughness Shear peak Fig Effect of confining pressure on the shear resistance of UHPFRCs 2 Shear peak toughness (MPa) Shear peak toughness (MPa) Figure Effect confining pressure shear resistance of confining UHPFRCs LS t conf =ont the + 1relation 951 sbetween SS SS of LS maxThe ls t shear strength of UHPFRCs and co pressure level of can be expressed by an empirical formulation based In which tmax is the=unconfined sl issteel confining pre those of short smooth steel fiber (SS, l/d ,= 13/0.2 65), while shear those strength, of mediumMPa; smooth st (= 10.90 in Eq (3)and 11.10toMPa (4)) are the post-cracking tens fiber (MS, l/d = 19/0.2 = 95) were in the middle according NgoinetEq al [23] A similar trend was experimentally by Tran etofal.UHPFRC [5] for tensile resistance with equation reinforced withand 1.5agree vol.-% thethe SStheoretical and LS fiber, respectively, a proposed by Wille et1 al [24]: the resistance of UHPFRC is proportional to the aspect ratio (l/d) of Tran et al [5] fiber reinforcement 40 The relation between confining shear strength 0.5 0.5 -1 t conf = t max + 863 s l s t of UHPFRCs and confining -1 pressure level can be5 Confining pressure (MPa) Confining pressure (MPa) 35 R = 934 expressed by an empirical formulation based on c) Shear peak toughness the experimental results c)[4] The failure in Shear peakshear toughness Fig Effect of confining pressure on the shear resistance of UHPFRCs this study governed by pressure diagonal tensile failure 30 Fig.was Effect of confining on the shear resistance of UHPFRCs Theshear relation between confining shear strength ofby UHPFRCs and confining alongThe the plane, which was demonstrated relation between confining shear strength of UHPFRCs and confining pressure level of and can experimental be expressed byanalysis an empirical formulation based the both theoretical results 25 onon the pressure level of can be expressed by an empirical formulation based [21] Therefore, the confined shear strength (τcon f ) 7 was proposed as a function of tensile strength (σt ) 20 and confining pressure (σl ) by Eqs (3) and (4) and t conf = t max + 951 s l s t their relationship is plotted in Fig 15 R = 978 √ τcon f = τmax + 1.863 σl σt (3) 10 √ τcon f = τmax + 1.951 σl σt (4) 0.5 Confined shear strength (MPa) 1.5 1.5 (s s ) t l (MPa) where τmax is the unconfined shear strength, MPa; σl is confining pressure, MPa; σt (= in Figure 5.equation Proposedfor prediction equation for Fig.10.90 Proposed prediction confined shear strengths of UHPF confined shear strengths of UHPFRCs Eq (3) and 11.10 MPa in Eq (4)) are the postcracking tensile strength of UHPFRC reinforced with 1.5 vol.-% the SS and LS4.Conclusions fiber, respectively, according to Tran et al [5] The effects of confining pressure on the shear resistance of UH investigated using a new shear test method The following observ Conclusions conclusions can be drawn from this study: The effects of confining pressure on the shear resistance of UHPFRC were investigated using a new shear test method The following observations and conclusions can be drawn this study: • The shear strength of UHPFRC was from strongly dependent on th pressure level: 113 the confined shear strength increased as the applie pressure increased • UHPFRC reinforced with 1.5 vol.-% long smooth steel fiber exhib shear resistance than those reinforced with short smooth steel fiber Thuong, N T / Journal of Science and Technology in Civil Engineering - The shear strength of UHPFRC was strongly dependent on the confining pressure level: the confined shear strength increased as the applied confining pressure increased - UHPFRC reinforced with 1.5 vol.-% long smooth steel fiber exhibited higher shear resistance than those reinforced with short smooth steel fiber, regardless of confining pressure levels - The confining shear strength could be predicted base on the unconfined shear strength, confining strength, and tensile strength by an empirical in this study Acknowledgements This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2019.03 References [1] Wille, K., Naaman, A E., Parra-Montesinos, G J (2011) Ultra-High Performance 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Effect of confining pressure on the shear resistance of UHPFRCs this study governed by pressure diagonal tensile failure 30 Fig.was Effect of confining on the shear resistance of UHPFRCs Theshear... characters confining represent pressure the level (“02” pressure for 2.0 level MPa (“02” confining confining pressure) pressure) Fiber types Confining pressure Short smooth fiber Shear resistance of