Mechanical Properties of High-Strength Pervious Concrete with Steel Fiber or Glass Fiber

Abstract

Pervious concrete (also called porous concrete) is one of the most promising sustainable and green building materials today. This study examined high-strength pervious concrete and ordinary-strength pervious concrete reinforced with steel fiber or glass fiber. A total of fifteen mixtures of normal- and high-strength pervious concretes with steel fiber or glass fiber were used. The goal of high-strength pervious concrete is that the 28-day compressive strength be above 42 MPa and the porosity be as close to 15% as possible to achieve technical specifications. Both normal- and high-strength pervious concretes reinforced with steel fiber (1%, 2%) or glass fiber (0.25%, 0.5%) were investigated in water permeability, porosity, compressive strength, flexural strength, elastic modulus, and toughness tests. The test results show that in both high-strength pervious concrete and ordinary pervious concrete with steel fibers added, the porosity and permeability coefficient are increased compared with the control group. The coefficient of permeability for high-strength, fiber-reinforced pervious concretes with two aggregate sizes meets the requirements of the ACI specification for structural concrete. In addition, the high-strength pervious concrete specimen H1-S2 (2% steel fiber) has the highest compressive strength of 52.8 MPa at the age of 28 days. The flexural strength of pervious concrete also increases with age. However, the flexural strength of fiber-reinforced pervious concrete did not follow this trend due to the large variation in the quality control of different fiber mixtures. However, both steel fiber and glass fiber have a certain degree of improvement in the flexural toughness, and the effect is better with steel fiber. After the flexural strength reaches the peak value, there is still about 30% of the bearing capacity, and it gradually decreases until it is completely destroyed.

1. Introduction

1.1. Background

Porous concrete, also known as permeable concrete or pervious concrete, or no-fines concrete and/or porous pavement, is a typical high-porosity concrete used in concrete paving applications [1,2]. It allows precipitation and other sources of water to pass through it. This can reduce rainwater runoff and transfer it to the recharge groundwater table. The porosity is usually designed to achieve a porosity of 18% to 35% and a compressive strength of 2.5 to 25 MPa. The drainage rate is usually in the range of 2 to 18 gallons/minute/ft2 [2,3]. Generally, permeable concrete mixes contain little or no fine aggregate, and there is only enough grout to cover the aggregate particles to maintain the interconnectivity of the voids [4]. In order to solve the rainwater runoff problem, prevent ecological damage, and reduce the heat-island effect, it is not a trivial matter to find a suitable permeable concrete mix design for Taiwan [5]. Traditionally used in parking lots, light traffic areas, sidewalks and greenhouses, pervious concrete plays a vital role in sustainable development [4,5].

1.2. Literature Review

The permeable concrete parking lot was also selected as the overall solution to the hot pavement problem in the Cool Communities program. The road surface has brought about the phenomenon of the heat-island effect in bigger cities. Generally speaking, the temperature measured in an asphalt parking lot is higher than that in a pervious concrete parking lot. Pervious concrete also reduces snow and ice build-up. In addition, pervious concrete is environmentally friendly and non-polluting [3].

Automobile exhaust and crankcase leakage cause hydrocarbons, heavy metals and suspended solids to be distributed on the road [6]. Automobile pollutants will accumulate on the road until the rainfall carries them away, eventually entering waterways or groundwater [7]. These contaminants may damage sensitive waterbody resource ecosystems, and pumping this water into the water supply through surface water or wells can be detrimental to human or livestock health. The water quality study on pervious concrete pavements reports the removal of pollutants from stormwater. According to the above studies, the permeable concrete pavement system can filter water, purify water and capture biodegradable oils [8]. The use of oil bacteria does not require the addition of oil-degrading bacteria; local bacteria can degrade oil by themselves. In cases where some oils are effectively degraded, nutrients are required to promote the lipid-degradable activity of bacteria. As nutrient levels drop, CO₂ levels also drop, which indicates bacterial activity [8]. With the increase of microbial diversity in the pavement structure, the utilization rate of oil also increases. This phenomenon remains unclear, and more experiments and studies are needed to determine why the best oil degradation activities show high diversity, even when only oil degradation by bacteria is observed [8,9]. The continuous voids formed inside and on the surface of pervious concrete and its large specific surface area provide habitat space for bacteria, phytoplankton and organisms, which are effective in water purification [8].

According to ACI 522R-10 [9], the application of pervious concrete can be also used in the scope of harbour engineering, including coastal structures, seawalls and artificial reefs. The application scope and applicability of pervious concrete are roughly divided into the following 13 items:

(1) Permeable pavement and walkway in parking lot;

(2) Rigid permeable pavement outside hypermarket;

(3) Greenhouse floor plate to prevent water accumulation;

(4) Structural walls with light weight or thermal insulation properties;

(5) Pavements, walls and slabs with good sound absorption properties;

(6) Base courses of urban roads, country roads, highways and airports;

(7) Surfaces of car parks and zoo areas;

(8) Bridge bases (embankments);

(9) Swimming pool floor slabs;

(10) Seaside structures and seawalls;

(11) Sludge beds for sewage treatment plants;

(12) Solar energy storage systems; and

(13) Artificial fishing reefs, etc.

Usually, the above-mentioned pervious concrete is not reinforced with steel reinforcement. If it is applied to reinforced concrete, the steel reinforcement needs to be anti-corrosion or have a galvanized coating [10,11].

Pervious concrete has the advantages of water retention, cooling, improving drainage and purifying water quality. However, with the increase of traffic volume and vehicle age, the drainage function of the pervious pavement will gradually decrease after the pores are blocked. This is one of the main problems and requires regular maintenance.

Steel fiber is a metal reinforcement material. Steel fibers for reinforced concrete are defined as short, discrete-length steel fibers with an aspect ratio (length-to-diameter ratio) of approximately 20 mm to 100 mm and have different cross-sections, and are small enough to be randomly dispersed in unhardened concrete. The concrete mixture uses the usual mixing procedure. Adding a certain amount of steel fiber to concrete can make the physical properties of concrete change qualitatively and greatly improve the properties of crack resistance, impact resistance, fatigue resistance, bending resistance, toughness and durability. Basically, steel fibers can be divided into five categories according to the manufacturing process and their shape and cross-section: cold drawing, cut sheet, melt extraction, grinding and cutting, and modified cold drawing [10]. With the addition of steel fibers to the concrete, it was found that the flexural strength was greatly improved. The flexural strength increased to 6.46 N/mm² with 1% steel fibers in the concrete, but was 5.36 N/mm² without steel fibers, i.e., a 21% increase in flexural strength [11]. The study investigated the use of hook-end steel fibers to increase the flexural strength of permeable concrete without affecting its permeability and porosity. It was found that 1.5% of steel fibers based on the volume of the concrete was sufficient to achieve the required target strength and permeability rate [12].

Fiberglass is also called glass fiber. It is a material made of extremely fine glass fibers. Fiberglass is a lightweight and very strong material. Although the strength performance is lower than that of steel fiber and the rigidity is lower, the material is generally less brittle, and the raw material is much cheaper. It has been determined that the compressive strength of the glass-fiber-reinforced concrete mixture with different amounts will increase by a certain percentage. The observed increase in compressive strength is 20% to 25%. The flexural strength and splitting tensile strength of different glass-fiber-reinforced concrete specimens at 28 days of age were also compared, and the percentages were found to increase from 15% to 20% [13]. The addition of glass and steel fibers slightly increases the surface hardness. In addition, the addition of glass fibers improves the ductility of self-compacting concrete, and the strength of steel fibers is higher than that of glass fibers [14]. In the toughness study of steel and polypropylene fiber concrete bending beams, it was found that steel fiber concrete (SFRC) and polypropylene fiber concrete (PFRC) behave differently in bending. Due to the characteristics of the fiber-reinforced concrete, the behaviour of PFRC is obviously a double-peak response, while the behaviour of SFRC is a single-peak [15]. It is mainly used for bridging cracks in concrete internal structures and plastically deforming concrete members while reducing stress concentration at the crack ends. Different studies have been conducted on the use of fibers such as polypropylene (PP), steel, glass, Polyvinyl alcohol (PVA), carbon, Nylon, Kevlar fibers, etc., in order to increase the mechanical properties of pervious concrete, as shown in

Table 1. Summary of research on fiber-reinforced pervious concrete.

Literature	Fiber Content (% in Volume)	w/c	Mechanical Properties			Permeability cm/s
			fc *	ft *	ff *
Pils et al. [16]	PP @ 1, 2, 4 (kg/m3)	0.25, 0.3, 0.35	↓	↑	↓	0.12–0.078
Kharbikar et al. [17]	PP @ 0.15–0.25%	0.27 to 0.33	↓	–	–	↑ (up to 0.2%)
Thakre et al. [18]	Nylon fiber 0.1–0.25%	0.36	↓	–	–	↑ (up to 0.2%)
Hesami et al. [19]	0.3% PP fiber	0.27 to 0.40	↑	↑	↑	↑ then ↓
	0.2% glass fiber
	0.5% steel fiber
Patidar et al. [20]	PP @ 2.54 g/mould size	0.30 to 0.40	↑	–	–	↑
Rangelov et al. [21]	Carbon Fiber @ 0.5–1.5%	0.28	↑	↑	–	↑ infiltration
Bukola et al. [22]	Kevlar fiber 0.2–0.4%	0.33	↓	↓	↑	↑
	PVA fiber 0.2–0.4%
	UHMWPE fiber 0.2–0.4%
Tang et al. [23]	PP @ 0.013–0.13 (kg/m3)	0.28 to 0.31	–	–	–	2.18–2.45

* Change of mechanical properties (fc: compressive strength, ft: tensile splitting strength, ff: flexural strength) compared to the group without fiber.

[16,17,18,19,20,21,22,23].

The research results of Hussain et al. [24] showed that the compressive strength and modulus of rupture of the steel hook, steel corrugated and polyolefin specimens were increased by 24.8%, 20% and 11%, respectively, and the ultimate bearing capacity of the slabs was 39%, 13% and 19%, respectively, compared with control specimens. The main purpose of this study was to find a high-strength pervious concrete mix proportion of glass fiber and steel fiber suitable for permeable concrete pavement, as well as perform laboratory research on the compressive strength, flexural strength, elastic modulus and toughness properties of pervious concrete. Few studies have evaluated the effects of steel fibers and glass fibers on the mechanical properties of high-strength pervious concrete.

2. Experiments

This research report first describes the preparation of high-strength pervious fiber concrete materials and mixtures, and then concrete sample preparation, factor combinations, porosity and water permeability tests, compressive strength, elastic modulus, flexural strength and toughness strength tests.

2.1. Pervious Concrete Materials and Mix Design

The materials used in this study were Type I Portland Cement conforming to ASTM C 150 [25], produced by Taiwan Cement Company, three kinds of coarse aggregates (dimensions 3.0 mm, 3.6 mm and 4.8~9.5 mm), SF (silica fume), superplasticizer (HRWR), water, steel fibers or glass fibers and no fine aggregate. The chemical composition and specific surface area of cement and silica fume is given in

Table 2. Chemical compositions of cement and silica fume (%).

Compositions	Cement	Silica Fume
SiO2	20.05	94.26
CaO	62.12	0.07
Al2O3	4.01	0.30
Fe2O3	2.87	0.05
MgO	2.70	0.18
SO3	2.60	–
Na2O	0.20	0.12
K2O	0.60	0.42
Free Lime	1.10	–
L.O.I.	2.00	3.00
Specific surface area (m2/g)	0.38	22.04

. Pervious concrete is a highly porous concrete material that allows water or liquids to pass through.

The pervious concrete mixtures with high-range water reducer (HRWR) admixture have a wet, metallic look or sheen. As the slurry flows into the spaces between the aggregates, a small amount of the mixture forms a ball with a non-sagging consistency that doesn’t crumble or lose its void structure [26]. The steel fibers (DRAMIX^® 3D 40/30BG) were 30 mm straight fibers with a diameter of 1.9 mm, made from cold drawing wire, and were used for experiments in

Table 3. Specification of the AR glass fiber and steel fiber.

Specification	Glass Fiber	Steel Fiber
Appearance	white slender	Hooked-end fiber
Length (mm)	36	30
Diameter (mm)	1.9	0.75
Aspect ratio	67	40
Specific gravity	2.68	7.8
Melting point (°C)	860	1500
Tensile strength (MPa)	1700	1225
Elastic modulus (GPa)	72	200

. Glass fiber Alkali Resistant (AR) Glass zirconium fiber, which is sold by local paint shops, contains zirconium dioxide ZrO₂ composition, suitable for cement alkaline environment, also in Table 3.

Table 4. Mix design for normal and high-strength pervious fiber concretes (kg/m³).

Mix		Cement	Aggregate	Water	SF	Steel Fiber	Glass Fiber	HRWR
1	N0	340	1530	100	0	0 (0)	0	2.0
2	NS1		1452			78 (S1)
3	NS2		1374			156 (S2)
4	NG1	340	1523	100	0	0	6.8 (G1)	2.0
5	NG2		1516				13.6 (G2)
6	H10	475	1484	68	119	0 (0)	0	13.7
7	H1S1		1406			78 (S1)
8	H1S2		1328			156 (S2)
9	H1G1	475	1477	68	119	0	6.8 (G1)	13.7
10	H1G2		1470				13.6 (G2)
11	H1.2	475	1484	68	119	0 (0)	0	12.5
12	H1.2S1		1406			78 (S1)
13	H1.2S2		1328			156 (S2)
14	H1.2G1	475	1477	68	119	0	6.8 (G1)	12.5
15	H1.2G2		1470				13.6 (G2)

shows fifteen pervious concrete mix designs used in this study. The slump of high-strength pervious concrete is close to zero with a water-binder ratio of 0.14. The slump of ordinary pervious concrete is also close to zero, with a water-binder ratio of 0.3. The #1 mix (N0) contained a pure concrete mix. The #2 mix (NS1) contained a 1% steel fiber, and the #3 mix (NS2) contained 2% steel fiber. The #4 mix (NG1) contained a 0.25% glass fiber and the #5 mix (NG2) contained a 0.5% glass fiber. The above five mix designs are normal-strength pervious concrete. The following five mix designs are high-strength pervious concrete with #1.0 (3.03 mm) stone, according to its maximum particle size. The #6 mix (H10) contained a concrete mix without fiber. The #7 mix (H1S1) contained a 1% steel fiber, and the #8 mix (H1S2) contained 2% steel fiber. The #9 mix (H1G1) contained a 0.25% glass fiber, and the #10 mix (H1G2) contained a 0.5% glass fiber. The final five mix designs are high-strength pervious concrete with #1.2 (3.64 mm) stone, according to its maximum particle size. The #11 mix (H1.2) contained a concrete mix without fiber. The #12 mix (H1.2S1) contained a 1% steel fiber, and the #13 mix (H1.2S2) contained 2% steel fiber. The #14 mix (H1.2G1) contained a 0.25% glass fiber, and the #15 mix (H1.2G2) contained a 0.25% glass fiber. The high-strength pervious concrete is designed to achieve a 28-day compressive strength of more than 42 MPa, and the porosity is as close to 10% as possible to meet the technical specifications.

Notation

In this experiment, a specific sample-number identifier was developed to identify the data. High-strength pervious concrete can be divided into #1 stone and #1.2 stone, according to its maximum particle size. H1 and H1.2 are used as identification codes, respectively. For normal strength pervious concrete, use N as the code. For added glass fiber (0%, 0.25% and 0.5%), use (O, G1 and G2), respectively; if steel fiber is added (0%, 1% and 2%), use (O, S1 and S2), respectively. For example, the high-strength #1 stone pervious concrete with a 28-day curing period is mixed with 0.5% glass fiber, and the sample number is H1-D28-G2.

2.2. Concrete Samples

Concrete specimens are available in two sizes. Cylinder specimens with a diameter of 100 mm and a height of 200 mm were prepared according to ASTM C39/39M-16 [27] for the study of compressive strength development and elastic modulus. Flexural strength was measured using beam specimens measuring 100 × 100 × 350 mm. The sample is filled in 2 layers and each layer is compacted with 25 compactions, maintaining the height of the plate. Curing should begin as soon as possible after placement and compaction [5]. The pervious concrete specimens were demolded after one day and cured in room temperature water for 27 days. The specimens were placed under laboratory conditions for 7, 28 and 90 days before the compressive strength, flexural strength, elastic modulus and toughness tests. The purpose of this study was to evaluate high-strength pervious concretes and use glass fiber and steel fiber to determine if it could improve its compressive strength, flexural strength, elastic modulus, or toughness. Pervious concrete specimens are available in two sizes. Cylinder specimens with a diameter of 100 mm and a height of 200 mm were prepared according to ASTM C39/39M-16 [27] for the tests of compressive strength development and elastic modulus. Flexural strength was measured using beam specimens measuring 100 × 100 × 350 mm. In addition, the number of samples for the compressive strength, elastic modulus, porosity and water permeability test of pervious concrete was 6, and the number of samples for the flexural strength and toughness strength test was 3 in this study.

2.3. Porosity and Permeability Coefficient Test

For porosity, we used the drainage volume method of the Japan Concrete Association, such as Formula (1). First, we immersed the specimen in a constant temperature water bath for 24 h, weighed the saturated weight of its surface dryness, and then placed the specimen in an oven at a temperature of 110 °C. After drying it for 24 h and putting it into water, we weighed it in water, and finally the connected porosity ($P_1$) was calculated.

$$P_1=\frac{1-\left(W_1-W_2\right)}{V_1}\times 100\%$$

(1)

where, $P_1$: connected porosity (%), $W_1$: weight of the specimen in water, $W_2$: weight of the saturated-surface-dry specimen, $V_1$: volume of the specimen.

The water permeability coefficient $K$ (cm/s) was measured by the falling head test mentioned in ACI 522R-10 [9], which is derived from soil mechanics, in low permeability soil ($K$< 10⁻² cm/s), and refers to the test instrument measured in the literature of Alalea et al. [28]. As shown in Figure 1, the inner diameter of the upper end of the water pipe was 9.5 mm acrylic pipe, and we connected the PVC pipe of pervious concrete specimen. Then, the two pipes were connected with a rubber sleeve and the iron ring was used to pressurize to prevent leakage. After the test, the water permeability coefficient $K$ was calculated by Formula (2).

$$K=\frac{A_1}{A_2}\times \frac{L}{t}\times \ln \left(\frac{h_1}{h_2}\right)$$

(2)

where, $K$: permeability coefficient (cm/s), $A_1$: cross-sectional area of pipe (cm²), $A_2$: cross-sectional area of specimen (cm²), $h_1$: initial head height (cm), $h_2$: final head position (cm), $L$: height of specimen (cm), $t$: time for water to flow from $h_1$ to $h_2$ (s).

2.4. Compressive Strength and Elastic Modulus Test

The compressive strength test was carried out with ASTM C39M-05 [27] in this study. The age of compressive strength test was carried out at 7, 28, and 90 days, and the elastic modulus test was carried out in accordance with ASTM C469 [29] in the specimen with the age of 28 days. The elastic modulus test equipment was used with a TML static data acquisition device (TDS 530), 100-ton thin load cell and elastic modulus strain ring, and the concrete elastic modulus was calculated by the secant method in ASTM C469. After the measurement was completed, the data file was captured and combined with Formula (3). The corresponding data was brought in and the elastic modulus was calculated.

$$Ec=\frac{0.4f^{\prime }c-f\prime c}{\epsilon ·0.4f^{\prime }c-0.00005}$$

(3)

where $Ec$: elastic modulus (MPa), $f\prime c$: compressive strength of concrete (MPa), $\epsilon$: strain.

2.5. Flexural Strength Test

The flexural strength test of this study was performed with reference to ASTM C78/C78M-18 [30], and the flexural test age was 7, 28, and 90 days, respectively. This test method covered the determination of the flexural strength of concrete by the use of a 10 cm × 10 cm × 35 cm simple beam with third-point loading. After the test, the flexural strength of the beam was calculated by Formula (4).

$$R=\frac{PL}{b{d}^2}$$

(4)

where R: flexural strength (MPa), P: maximum load (N), b: average width of section (mm), L: beam span (mm).

2.6. Flexural Toughness

The two most common methods to determine flexural toughness for the reinforced fiber concrete are based upon ASTM Cl0l8 [31] and JSCE SF-4 [32]. In ASTM C1018, toughness is specified in terms of toughness indices (I₅, I₁₀ and I₂₀), which refers to the area under the load-deflection curve calculated out to three different specified deflections. The JSCE SF-4 test method is for flexural strength and flexural toughness of reinforced fiber concrete by third-point loading. In contrast, in the case of JSCE SF-4, the area under the load deflection curve up to a specified deflection (L/150) is measured and referred to as the toughness.

Flexural toughness is a term used to quantify the energy absorption capacity of concrete; it is the area of concrete under the flexural load-deflection curve (Figure 2) up until a deflection of 1/150 times the span, corresponding to 2 mm for 10 cm × 10 cm × 35 cm specimens [33]. After the test, the flexural toughness ($T_b$) of the beam was calculated by Formula (5).

$$\overline{\sigma b} =\frac{T_b}{\delta tb}\times \frac{L}{b{h}^2}$$

(5)

where $\overline{\sigma b}$: toughness factor (N⁄mm²), $T_b$: flexural toughness (N-m), $\delta tb$: deflection at L⁄150 (mm), $L$: beam span (mm), $b$: beam width (mm), $h$: beam height (mm).

3. Experimental Results and Discussion

3.1. Porosity and Permeability Coefficient Test

According to ACI 522R-10 [9], the standard permeability coefficient of pervious concrete is about 0.1cm/s or more, and the porosity is about 18~35%. From Figure 3 and

Table 5. Results for porosity and permeability coefficient test.

Specimen ID		O	G1	G2	S1	S2	ACI 522R
Permeability coefficient (cm/s)	H1	0.14	0.18	0.14	0.36	0.52	≥0.1
	H1.2	0.12	0.23	0.29	0.42	0.65
	N	1.41	1.19	1.49	1.56	1.84
Porosity (%)	H1	9.23	7.33	8.50	12.03	13.96	18–35
	H1.2	11.04	9.23	8.13	11.93	16.65
	N	18.58	18.91	19.85	18.93	21.78

, it can be seen that the water permeability coefficients of each mix proportion and aggregate meet the minimum standard value of water permeability coefficient proposed by ACI 522R-10. It is worth noting that the steel fiber was added to the pervious concrete, and it had a better water permeability coefficient than the original one. In addition, the permeability coefficient of the pervious concrete with glass fiber showed no trend. However, regardless of whether high-strength or ordinary-strength pervious concrete was reinforced with steel fibers, both the porosity and permeability coefficient increased compared with the control group, which is consistent with the experimental results of the literature [34]. In contrast, the porosity of pervious concrete with glass fibers showed no trend.

3.2. Compressive Strength Test

In engineering applications, fibers are often used to reduce surface cracks caused by concrete shrinkage, and even provide the tensile force required for cracking when concrete is under compression, delaying the cracking and damage of the concrete bottom [12]. Generally, the compressive strength of pervious concrete is low, but high-strength pervious concrete uses a low water–cement ratio and aggregate with a smaller maximum particle size, which is beneficial to its compressive strength and higher elastic modulus. Figure 4, Figure 5 and Figure 6 show the development of the compressive strength of ordinary-strength and high-strength pervious concretes. Comparing H1.2-D7-G1 with H1.2-D28-G2, not only was the strength increased due to the increase of curing age, but the strength due to glass fiber reinforcement also increased. The strength of the steel fiber ratio of H1, H1.2, and N specimens increases with the increase of the curing age. In the 28-day curing age, the strength of the S2 specimens is higher than that of the S1 ones, and the D28-S2 specimens’ increased strength is more obvious. Compared with 0.5% glass fiber, the strength of glass fiber high-strength pervious concrete with a curing age of 28 days is slightly higher than that of 0.25% glass fiber. It is speculated that the low slump concrete during mixing shortened the setting time due to the addition of steel fibers. In addition, the time difference before and after pouring caused uneven cementation of the slurry, and the glass fiber was soft and easy to deform and cemented into a ball with the cement slurry. It was not evenly dispersed after hardening, so that a weak surface was formed when it was pressed, and it also resulted in high strength variability. Different studies have been conducted on the use of fibers such as polypropylene (PP), steel, glass, PVA, carbon, Nylon, Kevlar fibers, etc., in order to increase the mechanical properties of concrete, as shown in Table 1 [16,17,18,19,20,21,22,23]. After adding steel fibers, the mechanical properties and permeability were mostly improved in our research, but there are also studies that show otherwise, and there are other considerations to take into account. Among them, it is not easy to prove that the pervious concrete with steel fibers may produce clusters, which will make the slurry unevenly distributed in the concrete, resulting in the deviation of strength and permeability. Therefore, the research on the impact of steel fibers on pervious concrete is uncertain.

3.3. Elastic Modulus Test

The elastic modulus and its coefficient of the pervious concrete are shown in Figure 7, Figure 8 and Figure 9. The average elastic modulus of the high-strength pervious concrete specimen is about 20,000 MPa, while the elastic modulus of the ordinary-strength pervious concrete specimen is about 10,000 MPa. In addition, there is little research [34,35] on the coefficient of the elastic modulus. Regardless of whether high-strength pervious concrete was reinforced with fiber or not, it was slightly lower than the suggested coefficient of elastic modulus of ordinary concrete in Taiwan, which is 4734. Moreover, it was close to the suggested correction coefficient of elastic modulus of 3795 proposed by Liao W.C. et al. [35]. Yilan stone was used as the local aggregate material in this study. The strength of the high strength pervious concrete was high but the porosity was greater than that of ordinary concrete. Therefore, it is more appropriate to use 3795 to estimate the elastic modulus value of high-strength fiber pervious concrete. In addition, for ordinary-strength pervious concrete, it is approximately equal to 0.71 times the recommended value (3795). The reason may be that the poor grading degree of the pervious concrete aggregate makes the aggregate soft, and its porosity is large and its compressive strength is low. When the glass or steel fibers are not uniformly dispersed or have balling, the test results of fiber pervious concrete will also be affected.

3.4. Flexural Strength Test

In general, higher dosage level of fibers could increase the compressive or flexural strength of concrete specimens. The flexural strength of the fiber-reinforced pervious concrete is shown in Figure 10, Figure 11 and Figure 12. The average flexural strength of the high-strength pervious concrete specimen is about 6 MPa, while the flexural strength of the ordinary-strength pervious concrete specimen is about 4 MPa. The results show that the fiber content increased, but the flexural strength of the pervious concrete specimen did not increase significantly. In some proportion of a small amount of fibers, the flexural strength is lower than the proportion without fibers, which may due to the water-to-binder ratio of high strength pervious concrete, which was reduced to 0.14. Although a large amount of superplasticizer was added, it was still difficult to mix. When the fibers are not uniformly dispersed or have balling conditions, the hardened concrete easily forms weak joints, which easily causes bending-strength decline. In addition, compared with steel fiber, the appearance of glass fiber was weaker and had no hooks at the end, and the aspect ratio is much smaller than that of steel fiber, so that the cement slurry cannot produce a sufficient interlocking effect with the glass fiber. Therefore, the tensile force cannot be provided immediately at the moment of cracking of high-strength pervious concrete, resulting in a sharp drop in the applied load, and the bridging effect of glass fiber can only be exerted when the crack at the bottom of the beam is large [11]. The results show that the flexural strength of ordinary-strength pervious concrete was improved after adding fiber at 7 and 28 curing days, but the fiber content and fiber type did not improve the flexural strength after 90 days of curing.

Figure 13, Figure 14 and Figure 15 show the relationship between flexural strength and square root of compressive strength of the fiber-reinforced pervious concrete specimens. Taiwan’s general formula for general concrete cracking modulus (flexural strength) uses 0.63√fc′ (MPa) as a commonly used formula for predicting cracking load. The test results are somewhat similar to past research results [3,4,5]. However, the average coefficient of cracking load in this study is higher than 0.63, which is the generalized formula for cracking of ordinary concrete. The results show that using 0.63√fc′ as a common formula for predicting cracking loads is not appropriate because factors such as water–cement ratio, fiber and porosity are not considered. More information on the strength of fiber-reinforced pervious concrete will be collected in the future to obtain a formula for accurately predicting cracking loads.

3.5. Flexural Toughness

Through the flexural toughness calculation method provided by JSCE-SF4 [26], using the flexural load and displacement diagram, as shown in Figure 16, Figure 17 and Figure 18, the H1-G2 specimen (0.5% glass fiber) has the maximum bearing capacity, followed by the H1-O, H1-S1, H1-G1 and H1-S2 specimens in Figure 17. When subjected to flexural load, the S2 and S1 specimens with steel fibers have a larger displacement, followed by the G2 and G1 specimens with glass fibers, and the minimum displacement is O for the fiber-free specimens, as shown in Figure 16, Figure 17 and Figure 18. In addition, the area enclosed by the flexural load and displacement curve from 0 mm to 2 mm of displacement can be used to calculate the increase in the toughness and strength of pervious concrete beams due to the addition of fibers. The flexural toughness and toughness factor for fiber pervious concrete are given in

Table 6. Flexural toughness and toughness factor for fiber pervious concrete.

Pervious Concrete	Toughness (N-m)	Toughness Factor $(\mathrm{N}/\mathrm{m}{\mathrm{m}}^2)$
H1-D7-G1	6.43	964.50
H1-D7-G2	6.22	933.00
H1-D7-S1	15.01	2251.50
H1-D7-S2	16.73	2509.50
H1.2-D7-G1	7.65	1147.5
H1.2-D7-G2	8.62	1293
H1.2-D7-S1	9.81	1471.5
H1.2-D7-S2	12.44	1866
N-D7-G1	6.12	918
N-D7-G2	5.87	880.5
N-D7-S1	10.38	1557
N-D7-S2	14.39	2158.5

. The H1-S2 specimen (2% steel fiber) has the maximum flexural toughness and toughness factor. For the two types of fibers, steel fibers had the best reinforcing effect, and due to the increase in fiber content, the toughness and toughness factor also increased, which is partially consistent with the results of the literature on this subject [32,33]. Due to the strong stiffness of steel fiber, the tensile force at the bottom of the beam can be provided immediately when the pervious concrete cracks, and the end of the steel fiber has a hook to provide anchor force to the pervious concrete when it is under tension, whereas the glass fiber itself is relatively small and has low rigidity. When the concrete cracks, the load capacity will drop suddenly, and the pervious concrete will only show the tensile effect provided by the glass fiber when it needs to be continuously compressed, but the load capacity is much lower than that of the steel fiber.

4. Summary

The main findings from this study are summarized as follows:

• The compressive strength increased slightly with the increasing curing age of the pervious concrete samples; however, the strengths at 28 days and 90 days were very close. Whether it is high-strength pervious concrete or ordinary pervious concrete with steel fibers added, the porosity and permeability coefficient are increased compared with the control group. The permeability coefficients of high-strength fiber-reinforced pervious concretes in both aggregate sizes (3.18 mm and 3.81 mm) met the requirements of the ACI specification for structural concrete. Moreover, the high-strength pervious concrete specimen H1-S2 (2% steel fiber) had the highest compressive strength of 52.8 MPa at the age of 28 days.
• The average modulus of elasticity of high-strength, fiber-reinforced pervious concrete is about 20,000 MPa, which is close to that of ordinary (non-pervious) concrete, whereas the modulus of elasticity of ordinary pervious concrete is about 50% of that of ordinary concrete. In addition, the coefficient of the elastic modulus of high-strength pervious concrete is close to the value of 3795 suggested by Liao W.C. et al. [29], and the ordinary pervious concrete is about 0.71 times the suggested value, and the results are similar regardless of whether fiber is added or not.
• The results show that that the flexural strength of ordinary pervious concrete increases with the increase of fiber content, and the effect of steel fiber on improving the flexural strength is better than that of glass fiber. In addition, it was found that when the content of steel fiber or glass fiber in high-strength pervious concrete increases, its flexural strength will not increase significantly. However, both steel fiber and glass fiber have a certain degree of improvement in the flexural toughness and toughness factor, and the effect is better with steel fiber. There is still about 30% of the bearing capacity after the peak strength, which gradually decreases until it is completely destroyed.
• Taiwan’s general formula for general concrete cracking modulus (flexural strength) uses 0.63√fc′ (MPa) as a commonly used formula for predicting cracking load. The results show that using 0.63√fc′ as a common formula for predicting cracking loads is not appropriate because factors such as water–cement ratio, fiber and porosity are not considered. More information on the strength of fiber-reinforced pervious concrete will need to be collected in the future to obtain a formula for accurately predicting cracking loads.