The Strength and Elastic Modulus of Pervious Concrete Considering Pore and Fiber during Freeze– Thaw Cycles

: The interface between aggregate and cement matrix and the strength of the cementation layer between aggregates are the key factors affecting the strength of pervious concrete. The purpose of this paper is to evaluate the effects of porosity, compressive strength and elastic modulus of pervious concrete before and after freeze–thaw cycles. The effective porosity and total porosity were obtained by the underwater weighing and CT (computed tomography) image analysis methods. Uniaxial and triaxle compression tests were carried out to obtain the strength and elastic modulus of pervious concrete considering pore and ﬁber. The results indicated that the effective modulus and effective stress were closely related to the porosity, and the continuous fracture of cementation points between aggregates caused damage to pervious concrete. Inclined shear failure of pervious concrete occurred under uniaxial pressure, and the strength and elastic modulus increased with increases in conﬁning pressure. With the increase in freeze–thaw cycles, the porosity increased linearly, the strength and elastic modulus decreased and a mutational point appeared between 40 and 50 times during the freeze–thaw cycles. The ﬁber enhanced the strength of the cementation layer and increased the connection between aggregates, thus improving the strength and integrity of pervious concrete. This work is needed to serve as a reference for the fracture mechanism of pervious concrete and the effect of freeze–thaw cycles considering pore and ﬁber.


Introduction
Pervious concrete is composed of coarse aggregate, cement paste and admixtures, without or with less fine sand to meet a certain porosity to achieve the purpose of permeability.Pervious concrete plays an important role in improving urban climate and regulating urban rainwater runoff [1][2][3].However, high permeability is detrimental to the strength and freeze-thaw durability of pervious concrete, which limits the application of permeable pavements in large urban areas [4,5].In order to improve the strength and durability without affecting the permeability of pervious concrete, some scholars adopted the high-strength cement matrix, while others improved the aggregate particle size ratio or added fiber [6][7][8][9].For instance, Liu et al. [10] investigated the mechanical strength, porosity and permeability of pervious concrete modified with fly ash, silica fume and basalt fiber, and a mixture proportion of pervious concrete was obtained with a compressive strength greater than 40 MPa.Chindaprasirt et al. [11] tested the influence of binder strength and aggregate size on the compressive strength and porosity of porous concrete, and the general equations for pervious concrete were related to compressive strength and porosity for different binder strengths and aggregate sizes.Tarangini et al. [12] prepared various mix proportions using different sizes of coarse aggregates, and studied properties such as permeability, porosity, density, strength and durability of pervious concrete.Abdulwahid [13] focused on the effect of different types of stone powders as a partial replacement for coarse aggregate on the strength and porosity of pervious concrete, highlighting also the great role played by the fineness of stone filler in improving the strength of pervious concrete with acceptable porosity.Zhong and Wille [14] studied the effect of a high-strength cement matrix on the strength of pervious concrete, and based on the existing equations, proposed an extended equation verified by the enhanced agreement between predicted and experimentally measured compressive strength.
However, the strength and freeze-thaw durability of pervious concrete are closely related to pore characteristics [15].The larger the aggregate particle, the larger the pore, and the fewer the cementation points between aggregates.The smaller the aggregate particle, the smaller the pore, and the more cementation points between aggregates, which directly affects the strength of pervious concrete.Thus, Zhong and Wille [16] studied the relationship between compressive strength and mean pore size by linear path function, which was validated by an image analysis method, so as to predict the compressive stress versus strain behavior of pervious concrete.Rehder et al. [17] studied the influence of pore structure (porosity, sizes, and tortuosity) and fibers on the fracture response of pervious concretes, and a sensitivity analysis was employed to quantify the influence of material design parameters on fracture toughness.Lian et al. [18] described the development of a mathematical model to characterize the relationship between compressive strength and porosity: the suitability of existing equations for pervious concrete was assessed and a new model was proposed.Chandrappa et al. [19] used X-ray microcomputed tomography to understand and quantify three-dimensional pore morphology, shape factors, and size descriptors in pervious concrete mixtures, and the findings on the pore structure will assist in mix design optimization, selection of mixtures, and modeling of pervious concrete.
In the process of use, the main factors affecting the freeze-thaw durability of pervious concrete include environment temperature, rain and vehicle load [20][21][22][23].Among these, the environmental temperature is the main factor limiting the application of pervious concrete in cold areas.The pervious concrete pavement is mainly used in gardens, sidewalks and parking lots, and is rarely used for driveways, while the service period of pervious concrete pavement in the northern cities is shorter than that in the southern cities of China, such as Xi'an and Zhengzhou.In the winter of northern cities, the freezing of pavement rainwater easily causes the fracture of pervious concrete structures, the pores are easy to plug, and the service effect is poor.On the other hand, the cementation layer between aggregate particles directly affects the strength and durability of pervious concrete.Ruyan et al. [24] investigated the relationship between porosity, permeability, compressive strength, durability and the pore structure characteristics of pervious concrete, discussed the influence of basalt fiber and fine aggregate on the pervious concrete, and found that the pore structure characteristics of pervious concrete had an effect on mechanical behavior and durability.Hui et al. [25] obtained the evolution of the compressive strength of pervious concrete under water and salt freeze-thaw conditions by uniaxial compression tests, and examined the development of the ultrasonic velocities and the relative dynamic modulus of elasticity to investigate the deterioration of the transitional interface zone of pervious concrete during freeze-thaw cycles.Liu et al. [26] studied the effects of waste fly ash on the properties of pervious concrete and tested the porosity, permeability, compressive strength, flexural strength and freeze-thaw resistance of all mixtures.
The degradation mechanism of common concrete under freeze-thaw is mainly caused by frost heaving of the internal pore water [27], but the degradation mechanism of pervious concrete under freeze-thaw is mainly due to the weakening of the cementation layer between aggregates and the interface zone between the aggregate and cement matrix [28].In addition, the elastic modulus is the main parameter reflecting the mechanical properties of pervious concrete.Alam et al. [29] estimated the elastic modulus of pervious concrete based on porosity, and three performance zones were proposed for estimating the elastic modulus based on porosity at the stress levels of 2.2 and 2.8 MPa for risk-based assessments.It is necessary to study the strength and elastic modulus of pervious concrete in a freezethaw environment.Therefore, the strength and elastic modulus of pervious concrete under freezing and thawing need to be studied, which can reflect the internal deterioration mechanism of pervious concrete from a macro perspective.
In this paper, based on the fracture criterion of the cementation layer between aggregate particles, the strength and freeze-thaw damage characteristics of pervious concrete were studied considering pore and fiber through the strength and elastic modulus.The pore characteristics of pervious concrete can be obtained by CT scanning, and the elastic modulus of pervious concrete can be obtained by the tangent slope of the stress-strain curve.The primary goal of this paper is to investigate the effective porosity, total porosity, compressive strength and elastic modulus of pervious concrete under freeze-thaw cycles, which would provide a basis for the popularization and application of pervious concrete in urban permeable pavements.

Materials
The raw materials used for preparing the pervious concrete specimens include ordinary Portland cement (P.O42.5),coarse aggregates, basalt fiber and hooked steel fiber, C1029 polycarboxylate superplasticizer and fine silicon powder.The physical properties of ordinary Portland cement purchased from Shanxi Qinfen Building Material Co., Ltd.(Xi'an, China) are shown in Table 1.According to the correlation between the aggregate and mechanical properties of pervious concrete [30], the coarse aggregate sizes used were 4.5-9.5 mm with a 50 GPa elastic modulus, 0.18 Poisson's ratio and 2.59 × 10 3 kg/m 3 apparent density, as shown in Figure 1a.According to the correlation between aggregate and fiber [17], the length of basalt fiber and hooked steel fiber purchased from Shanghai Chenqi Chemical Technology Co., Ltd.(Shanghai, China) is 30 mm, as shown in Figure 1b,c.The density of basalt fiber was 2.63 × 10 3 kg/m 3 with a 91 GPa elastic modulus and 3.6 GPa tensile strength, and the density of hooked steel fiber was 4.60 × 10 3 kg/m 3 with a 160 GPa elastic modulus and 1.1 GPa tensile strength.The densities of superplasticizer and silicon powder purchased from Phuc Technology Co., Ltd.(Suzhou, China) were 0.64 × 10 3 kg/m 3 and 0.41 × 10 3 kg/m 3 , respectively.

Mix Design and Specimens Preparation
According to the Chinese national standard "Technical code for pervious cement concrete pavement" (CJJ/T 135-2009), the volume method was used for the mix of pervious concrete, as shown in Equation (1).
where M a , M c , M w and M z are respectively the dosage of aggregate, cement, water and admixtures per unit cubic meter of pervious concrete.ρ a , ρ c , ρ w and ρ z are respectively the apparent densities of aggregate, cement, water and admixtures.P is the designed porosity.
A water-cement ratio of 0.3 was used in this study without fine aggregates [31], and pervious concrete mixtures were designed to achieve the target porosity of 18%.The contents of fiber, superplasticizer and silicon powder were 0.16%, 0.2% and 6%, respectively.The distribution and dispersion degree of fibers in specimens have a great influence on its effect [32], so an HJW-60 forced single horizontal shaft mixer was used to mix the aggregate and fiber with 50% water, and then cement and admixtures were added to apply evenly on the surface of aggregates.Finally, the remaining water was used to mix well.The mixtures were cast in cylindrical molds of Φ50 mm × 100 mm.Micro vibration and tamping were used to make the mixtures compact in the mold.A total of 81 pervious concrete cylinders were made; they were demolded after 24 h of curing in the molds and then moist-cured for 28 days by a film covering (>98% RH).
The cylindrical specimens of Φ50 × 100 mm were used for effective porosity, CT image analysis of pore characteristics, compression and freeze-thaw (F-T) cycle tests.The effective porosity was determined by the underwater weighing method, and the total porosity was calculated from CT image analysis.The specimens were divided into three groups-the control group (CG), basalt fiber (BF) and hooked steel fiber (HSF)-which were subjected to the same freeze-thaw cycles of 10, 20, 30, 40, 50 and 60 times, as shown in Figure 2.There were 27 specimens in each group, for a total of 81 specimens, and the preparation of different tests is shown in Figure 3.

Testing Methods
According to the ASTM C1688 and the Chinese national standard "Pervious Concrete" (JC/T 2558-2020), the effective porosity of pervious concrete was determined by the underwater weighing method, as shown in Figure 4a.The effective porosity P e can be expressed as follows: where P e is effective porosity, m 1 is the weight of the specimen in water, m 2 is the weight of the specimen after 24 h drying in drying box, ρ is the density of water and V is the volume of the specimen.Usually, there are closed pores in pervious concrete specimens, which are not connected with the outside and form a closed space.The closed pores do not provide passage for water, and CT scanning can obtain all pores inside specimens in a non-destructive state, as shown in Figure 4b.In this paper, a Siemens CT scanner with a 256-row Definition Flash was used to obtain the internal pore structure of specimens, and the total porosity was calculated according to the ImageJ processing software [15].The total porosity includes the connected and the closed pores.
An RMT-150C rock mechanics test system of the Chang'an University laboratory was used in accordance with the Chinese national standard GB/T 50081-2002 in this paper.The test system was composed of a structural frame, base, vertical hydraulic cylinder, sample fixing cap, axial and radial strain sensors, and triaxle confining ring, which can be used for uniaxial and triaxle compressive strength tests with the maximum axial force of 1000 kN.The uniaxial and triaxle compressive strength tests of pervious concrete are shown in Figure 5a,b.The axial loading displacement velocity is 0.1 mm/min, the confining pressures of the triaxle compressive strength test are 3 MPa and 5 Mpa, respectively.The axial displacement was measured by the axial sensor, and the axial stress-strain results were obtained immediately after specimen failure.According to the ASTM C1747 and the Chinese national standard "Standard Test Method for Long-term Performance and Durability of Ordinary Concrete" (GBT50082-2009), freeze-thaw cycles were carried out by the slow freezing method, and the compressive strength of each group of specimens was tested every 10 freeze-thaw cycles.When the loss of compressive strength exceeded 25%, the test was stopped and the number of freeze-thaw cycles recorded.In this paper, pervious concrete specimens were first immersed in water for 24 h, frozen using a Midea refrigerator BCD-112CM for 4 h at (−20 ± 2) • C, and then put into water at (20 ± 2) • C to melt for 4 h.After wiping the moisture from the surface of the specimens, they were put into the refrigerator again, and then cycled in turn.The tests were divided into the control group, 10 times, 20 times, 30 times, 40 times, 50 times and 60 times groups, for a total of seven groups, with three specimens in each group.The average value of three specimens in each group is taken as the test result.If the maximum or minimum value of the three specimens exceeds 20% of the intermediate value, the intermediate value will be taken as the compressive strength of the group.

Effective Modulus Analysis
In order to analyze the relationship between the effective elastic modulus and porosity, Poisson's ratio and porosity of pervious concrete, a circular element model is adopted [33], as shown in Figure 6a.Assuming that the inner pore radius is a, the outer matrix radius is b, and the outer matrix is subjected to a load of F. A micro unit in the ring matrix is subjected to the radial and toroidal stresses, as shown in Figure 6b.The pore in pervious concrete is gas phase, the volume modulus and shear modulus of which are zero.Due to the symmetry of the model, the micro unit in the matrix is not subjected to shear stress without considering gravity.The differential equation of micro unit can be expressed as follows:

−
The displacement and stress field generated by the external force F are: where r is the distance from the microunit to the center of circle; K m is the matrix volume modulus; µ m is the matrix shear modulus; and A m are B m the related parameters.
The boundary conditions of the circular element model are: Substituting Equation (5) into Equation ( 4), it can be obtained: where p = a 3 /b 3 is the volume fraction of pores.Thus, the effective volume modulus of the circular element model with pores can be obtained: According to the torsion of the circular element model, the effective shear modulus can be obtained: In engineering practice, the internal pore structure of pervious concrete can be regarded as an isotropic distribution.Based on the theory of effective volume modulus and effective shear modulus, the effective Young's modulus and effective Poisson's ratio of pervious concrete are determined as:

Effective Stress Analysis
The mechanical characteristics of pervious concrete are mainly reflected in the interaction between aggregate particles.Under the action of external load, the aggregate particles will stagger or slip and the cementation layer between particles breaks.When the cementation layer between aggregate particles is undamaged, the solid skeleton deformation (SSD) of pervious concrete occurs under the action of external total stress and internal pore stress.A section inside the pervious concrete specimen is taken, and the porosity is P t .According to the principle of force balance, it can be obtained [34][35][36]: where σ is the total stress; σ p is the pore stress; σ s is the solid skeleton stress; P t is the porosity.In the formula above, the σ s is the main factor reflecting SSD.The solid skeleton effective stress of pervious concrete in the whole section is: The solid skeleton determines the strain behavior of permeable concrete; according to Hooke's law, Equation ( 12) exists: where E p is the solid skeleton elastic modulus of pervious concrete; ε p is the solid skeleton strain of pervious concrete.According to the above, it can be obtained: A fracture of the cementation layer between aggregate particles often occurs in pervious concrete.When the fractures of cementation layers between aggregate particles are connected through, a failure surface is formed, as shown in Figure 7. Hypothetically, a stress equilibrium relation on the failure surface can be obtained: where A is the failure surface area; σ is the total stress; σ ci is the stress of the ith cementation point; A ci is the vertical area of stress action of the ith cementation point; σ p is the pore stress.
By converting the stress of the cementation point between particles to the whole failure surface area of pervious concrete, the effective stress on the failure surface can be obtained: σ s e = ∑ σ ci A ci /A, which determines the spatial change on the failure surface of pervious concrete.From the effective stress σ s e and strain ε s on the failure surface, the stress-strain relationship on the failure surface can be obtained: where P c is the porosity on the failure surface.

Uniaxial Compressive Strength
Under uniaxial pressure, mainly an inclined section shear failure of pervious concrete specimens occurred, as shown in Figure 8.With the continuous load application, the cementation layer between aggregate particles on the failure surface gradually broke.According to the failure form analysis of pervious concrete, the fracture of the cementation layer between aggregate particles mainly occurs on the failure surface.The pores in pervious concrete are large and numerous, and a stress concentration occurs easily in the cementation layer between aggregate particles.The failure form of pervious concrete is between ultimate strength failure and fracture failure of the cementation layer between aggregate particles.Larger porosity increases the probability of non-uniform deformation and sudden failure of pervious concrete under loading to a certain extent.The fiber can increase the cohesion of pervious concrete, increase the strength of the cementation layer and the connection between aggregate particles, and improve the stress uniformity and integrity of specimens.It can be seen from Figure 8b,c that the integrity of the hooked steel fiber pervious concrete specimen is better than that of the basalt fiber pervious concrete specimen after failure, but in application, the hooked steel fiber rusts easily and loses its function.The uniaxial stress-strain curves of pervious cement concrete specimens with different fibers are different, as shown in Figure 9.At the beginning, the stress-strain curves basically coincide, and with the increase in load, the stress increases rapidly at first and then slowly, which is mainly caused by the end effect of the specimen.With the further increase in load, the effect of the fiber gradually works, and the stress-strain curves begin to show differences.The control group pervious concrete specimens mainly exhibit brittle fracture characteristic, whereas fiber pervious concrete specimens show a certain plastic characteristic.This is because, after the cement paste cracks, the fibers can still bear some force in the further strain under the load.The strain is obvious in the lower concave stage between the linear elastic and peak strength of fiber groups than that of control group.The elastic modulus of the control group pervious concrete is 7.32 GPa, the elastic modulus of basalt fiber is 8.21 GPa and the elastic modulus of hooked steel fiber is 8.18 GPa.According to Figure 9, the stress-strain curves of pervious concrete can be divided into four stages.
Firstly, a small sharp rise occurred in the stress-strain curve caused by the end effect of the specimen, and then the stress-strain curve showed an upper concave shape.Under the action of loading, the pores inside the specimen were slightly squeezed and adjusted, local pores were compressed and deformed, and aggregate particles began to interact with each other.With the continuous increase in load, the aggregate particles and cementation layer bore all the loads, and the aggregate particles and cementation layer showed a linear elastic stress-strain relationship.There was no fracture of aggregate particles and cementation layer, the effect of fiber was not obvious and the types of fiber had little influence on the stress-strain curve.In the late elastic stage, with the gradual increase in load, cracks in the interface or cementation layer continued to emerge and expand, and the stress-strain curve gradually developed in the nonlinear direction, showing an upper convex shape.With the further increase in load, more and more cementation points inside the specimen broke through, a slight cracking sound could be heard and the specimen reached the maximum stress peak.The fiber had a great influence on the strength and deformation of specimens, which could effectively improve the strength and integrity of the specimens.
After reaching the peak value, the strength of the specimen decreased rapidly and the deformation increased sharply, the effect of fiber wore off and the specimen was damaged.

Triaxle Compressive Strength
Under the action of triaxle pressure, the strength of pervious concrete was mainly provided by aggregate particles and the cementation layer, among which the cementation layer provided the early strength, and the aggregate particles provided the late strength.When reaching the peak strength, the cementation layer failed first, and elastic modulus of the pervious concrete was closely related to the test device and loading rate.Due to pore collapse and aggregate rearrangement in the process of loading, the test results of pervious concrete on ordinary test machines show great fluctuations.Zhong and Wille [16] proposed a regression model between elastic modulus and compressive strength of pervious concrete.The fiber can reduce the permeability of pervious concrete to a certain extent, and has little effect on the fracture toughness of pervious concrete, which is mainly related to porosity.The length of fiber that is beneficial to the strength and other properties of pervious concrete ranges from 12 mm to 54 mm.Fiber plays a great role in improving the wear resistance and frost resistance of pervious concrete, increasing the elastic modulus, and increasing the peak strength and peak strain, as shown in Figure 10.Triaxle compression test results of pervious concrete under different confining pressures are shown in Table 2.

Effect of Freeze-Thaw Cycles on Strength and Elastic Modulus
Under the action of freeze-thaw cycles shown in Figure 11, the strength of the cementation layer between aggregate particles inside pervious concrete specimens decreased, and some fractures occurred, which increased the connectivity between pores and increased the porosity.With the increase in freeze-thaw cycles, the effective porosity and total porosity of pervious concrete specimens increased gradually, and the effective porosity was gradually growing closer to the total porosity.The porosity of the control group specimens is higher than that of the basalt fiber specimens and hooked steel fiber specimens, and the porosity of the basalt fiber specimens is close to that of the hooked steel fiber specimens.After measuring the porosity of the control group, basalt fiber and hooked steel fiber specimens, the compressive strength tests were carried out to obtain peak strength and elastic modulus of pervious concrete, as shown in Figure 12.The peak strength and elastic modulus of pervious concrete decreased with the increase in freeze-thaw cycles, decreased slowly in the early stage, and decreased sharply when the freeze-thaw cycles were greater than 40 times.Based on the same results [26], it is can be obtained that the compressive strength and elastic modulus of pervious concrete specimens decreased with the increase in the freeze-thaw cycles, as shown in Figure 12.The compressive strength and elastic modulus decreased slowly within 40 freeze-thaw cycles, while the compressive strength and elastic modulus decreased sharply after more than 40 freeze-thaw cycles, and a mutational point appeared at 40 and 50 freeze-thaw cycles.The law of peak compressive strength in combination with the elastic modulus of pervious concrete under freeze-thaw cycle tests can provide a reference for the maintenance and service period of pervious concrete in the northern cities of China, and improve the performance of cement paste between aggregates, which is the key to popularizing the application of pervious concrete.

Conclusions
The primary objective of the present paper was to analyze the effective porosity, total porosity, compressive strength and elastic modulus of pervious concrete of the control group, basalt fiber and hooked steel fiber under freeze-thaw cycles, as well as the effective modulus and effective stress.The key findings in this work are as follows:

•
According to the circular element model, there is a square relation between effective elastic modulus and porosity of pervious concrete.The effective stress is related to the number and area of cementation points on a section of pervious concrete, and the damage of pervious concrete can be considered as the result of the failure of all cementation points on the section.The improved performance of cement paste between aggregates is suggested to popularize the application of pervious concrete.

•
The elastic moduli of pervious concrete of CG, BF and HSF under uniaxial compression were 7.32 GPa, 8.21 GPa and 8.18 GPa, respectively, and an inclined section shear failure of specimens occurred.When the confining pressure was 3 MPa, the elastic moduli of CG, BF and HSF were 8.45 GPa, 9.34 GPa and 9.25 GPa, respectively.When the confining pressure was 5 MPa, the elastic moduli of CG, BF and HSF were 10.12 GPa, 11.03 GPa and 10.96 GPa, respectively.

•
With the increase in freeze-thaw cycles, the porosity of pervious concrete increased linearly, and the effective porosity and total porosity were gradually equal, the strength and elastic modulus decreased, and a mutational point appeared between 40 and 50 freeze-thaw cycles.The fiber enhanced the strength of the cementation layer and increased the connection between aggregates, thus improving the strength and integrity of pervious concrete.This can provide a reference for the maintenance and service period of pervious concrete in the northern cities of China.

Figure 6 .
Figure 6.Force analysis of circle pore model: (a) circular element model; (b) force analysis of micro unit.

Figure 10 .
Figure 10.Peak strength and elastic modulus of pervious concrete with confining pressure.

Figure 11 .
Figure 11.Porosity of different groups with freeze-thaw cycles.

Figure 12 .
Figure 12.Peak strength and elastic modulus of pervious concrete with freeze-thaw cycles.

Table 1 .
Physical properties of ordinary Portland cement.

Table 2 .
Triaxle compression test results of pervious concrete under different confining pressures.