Hydraulic conductivity and water level in the reservoir layer of porous pavement considering gradation of aggregate and compaction level

Construction and Building Materials 203 (2019) 27–44

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Hydraulic conductivity and water level in the reservoir layer of porous pavement considering gradation of aggregate and compaction level Mehdi Koohmishi School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

h i g h l i g h t s
Drainage of reservoir course was investigated by considering properties of aggregate.
Effect of gradation and compaction on permeability of aggregate assembly was evaluated.
Crushed and river aggregates were established to consider morphological properties.
Gradation is the most important property which affects permeability and water level of layer.
Uniform gradation with low compaction shows completely turbulent flow regime.

a r t i c l e

i n f o

Article history: Received 16 September 2018 Received in revised form 9 January 2019 Accepted 10 January 2019

Keywords: Reservoir course Hydraulic conductivity Aggregate gradation Compaction level Water table Turbulent flow

a b s t r a c t The reservoir layer of porous pavement comprised of coarse aggregate provides a structure for temporarily retention of water inside the porous media and gradually discharging water into the underlying layers. The main objective of the present study is to evaluate the influence of appointed gradation of aggregate, morphological properties as well as compaction level on the permeability and water elevation in the reservoir course. For this purpose, large-scale permeability test is carried out on two types of aggregate including crushed stone and river aggregate by establishment of different compaction level of considered gradations. Then, the water level in the reservoir course is assessed by developed analytical models. As expected, the hydraulic conductivity and turbulence of water flow are higher for rounded aggregate with more uniform gradation and lower compaction. Evidently, the permeability of aggregate specimen and consequently the estimated water level of the reservoir course are substantially influenced by the established particle size distribution rather than the compaction level or aggregate morphology. Finally, provision of specimen comprised of broader range of crushed aggregate with high-level compaction leads to the increment of water level in the reservoir course and flow regime between fully turbulent and laminar as characterized by power law. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Permeable pavement system is categorized as a green construction method which reduces runoff volume and consequently enhances controlling storm water in urban areas [30,12]. Meanwhile, establishment of permeable pavement purifies the water derived from precipitation over surface by filtering effects [15]. Furthermore, construction of porous pavement instead of the conventional nonporous surfaces eventuates in elimination of side ditches and hence increasing the effective width of the urban streets. The goal to provide a permeable system is attained by pro-

E-mail address: [email protected] https://doi.org/10.1016/j.conbuildmat.2019.01.060 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

vision of porous materials such as pervious concrete or porous asphalt as surface layer as well as laying a coarse-grained granular media under these porous mixtures. The above-mentioned advantages of porous pavement system are derived whenever the desirable permeability of this pervious structure is assured. To elaborate the effectiveness of porous pavement, the drainage performance of these structures has been investigated in the previous researches. Sansalone et al. [27] evaluated the porosity and hydraulic conductivity of cementitious permeable pavement (CPP) comprised of coarse aggregate with significant separation between particles. It was reported that provision of a CPP cleaning schedule of every 6 months was requisite to maintain the hydraulic conductivity of the CPP matrix [27]. In this relation, Dougherty et al. [10] established a test method to

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

evaluate the drainage potential of small pervious concrete sites. As final conclusion, the quick field infiltration test (QFIT) method was recommended as a fast procedure to specify the necessity for pavement cleaning. Rodriguez-Hernandez et al. [26] applied Cantabrian fixed infiltrometer to measure the infiltration potential of permeable pavement in which porous asphalt mixture with air void range of 20% to 33% was used as surface layer. It was found that design of mixture of porous asphalt with higher percentage of air void in depth as well as timely surface brushing were sufficient to maintain the permeability capacity of pavement. Generally, the underlying layers play an important role in permeability of pavement structures. For conventional pavements, applying a subbase layer under the pavement significantly enhances the quality of drainage and better performance of the base layer [22]. In the case of permeable pavement, the pervious granular media under the porous asphalt layer named as reservoir course functions as a crucial structural layer in order to provisionally retain precipitation falling over the urban street surface until stored water can penetrate into the underlying soil or subsurface drainage systems [28]. The reservoir layer comprises of relatively uniform coarse-grained particle size distribution of aggregate which results in a penetrable media with air void content of around 40%. The geometrical properties (gradation and morphological indices) as well as the level of compaction gently influence the behavior of granular media to provide adequate void space along with enough structural performance. In this relation, Xiao and Tutumluer [35] established discrete element model to minimize the rutting potential of pavement granular layers by evaluation of effect of gradation and particle shape characteristics on particle contact and air void content. Zaika and Djakfar [36] reported that increment of degree of angularity resulted in lower porosity for reservoir base of porous pavement. Also, Cetin et al. [7] compared the performance of two compaction methods including the vibratory and impact compaction procedures applied on unbound granular base materials. It was observed that impact compaction incremented the content of fine particles which led to the decrement of hydraulic conductivity. Furthermore, Xiao et al. [34] observed that small increment in compaction degree enhanced the shear strength of unbound granular material especially at lower normal stress level. The water movement through porous pavement layers has been analyzed in the previous researches to elaborate the drainage of permeable friction courses as well. Generally, the flow regime through porous media can deviate from Darcy law due to turbulent flow condition. As characterized by Fwa et al. [13], the measurement of water movement through base course aggregate was conducted at diverse hydraulic gradients due to invalidity of linear flow regime. Also, Ranieri et al. [25] figured out limitation of considering linear flow condition through porous friction courses. The same trend was found between discharge velocity and hydraulic gradient in the previous performed permeability tests on degraded railway ballast [29]. In this relation, Charbeneau and Barrett [8] investigated the drainage of pervious friction courses by considering linear condition for water flow. Also, analytical methods were developed by considering nonlinearity of flow through porous materials to determine the water table under different values of rainfall rate [11]. The geometrical properties of individual particles and the overall arrangement of aggregate assembly are important factors which influence the hydraulic conductivity of reservoir course. In the previous researches, the role of provided gradation on the permeability of reservoir course aggregate has been evaluated. However, the combined effect of particle size distribution (PSD) of aggregate, morphological properties of individual particles and level of compaction of layer on the drainage potential and water level of the reservoir course has not been well established. Furthermore, the

water flow regime is conventionally simplified by assuming linear flow condition. The present study evaluates the permeability of aggregate as well as the estimated water elevation in the reservoir course of the porous pavement by considering diverse gradations suited for this porous media and taking into account the morphological properties of individual particles and the level of compaction of aggregate assembly. To assess the water flow regime through the reservoir course aggregate, different models (including linear and nonlinear) are utilized for evaluation of drainage potential of this porous structure. 2. Methodology 2.1. Scope of study The main objective of the present research is to evaluate the permeability as well as the water elevation in the reservoir course by appointing various gradations of coarse aggregate, disparate morphological properties of particles as well as different compaction levels in which the flow regime condition is also assessed. For this purpose, the hydraulic conductivity of aggregate is determined by carrying out the large-scale constant head permeability test on diverse gradations with different levels of compaction and then the water level in the reservoir layer of the permeable pavement structure is estimated by applying the developed analytical approach. 2.2. Geometric properties of aggregate The considered geometric properties of aggregate include the particle size distribution as well as the morphological characteristic. To assess the PSD specifications, six different gradation curves are established (as shown in Fig. 1) which the considered gradations mainly accommodate the ASTM and AASHTO recommendations [4,1]. Table 1 presents the general properties of characterized PSDs. To elaborate the morphological properties, the crushed stone and river aggregate are used as the granular material of the reservoir course (as demonstrated in Fig. 2). 2.3. Constant head permeability test setup and procedure A large-scale constant head permeability tester is utilized to measure the hydraulic conductivity of reservoir course aggregate. The testing device comprises of a water tank to regulate the applied water load (Fig. 3a) as well as a cylindrical chamber with

Gradation of reservoir course aggregate 100

80

Fraction Passing (%)

28

60

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

40

20

0 0

10

20

30

40

50

60

70

Sieve Size (mm) Fig. 1. Appointed gradation curves for the reservoir course aggregate in the present study.

29

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44 Table 1 General properties of characterized gradation curves for reservoir course aggregate. Grading type

dmax (mm)

dmin (mm)

d10 (mm)

d60 (mm)

d50 (mm)

Cu (d60/d10)

G62.5/37.5 (ASTM No. 2) G62.5/25 G50/25 (ASTM No. 3) G62.5/9.5 G37.5/2.35 (ASTM No. 57) G62.5/0.075

62.5 62.5 50 62.5 37.5 62.5

37.5 25 25 9.5 2.35 0.075

39.1 30.5 28 15.7 5.85 3.2

48.1 45.5 41.2 41.7 18.2 29.6

46.5 43.5 39.5 37.5 16.3 25

1.23 1.49 1.47 2.66 3.11 9.25

a Crushed stone aggregate

b River aggregate

Fig. 2. River and crushed stone aggregate used as the material of the reservoir layer.

a Water reservoir

b Cylindrical chamber

c Aggregate inside the main chamber

d Water discharge through reservoir course aggregate

Fig. 3. Large-scale constant head permeability test device established for measurement of hydraulic conductivity of reservoir course aggregate.

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

large size (460 mm diameter and 720 mm height) to accommodate continuous water stream through porous specimens with 450 mm in diameter and 300 mm in height (Fig. 3b, c). A cylindrical chamber with larger dimensions is utilized to lessen the effect of boundary condition based on the ASTM D 2434-68 [3]. An outlet installed overhead of the tested specimen preserves constant water head condition during upward movement of water through the aggregate specimen (Fig. 3d). Fig. 4 schematically demonstrates the preceding explanation about layout of the developed constant head permeability test apparatus. 2.4. Control compaction level of aggregate in the permeability test To quantify the maximum compaction level of aggregate for each specific gradation, the prepared sample is first poured into the 250 mm diameter mold with aspect ratio of 1. The specimen is then compacted to the utmost possible degree by combination of using a tamping rod as well as implementation of jigging method [2]. Fig. 5 illustrates the aggregate sample inside the main chamber of the permeability test apparatus as well as the compacted specimen in the scale mold for different characterized PSDs. The derived maximum value of unit weight of aggregate in the scale mold is used to provide samples compacted in the main chamber of the permeability tester with compaction degree of 100%, 95% and 90%, respectively. 2.5. Structure considered for the reservoir course of the porous pavement To elaborate the water level of the reservoir course, the structure of the porous pavement (specifically the reservoir layer) is considered according to the Fig. 6. The subgrade under the reservoir layer is assumed to be impermeable and consequently rainwater is fully discharged by the reservoir course. Impermeable subgrade characterizes whether construction of a porous pavement over underlying soil with low permeability [6,32] or provision of an impervious liner between the reservoir layer and subgrade. Generally, impermeable subgrade eventuates in drainage of water through the reservoir course into the sides of the urban streets which enhances the structural performance of pavement under light traffic loading condition by feasibility of further compaction of the subgrade soil. The stored water inside the porous media can then gradually infiltrate into the underlying soil on two sides of the urban street in cases associated with low

compacted subgrade. However, consideration of subsurface drainage may be necessary in cases associated with low-infiltration subgrade soil and remarkable rainfall rate to drain excess water through perforated pipes placed on two sides of the stone reservoir course (as shown in Fig. 6). 3. Determination of water table in the reservoir course As initial step for determination of water table in the reservoir course of porous pavement structure, characterization of water flow model is essential. Darcy’s law provides a linear relationship between flow velocity and hydraulic gradient for water flow through permeable media by assuming laminar flow condition. Based on the proposed law, the relationship is expressed by Eq. (1) [9]:


 DH ¼ ki V¼k L

ð1Þ

V = Flow velocity (cm/s) k = Hydraulic conductivity coefficient (cm/s) DH = Head difference between two points (cm) L = Length of the porous specimen in the flow direction (cm) i = Hydraulic gradient Generally, reservoir course is characterized as a porous granular media due to comprising of coarse aggregate. Therefore, establishment of nonlinear formula can better characterize the relationship between flow velocity and hydraulic gradient. A well-established model for considering nonlinear flow through base course material was proposed by Fwa et al. [13]:

V ¼ k1 i

m

ð2Þ

k1 ; m = Experimental coefficients Similarly, Izbash’s law/power law is another well-established equation to consider non-laminar flow through porous media [16]:

dH ¼ c1 Vn dx

ð3Þ

H = Hydraulic head (cm) c1 ; n = Experimental coefficients According to Fig. 7, the stored water inside the reservoir course drains out the side of the porous pavement. Therefore, the flow rate per unit length of the porous pavement is calculated by Eq. (4):

UðxÞ ¼ VhðxÞ

Fig. 4. Schematic drawing of the laboratory arrangement of the permeability test.

ð4Þ

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

G62.5/37.5

G62.5/37.5

G62.5/37.5

G50/25

G50/25

G50/25

G62.5/0.075

G62.5/0.075

G62.5/0.075

a Original 2D image inside the main chamber of apparatus

b Binary format of 2D image (Pores in black)

c Mold for measurement of unit weight of compacted specimen

Fig. 5. Control the compaction level of aggregate specimen inside the main chamber of the permeability test apparatus by establishment of scale mold and measurement of unit weight.

Fig. 6. Schematic cross-section of the reservoir layer of the porous pavement structure.

UðxÞ = Flow rate per unit length of the porous pavement of urban street (cm2/s) hðxÞ = Elevation of water in the reservoir layer (cm)

Furthermore, the flow rate per unit length along the longitudinal direction of the porous pavement can be computed by the Eq. (5):

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Fig. 7. Water table in the reservoir course of the porous pavement structure (after Charbeneau and Barrett 2008 [8]).

UðxÞ ¼ rx

ð5Þ

3.1. Laminar flow condition

r = Constant rainfall rate (cm/s) x = Distance from the centerline of the urban street based on the Fig. 5 (cm)

The Eq. (13) is simplified by assuming the laminar flow condition (n = 1) as follows:

Incorporating Eqs. (4) and (5) results in:



rx V¼ hðxÞ By substitution of the obtained equation for flow velocity in Izbash’s law, Eq.

ð6Þ (7) is

derived:

rxn dH ¼ c1 dx h

ð7Þ

Fig. 7 illustrates that the hydraulic gradient is comprised of gradient from inclination of the base of the reservoir layer and gradient from saturated thickness of the reservoir course as follows:

dH dh ¼ þs dx dx

ð8Þ

s = Inclination of the base of the reservoir layer (%) Combining Eqs. (7) and (8) leads to the main differential equation for steady flow through porous layer given by:

rxn dh ¼ c1 s dx h

ð9Þ

To further separate the Eq. (9), the following new variable is defined:

g¼

h x

ð10Þ

dx gdg ¼ 2 g þ sg þ c 1 r x

ð14Þ

Charbeneau and Barrett [8] presented a solution for Eq. (14) by considering different rainfall rates. For this purpose, the following quantity was defined:

u ¼ 4c1 r  s2

ð15Þ

The positive values of u (u > 0) corresponds to the higher rainfall rates. In this case, the solution of Eq. (14) was found as follows [8]: 2

1 h þ sxh þ c1 rx2 ln 2 s hL þ sxhL þ c1 rL2

!

! h 2 1 2 =x þ s  pffiffiffiffi tan pffiffiffiffi

2 2hL =L þ s þ pffiffiffiffi tan1 pffiffiffiffi

u

u

u

!

¼0

u

ð16Þ

In which, boundary condition was provided by assuming water elevation in the downstream of the reservoir layer as hL (hðLÞ ¼ hL ). As presented in the Eq. (16), the analytical solution of Charbeneau and Barrett [8] is modified by incorporating reverse of the hydraulic conductivity coefficient based on the Darcy’s law (i.e. c1) and assuming a negative value for the slope of the base of the reservoir layer (i.e. s).

In which,

dh dg ¼gþx dx dx

3.2. Turbulent flow condition

ð11Þ

Substitution of the Eq. (11) and new defined variable g into the differential equation (9), results in:

x


n dg r þgþs ¼ c1 dx g

ð12Þ

Generally, by making transformation, the Eq. (13) is derived:



dx gn dg ¼ nþ1 g x þ sgn þ c1 rn

ð13Þ

The following subsections explain the solution of the obtained differential equation by considering various flow conditions.

The Eq. (13) is converted to the following equation in the case of the turbulent flow condition by considering the value of 2 for coefficient n (based on the power law or Izbash’s law):



dx g2 dg ¼ 3 g þ sg2 þ c1 r2 x

ð17Þ

Generally, the derived differential equation based on the power law for water flow though porous layer is the same as the differential equation obtained by Eck et al. [11] in which Forchheimer’s equation was assumed for nonlinear flow. The following discriminant was used in the study conducted by Eck et al. [11]:

D ¼ P2  Q 3

ð18Þ

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

a ¼ g1=2

Where, P and Q were given by Press et al. [24]:

2s þ 27c1 r 54 3

P¼ Q¼

2

2

s 9

ð19Þ ð20Þ

33

ð32Þ

In which,

dg ¼ 2ada

ð33Þ

By transformation of the Eq. (31), the differential equation is given by:

dx 2a4 da ¼ 5 a þ Sa3 þ c1 r1:5 x

Eck et al. [11] presented the solution of Eq. (17) by considering various rainfall rates. For higher rainfall rates (D > 0), the Eq. (17) was factorized as follows [11]:



dx g2 dg  ¼ x ðg  k1 Þðg2 þ Bg þ CÞ

Fourth order Runge-Kutta method is used to numerically solve derived differential equation for determination of drainage potential of reservoir layer as a porous course.

ð21Þ

ð34Þ

In which, the introduced parameters were given by:

B ¼ s þ k1

ð22Þ

4. Results and discussion

C ¼ k1 B

ð23Þ

4.1. Results of large-scale constant head permeability test


 Q s  k1 ¼ M þ M 3

ð24Þ

where,

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=3 M ¼ sgnðPÞ jPj þ P2  Q 3

ð25Þ

Based on the above-mentioned parameters, the solution of the differential equation (21) was given by Eck et al. [11]: 0

1
 2 x  h=x  k1 E @ hx þ B hx þ C A ln þ :ln þ D:ln 2 L 2 hL =L  k1 ðhLL Þ þ B hLL þ C 2 0 1 0 13 G 6 B h=x þ B=2 C B hL =L þ B=2 C7 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4arctan@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA  arctan@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA5 ¼ 0 2 2 C  B =4 C  B =4 C  B2 =4 ð26Þ

In which, the provided boundary condition was considered the same as the laminar flow regime (hðLÞ ¼ hL ). Also, the presented parameters were defined as follows [11]:

D¼

k1 B þ k1 þ C=k1

ð27Þ

E¼1D

ð28Þ

DC k1

ð29Þ

F¼

G¼F

BE 2

ð30Þ

In the present study, the solution given by Eck et al. [11] is modified by considering the constant value of c1r2 based on the assumed power law for water flow condition. 3.3. Flow condition between laminar and turbulent



dx g dg ¼ 2:5 g þ Sg1:5 þ c1 r1:5 x

4.1.2. Effect of aggregate gradation, morphology and compaction level on permeability To investigate the relative effect of change in gradation of aggregate, morphological properties of particles as well as compaction level of granular assembly on hydraulic conductivity, the percentage of variation of permeability coefficient for each specific property is computed. The percentage of variation of k1 due to change in compaction level from 100% to 90% is computed as follows:

Dk1; 100%!90% ¼

To further elaborate the flow regime through porous material (such as reservoir layer of porous pavement), the water movement is considered between laminar and turbulent flow condition. The Eq. (13) can be simplified to the following equation by assuming a value of 1.5 for coefficient n to characterize flow regime between laminar and turbulent conditions: 1:5

4.1.1. Summary results In the present study, large-scale permeability test under constant head condition was conducted on crushed stone aggregate as well river aggregate with different characterized gradation curves and compaction levels. Fig. 8 shows the relationship between water flow velocity and hydraulic gradient for some specific PSDs of river aggregate with 100% compaction level. As shown, the correlation of i and V is nonlinear for established gradations of aggregate. The same trend was observed for permeability tests carried out on crushed stone aggregate as reported in the research work conducted by Koohmishi and Shafabakhsh [21]. Also, Koohmishi and Palassi [20] found a nonlinear flow condition through railway ballast samples by carrying out constant head permeability test. Generally, increasing the water flow velocity eventuates in dominating the inertia forces and consequently completely turbulent flow regime [5]. Table 2 presents the summary results of permeability tests on river and crushed stone aggregate by presuming power law model (characterized in Eqs. (2) and (3)). It is obvious that decreasing the size of particles results in lower values of permeability coefficients (k1). In this relation, investigation of permeability of clogged porous asphalt mixtures with diverse initial PSD of aggregate showed that the property of aggregate gradation well-correlated with measured hydraulic conductivity was d15 (the size of particle for which 15% of material is finer). The obtained results demonstrated that increment of the size of d15 resulted in higher permeability values [23].

ð31Þ

To simplify the Eq. (31), the following new variable is defined:

k1;

 k1; 100%  100 k1; 100%

90%

ð35Þ

Dk1; 100%!90% = Percent change of k1 (%) k1; 100% = The value of k1 for compaction level of 100% k1; 90% = The value of k1 for compaction level of 90% Similarly, the percent change of k1 is calculated for variation of gradation (from G62.5/37.5 to G 62.5/0.075) and rock type (from crushed stone to river aggregate). Fig. 9 represents the percent change of permeability coefficient by variation of different characterized properties of reservoir course aggregate. Evidently,

34

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

1.00

Grading type: G62.5/37.5

1.00

Sample 1 Sample 2 Sample 3 Power Law (Average)

0.90

Hydraulic gradient

Hydraulic gradient

1.20

0.80 0.60

y = 5.017x2.221 R² = 0.950

0.40 0.20

0.80 0.70

Grading type: G62.5/25 Sample 1 Sample 2 Sample 3 Power Law (Average)

0.60

y = 5.004x2.002 R² = 0.946

0.50 0.40 0.30 0.20 0.10

0.00 0.00

0.10

0.20

0.30

0.40

0.00 0.00

0.50

Discharge velocity (cm/s)

1.00 0.80

Grading type: G50/25

1.20

Sample 1 Sample 2 Sample 3 Power Law (Average)

0.60

y = 4.909x1.975 R² = 0.976 0.40 0.20 0.00 0.00

1.00 0.80 0.60 0.40

0.10

0.20

0.30

0.40

0.00 0.00

0.50

0.80 0.60

Grading type: G37.5/2.35

1.20

Sample 1 Sample 2 Sample 3 Power Law (Average)

y = 6.256x1.750 R² = 0.994

0.40 0.20 0.00 0.00

0.40

Grading type: G62.5/9.5 Sample 1 Sample 2 Sample 3 Power Law (Average)

y = 5.803x1.908 R² = 0.993

0.10

0.20

0.30

0.40

0.50

Discharge velocity (cm/s)

Hydraulic gradient

Hydraulic gradient

1.00

0.30

0.20

Discharge velocity (cm/s)

1.20

0.20

Discharge velocity (cm/s)

Hydraulic gradient

Hydraulic gradient

1.20

0.10

1.00 0.80 0.60

Grading type: G62.5/0.075 Sample 1 Sample 2 Sample 3 Power Law (Average)

y = 5.499x1.413 R² = 0.949

0.40 0.20

0.10

0.20

0.30

0.40

Discharge velocity (cm/s)

0.00 0.00

0.10

0.20

0.30

Discharge velocity (cm/s)

Fig. 8. Correlation of water discharge velocity with hydraulic gradient based on the results of large-scale constant head permeability test on reservoir course aggregate (Rock type: River aggregate – Compaction level: 100%).

the change in gradation has substantial effect on the permeability coefficient (around 35% to 45%). The influence of variation of compaction level on hydraulic conductivity is lower (less than 15%). Finally, the change in aggregate morphology (from crushed to river) has the least effect on drainage of reservoir course aggregate. 4.1.3. Effect of gradation, aggregate morphology and compaction on water flow regime To further elucidate the water flow regime through river and crushed stone aggregate, Fig. 10 illustrates the variation of m and n values (based on the power trend line characterized in Eqs. (2) and (3)) for different considered compaction levels of each specific gradation. As expected, the change in gradation from more uniform to finer gradation with a broader range of particle sizes eventuates in variation of exponent coefficient (n value) from more than 2 to

less than 1.5. The average values of n are a little bit higher for river aggregate which characterizes more turbulence of flow through porous media comprised of rounded river aggregate. Higher nonlaminar flow regime through reservoir layer comprised of river aggregate can be associated with morphological properties (less angularity and more smooth surface texture) of rounded aggregate which causes less tortuosity of water movement path through porous media. Ghabchi et al. [14] conducted falling head permeability test on aggregate used as base layer and similarly observed that the value of permeability coefficient increased as long as the morphological properties of aggregate characterized lower angularity and higher sphericity. In the previous research work conducted by Koohmishi and Palassi [17], quantification of morphological properties of coarse aggregate showed substantial increment of surface roughness and corner angularity of crushed aggregate in comparison with river aggregate.

35

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44 Table 2 Results of conducting permeability test on aggregate of reservoir layer for two different rock types, diverse characterized gradations and various compaction levels. Compaction level

Gradation type

Average values of coefficients of power law relationship V = k1im [13]

Aggregate type: Crushed stone 100% G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

i = c1Vn [16]

k1 (cm/h)

m

R2

c1

n

R2

0.435 0.409 0.411 0.353 0.328 0.242

0.459 0.506 0.512 0.589 0.613 0.743

0.945 0.989 0.936 0.969 0.984 0.992

5.015 5.638 4.504 5.253 5.800 6.572

2.060 1.954 1.828 1.644 1.604 1.335

0.945 0.989 0.936 0.969 0.984 0.992

95%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

0.456 0.429 0.428 0.375 0.351 0.281

0.408 0.436 0.440 0.482 0.518 0.632

0.958 0.991 0.943 0.973 0.989 0.986

5.834 6.765 5.542 6.915 7.225 7.058

2.347 2.273 2.145 2.020 1.910 1.560

0.958 0.991 0.943 0.973 0.989 0.986

90%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

0.472 0.442 0.440 0.390 0.366 0.294

0.390 0.410 0.412 0.453 0.480 0.565

0.961 0.991 0.941 0.969 0.987 0.986

5.920 7.100 5.841 7.100 7.721 8.250

2.468 2.416 2.283 2.142 2.056 1.744

0.961 0.991 0.941 0.969 0.987 0.986

Aggregate type: River aggregate 100% G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

0.462 0.422 0.435 0.395 0.349 0.280

0.428 0.473 0.494 0.520 0.568 0.671

0.950 0.946 0.976 0.993 0.994 0.949

5.017 5.004 4.909 5.803 6.256 5.499

2.221 2.002 1.975 1.908 1.750 1.413

0.950 0.946 0.976 0.993 0.994 0.949

95%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

0.488 0.462 0.470 0.426 0.381 0.300

0.389 0.434 0.441 0.450 0.504 0.544

0.963 0.940 0.967 0.990 0.990 0.971

5.506 4.674 4.892 6.403 6.537 8.136

2.479 2.164 2.192 2.201 1.963 1.785

0.963 0.940 0.967 0.990 0.990 0.971

90%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

0.505 0.479 0.477 0.442 0.396 0.317

0.374 0.402 0.411 0.424 0.472 0.518

0.968 0.937 0.963 0.986 0.990 0.951

5.485 4.846 5.220 6.509 6.861 7.505

2.589 2.329 2.341 2.325 2.100 1.836

0.968 0.937 0.963 0.986 0.990 0.951

Fig. 11 illustrates different models considered for establishment of correlation between i and V in logarithmic scale to further elaborate water flow regime through reservoir course aggregate. Fully turbulent flow regime as an extreme condition is modeled by establishment of n value of 2 based on the Izbash’s law, while the transitional flow regime is characterized by considering n value of 1.5 to develop a trend line between discharge velocity and hydraulic gradient. A cursory glance at Fig. 11 shows that considering the extreme value of 2 for exponent coefficient can better characterize the flow condition in the case of provision of more uniform gradation (G62.5/37.5). While, the hydraulic gradient and flow velocity are well-correlated in logarithmic scale by establishment of n value of 1.5 based on the power law model for finer PSD comprised of broader range of aggregate (G62.5/0.075). These variations based on the applied trend lines clarify that finer gradation of aggregate with higher values of Cu results in less turbulence of flow regime; nevertheless, Darcy’s equation does not still specify water flow condition. Table 3 presents the summary results of applying different models on derived laboratory data. The abovementioned correlation between i and V is also recognized as Missbach’s equation, in which the exponent coefficient comes close to 1

for laminar flow condition and tends to 2 for turbulent flow regime [31]. Similarly, Ranieri et al. [25] observed that the water movement through permeable friction courses was transitional flow regime and the laminar flow condition was attained as long as hydraulic heads between 0.1 and 1 cm were applied. 4.2. Results of estimation of water level in the reservoir course of the porous pavement 4.2.1. Considered conditions for determination of water level of the reservoir layer The permeability of different considered gradations suited for reservoir layer of the porous pavement was determined by conducting the laboratory tests on aggregate specimens. In this section, the obtained results from constant head permeability test are combined with the developed analytical procedure to estimate the water level in the reservoir course of the porous pavement structure. Also, fourth order Runge-Kutta method is used to numerically solve the derived differential equations. Fig. 12 schematically demonstrates three different conditions assumed for water flow regime based on the analytical solutions including:

36

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Fig. 9. Effect of variation of aggregate gradation, particle morphology and compaction level on hydraulic conductivity of reservoir course aggregate.

37

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Average value of coefficient m

100%

0.74

95%

0.7

0.67 2.47 0.59

0.6 0.5

0.61 0.57

0.46

0.39

0.41 0.41

0.45

0.48

0.3 0.2 0.1

0.47

0.49

2.28

0.52 0.47

0.43 0.37

0.40 0.41

Crushed

1.95

2.5 2.10

2.06

2.22 1.74

1.83

1.84 2 2.00 1.98

1.91 1.75

1.64 1.60

0.42

Crushed

m Value

1.5 1.41

1.34

River

3

2.33 2.34 2.33 2.14

0.52 2.06

i=c1.Vn 2.59

2.42

0.57

0.51 0.51

0.4

90%

1

River

0.5

Average value of coefficient n

V=k1.im

0.8

n Value

0

0

Grading type Fig. 10. Variation of exponent coefficients (m and n) of applied power law on experimental data for various characterized properties of aggregate of reservoir layer.

laminar flow, turbulent flow, and flow regime between extreme conditions. As represented in Fig. 7, the slope of the base of the reservoir layer (s) and the distance between the centerline of the urban roadway and downstream of the reservoir course (L) is specified based on the typical cross-section for urban streets. Initially, the hydraulic boundary condition at right-hand side (hL) is considered equal to 1 cm which characterizes a low water level in the vicinity of the downstream. Furthermore, higher value of rainfall rate (r) is established since porous pavement is conventionally considered as an economical construction method in region with substantial rate of precipitation. Meanwhile, variable values of hL and r are finally considered to apply a sensitivity analysis on the effect of boundary condition and rainfall rate on predicted water level. 4.2.2. Effect of gradation and compaction level on water level of the reservoir layer Fig. 13 compares the estimated water level in the reservoir layer for two extreme gradations of aggregate (G62.5/37.5 and G62.5/0.075) to figure out the influence of assumed flow conditions on drainage potential. Generally, considering linear flow regime (n = 1) results in higher values of water level in comparison with fully turbulent flow condition (n = 2). As expected, the determined water level is considerably higher for finer gradation with broader range of aggregate, i.e. G62.5/0.075. By assuming completely turbulent flow condition, the predicted water table of the reservoir course comprised of broader range of aggregate (G62.5/0.075) is around 100% higher than the estimated values for reservoir layer with more uniform gradation of aggregate (G62.5/37.5). Fig. 14 relatively compares the effect of PSD and compaction level on average value of estimated water level in the reservoir course. It is apparent that provision of finer gradation with broader size range (G62.5/0.075) results in remarkable increment of average water level in this granular layer (around 50% to 150%). Nevertheless, the average value of estimated water level is less influenced by change in compaction level (around 10% to 50%).

models, lower values of water level of the reservoir course are estimated in the case of river aggregate. The percentage of reduction of water film depth along the reservoir layer is around 10% to 20% by provision of rounded aggregate. Generally, less tortuosity of porous media comprised of river aggregate leads to enhancement of permeability potential of coarse particles and consequently estimation of lower values of water level in the reservoir course. Meanwhile, the granular layer comprised of crushed stone aggregate creates structurally stronger course yet with an acceptable pervious potential. Again, Fig. 15 indicates substantial effect of considered gradation on predicted water table in the reservoir course whether crushed stone is used as granular material or river aggregate. 4.2.4. Effect of rainfall rate and boundary condition on water level of the reservoir course Commonly, the predicted water table of this porous media can fundamentally change by variation of amount of precipitation over porous pavement surface and assumed water elevation in the downstream of the reservoir layer. Fig. 16 concisely shows the average values of estimated water level in the reservoir course derived by variation of rainfall rate (r) and boundary condition (hL) for different characterized properties of aggregate assembly. As expected, the average water level of the reservoir course increases by increment of rainfall rate and water elevation in the downstream of the reservoir layer (hL). A cursory glance at Fig. 16 demonstrates that the average value of predicted water level is less affected by variation of hL for higher rainfall rates. In the case of non-uniform gradation of aggregate (G62.5/0.075), change in value of hL from 1 cm to 15 cm increases water level by 97% for low rainfall rate (i.e. 2.5 cm/h), while the maximum increment of water level is around 16% for high rainfall rate (i.e. 20 cm/h). Also, Fig. 16 emphasizes that increment of water height on boundary of reservoir course leads to the reduction of the effect of change in rainfall rate on average value of estimated water level (especially in cases associated with more uniform PSD). 4.3. Discussion

4.2.3. Effect of aggregate morphology on water level of the reservoir course To further compare the drainage potential of reservoir course comprised of river aggregate with that of porous media made up of crushed stone, Fig. 15 is drawn. Based on the different statistical

Previous researches have further elaborated the mechanical performance of coarse-grained granular layers (such as railway ballast layer and reservoir course) comprised of crushed-stone aggregate with a broader range of particle size distribution

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

ln (V)

0 -5 -1

-4

-3

ln (V)

0 -2

-1

-4

0

n=1.335: ln(i) = 1.335 ln(V)+1.88 R² = 0.992 n=2: ln(i) = 2 ln(V)+3.68 n=1.5: ln(i) = 1.5 ln(V)+2.33

-1

-3

-2

-1

0

n=1.744: ln(i) = 1.744 ln(V)+2.11 R² = 0.986 n=2: ln(i) = 2 ln(V)+2.67 n=1.5: ln(i) = 1.5 ln(V)+1.57

-2 -2

ln (i)

ln (i)

-3

-4

n=2.060: ln(i) = 2.060 ln(V)+1.61 R² = 0.945 n=2: ln(i) = 2 ln(V)+1.51 n=1.5: ln(i) = 1.5 ln(V)+0.65

-5

-3 n=2.468: ln(i) = 2.468 ln(V)+1.78 R² = 0.961 n=2: ln(i) = 2 ln(V)+1.08

-4

n=1.5: ln(i) = 1.5 ln(V)+0.33

-5

-6

Main data (G62.5/37.5) Main data (G62.5/0.075) Trend line (Main data) Trend line (n=2) Trend line (n=1.5)

-7

Main data (G62.5/37.5) Main data (G62.5/0.075) Trend line (Main data) Trend line (n=2) Trend line (n=1.5)

-6

Grading type: G62.5/37.5 and G62.5/0.075

Grading type: G62.5/37.5 and G62.5/0.075

Compaction level: 100%

Compaction level: 90%

a Rock type: Crushed stone

ln (V)

0 -5 -1

-4

-3

ln (V)

0 -2

-1

-5

0

n=1.413: ln(i) = 1.413 ln(V)+1.70 R² = 0.949 n=2: ln(i) = 2 ln(V)+3.18 n=1.5: ln(i) = 1.5 ln(V)+1.92

-1

-4

-3

-2

-1

0

n=1.836: ln(i) = 1.836 ln(V)+2.02 R² = 0.951 n=2: ln(i) = 2 ln(V)+2.36 n=1.5: ln(i) = 1.5 ln(V)+1.31

-2 -2

ln (i)

ln (i)

-3

-3

-4

-5

n=2.221: ln(i) = 2.221 ln(V)+1.61 R² = 0.950 n=2: ln(i) = 2 ln(V)+1.25

n=2.589: ln(i) = 2.589 ln(V)+1.70 R² = 0.968 n=2: ln(i) = 2 ln(V)+0.86 n=1.5: ln(i) = 1.5 ln(V)+0.14

-4

n=1.5: ln(i) = 1.5 ln(V)+0.44

-6

-7

Main data (G62.5/37.5) Main data (G62.5/0.075) Trend line (Main data) Trend line (n=2) Trend line (n=1.5)

Grading type: G62.5/37.5 and G62.5/0.075

-5 Main data (G62.5/37.5) Main data (G62.5/0.075) Trend line (Main data) Trend line (n=2) Trend line (n=1.5)

-6

Grading type: G62.5/37.5 and G62.5/0.075

Compaction level: 100%

Compaction level: 90%

b Rock type: River aggregate Fig. 11. Application of different statistical models on variation of water discharge velocity with hydraulic gradient derived from conducting permeability test on aggregate of reservoir layer.

[18,19,33,35,36]. Koohmishi and Palassi [18] resembled the dynamic loading of passing train by conducting large-scale impact test on ballast aggregate. The obtained results showed that the degradation of ballast aggregate decreased by establishment of a broader range of aggregate. Xiao et al. [33] experimentally determined the resilient modulus as well as the shear

strength of base and subbase materials with diverse gradation. They concluded that the gravel-to-sand ratio (a parameter related to the gradation) directly influenced the shear strength of aggregate. Also, Zaika and Djakfar [36] observed higher values of California bearing ratio (CBR) for crushed stone material and figured out contradict relation between CBR value and porosity by con-

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Table 3 Summary results of establishment of different statistical models on laboratory data of carrying out large-scale constant head permeability test on material of reservoir layer. Compaction level

Gradation type

Established statistical model on derived experimental data (with fixed exponent coefficient) i = c1Vn Linear (Darcy’s law) i = c1V

Aggregate type: Crushed stone 100% G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075 90%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

Aggregate type: River aggregate 100% G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075 90%

G62.5/37.5 G62.5/25 G50/25 G62.5/9.5 G37.5/2.35 G62.5/0.075

Nonlinear (Izbash’s law/Power law) i = c1V2

Nonlinear (Izbash’s law/Power law) i = c1V1.5

n

c1

R2

n

c1

R2

n

c1

R2

n=1

1.670 1.992 1.964 2.424 2.657 3.808

0.723 0.868 0.751 0.878 0.881 0.931

n=2

4.524 6.091 6.188 11.012 13.965 39.777

0.945 0.989 0.928 0.924 0.924 0.746

n = 1.5

1.923 2.648 2.454 3.893 4.605 10.269

0.875 0.936 0.907 0.962 0.980 0.977

n=1

1.405 1.721 1.639 1.946 2.119 2.744

0.663 0.805 0.671 0.784 0.835 0.855

n=2

2.942 3.896 3.719 5.552 6.955 14.493

0.927 0.962 0.927 0.965 0.986 0.964

n = 1.5

1.393 1.894 1.675 2.329 2.730 4.816

0.813 0.849 0.831 0.882 0.915 0.966

n=1

1.447 1.727 1.781 2.095 2.317 3.365

0.698 0.675 0.804 0.887 0.904 0.867

n=2

3.504 4.988 5.144 6.938 10.581 24.141

0.941 0.946 0.976 0.991 0.974 0.785

n = 1.5

1.553 1.943 2.000 2.630 3.695 6.840

0.850 0.887 0.920 0.947 0.974 0.945

n=1

1.231 1.373 1.479 1.746 1.895 2.653

0.644 0.592 0.715 0.811 0.859 0.811

n=2

2.362 2.856 3.002 3.818 5.732 10.610

0.917 0.918 0.942 0.967 0.988 0.943

n = 1.5

1.156 1.279 1.335 1.680 2.333 3.692

0.796 0.818 0.838 0.862 0.910 0.919

Fig. 12. Flowchart of considered conditions for determination of water level in the reservoir layer of the porous pavement structure.

sidering different gradation band of reservoir base aggregate. However, more uniform gradation of aggregate leads to higher porosity of media, more permeability of layer and consequently less water elevation of the reservoir course. In regard to the drainage properties, Fig. 17 presents the maximum values of predicted water level (typically at the centerline of the urban street) in the reservoir course by taking into account the rainfall

rate, boundary condition, gradation of aggregate and type of material. Although, Fig. 17 confirms better drainage capability of reservoir layer comprised of river aggregate with single-sized PSD, the effect of gradation is more evident. As illustrated, the estimated water elevation is considerably lower than the typical thickness of the reservoir layer (i.e. 300 mm) as long as more uniform gradation (G62.5/37.5) is established. Nevertheless, the

40

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Gradation: G62.5/37.5 and G62.5/0.075 r= 5 cm/h ; L=3 m ; S= -1.5% Linear (n=1) Power Law (n=2) Linear (n=1) Power Law (n=2) Runge-Kutta (n=1) Runge-Kutta (n=2) Runge-Kutta (n=1.5) Runge-Kutta (n=1.5)

25

Gradation: G62.5/37.5 and G62.5/0.075 r= 5 cm/h ; L=3 m ; S= -1.5% Linear (n=1) Power Law (n=2) Linear (n=1) Power Law (n=2) Runge-Kutta (n=1) Runge-Kutta (n=2) Runge-Kutta (n=1.5) Runge-Kutta (n=1.5)

25

20

15

15 H (cm)

H (cm)

20

10

10

5

5

0

0 0

50

100

150 x (cm)

200

250

0

300

50

100

150 x (cm)

200

250

300

b River aggregate (G62.5/37.5 and G62.5/0.075)

a Crushed stone (G62.5/37.5 and G62.5/0.075)

2

n=1

n = 1.5

n=1

40%

34%

49%

n=2

20%

4

17%

19%

6

21%

8

42%

12 10

River aggregate 14%

14

Crushed stone

10%

20%

16

i=c1.Vn

18

Aggregate type: crushed and river --- Gradation: G62.5/37.5 and G62.5/0.075 Compaction level: 100% and 90% r= 5 cm/h ; L=3 m ; S= -1.5%

11%

Average water level in the reservoir course (cm)

Fig. 13. Effect of considered statistical model of flow regime on water level in the reservoir course of the porous pavement structure for two different extreme gradations (Compaction level: 100%).

n = 1.5

n=2

0

100% Gradation type

90%

Fig. 14. Effect of aggregate gradation and compaction level on average water level in the reservoir course for two different types of aggregate based on various considered models of flow regime.

maximum amount of predicted water level approaches to the values more than the thickness of the reservoir layer in the cases associated with finer gradation of aggregate (G62.5/0.075) under higher rainfall rates. This figure further corroborates minor effect of boundary condition on estimated water level in the reservoir course subjected to considerable amount of rainfall rate.

5. Conclusions Present study evaluated the drainage capacity of reservoir layer of porous pavement by establishment of experimental as well as analytical approaches. Various important properties of granular material including the morphological characteristic, the particle size

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Crushed stone and river aggregate - n=1 r= 5 cm/h ; L=3 m ; S= -1.5%

25

Crushed stone and river aggregate - n=2 r= 5 cm/h ; L=3 m ; S= -1.5%

14

12 20 10

H (cm)

H (cm)

15

8

6 10

Crushed stone-G62.5/37.5 River aggregate-G62.5/37.5 Crushed stone-G37.5/2.35 River aggregate-G37.5/2.35 Crushed stone-G62.5/0.075 River-G62.5/0.075 Crushed stone-Runge-Kutta River aggregate-Runge-Kutta

5

0 0

50

100

150 x (cm)

200

250

Crushed stone-G62.5/37.5 River aggregate-G62.5/37.5 Crushed stone-G37.5/2.35 River aggregate-G37.5/2.35 Crushed stone-G62.5/0.075 River-G62.5/0.075 Crushed stone-Runge-Kutta River aggregate-Runge-Kutta

4

2

0 0

300

a Linear flow condition (n=1)

50

100

150 x (cm)

200

250

300

b Fully turbulent flow condition (n=2)

Crushed stone and river aggregate - n=1.5 r= 5 cm/h ; L=3 m ; S= -1.5%

16 14 12

H (cm)

10 8 6 Crushed stone-G62.5/37.5-Runge-Kutta River aggregate-G62.5/37.5-Runge-Kutta Crushed stone-G37.5/2.35-Runge-Kutta River aggregate-G37.5/2.35-Runge-Kutta Crushed stone-G62.5/0.075-Runge-Kutta River aggregate-G62.5/0.075-Runge-Kutta

4 2 0 0

50

100

150 x (cm)

200

250

300

c Flow condition between laminar and turbulent (n=1.5) Fig. 15. Comparison of estimated water level in the reservoir course of porous pavement structure for two different rock types and diverse PSDs of aggregate under various assumed flow conditions (Compaction level: 100%).

distribution and level of compaction are considered. The hydraulic conductivity of reservoir course aggregate was measured by carrying out large-scale constant head permeability test on crushed stone aggregate as well as river aggregate. Then, the analytical method was utilized to determine the water table in the reservoir layer. The following conclusion can be drawn from the present study:

– The hydraulic conductivity is relatively higher for river aggregate in comparison with crushed stone which results in estimation of lower values of water elevation in the reservoir course. – The effect of level of compaction on hydraulic conductivity of reservoir course aggregate is more than the type of rock

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M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

Gradation: G62.5/37.5 --- Fully turbulent flow condition (n=2) hL= 1, 7.5,10 cm --- r= 2.5, 10, 20 cm/h --- S= -1.5% --- L= 3 m River aggregate

Compaction: 100%

Compaction: 90%

4% 11%

7% 15%

44% 75%

34%

2.5 cm/h 10 cm/h 20 cm/h

275%

2.5

48%

259%

40%

45%

73%

46%

73% 265%

5

52%

7.5

51%

10

71%

12.5

5% 13%

8% 18%

Crushed stone

15

250%

Average water level of the reservoir course (cm)

17.5

Compaction: 100%

Compaction: 90%

0 1

7.5

15

1

7.5

15 1 hL (cm)

7.5

15

1

7.5

15

a Gradation type: G62.5/37.5

Crushed stone

River aggregate

2.5 cm/h 10 cm/h 20 cm/h

Compaction: 90%

49% 80%

176%

Compaction: 100%

24% 28%

35% 37%

5 Compaction: 100%

59%

51% 99%

165%

57%

31% 29%

50% 89%

52%

171%

10

58%

15

109%

47%

20

56%

25

40%

30

159%

Average water level of the reservoir course (cm)

35

Gradation:G62.5/0.075--Flow condition between laminar and turbulent (n=1.5) hL= 1, 7.5,10 cm --- r= 2.5, 10, 20 cm/h --- S= -1.5% --- L= 3 m

Compaction: 90%

0 1

7.5

15

1

7.5

15 1 hL (cm)

7.5

15

1

7.5

15

b Gradation type: G62.5/0.075 Fig. 16. Sensitive analysis of influence of rainfall rate and boundary condition on average value of estimated water level in the reservoir course of porous pavement structure for various characterized properties of aggregate.

material. Meanwhile, the established gradation is the most important property which affects the hydraulic conductivity of aggregate. – Generally, water flow through specimen comprised of more uniform coarse gradation with lower compaction level shows extremely turbulent flow condition (with exponent coefficient of Izbash’s law/power law around 2). River aggregate exacerbates the nonlinearity of flow due to less tortuosity of sample. – Increasing the non-uniformity of aggregate gradation along with improvement of compaction level results in less turbulence of water flow as characterized by changing the exponent of Izbash’s law/power law toward value less than 1.5.

– The average water level of the reservoir course is mainly influenced by PSD rather than the compaction level or aggregate morphology. – Generally, the change in rainfall rate remarkably affects the water elevation of the reservoir course wherever water height on boundary of this granular media is lower. Similarly, variation of boundary condition substantially influences the estimated water level in case of lesser rainfall rate. – Considering linear flow condition leads to estimation higher water level in the reservoir course of the permeable pavement. Therefore, considering real flow condition eventuates in more precise determination of the water level in this porous media.

43

M. Koohmishi / Construction and Building Materials 203 (2019) 27–44

hL= cm 0 cm hL=0

hL= cm 5 cm hL=5

hL= 7.5cm cm hL=7.5

hL=10 cmcm hL= 10

hL= 12.5cm cm hL=12.5

hL=15 cm hL= 15 cm

Maximum water level in the reservoir course (cm)

35 G62.5/37.5

G62.5/0.075

30 Thickness of reservoir course = 30 cm

25 20

Crushed stone aggregate

River aggregate

15 10 5

Crushed stone aggregate

River aggregate

0 2.5 5

10 15 20 2.5 5

10 15 20 2.5 5 r (cm/h)

10 15 20 2.5 5

10 15 20

Fig. 17. Range of maximum water level in the reservoir course of porous pavement by establishment of various values of rainfall rate and boundary condition (Characterized for two different rock types and two extreme gradations of aggregate).

Conflict of interest The author declares that he has no conflict of interest

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