Dynamics of the water infiltration process in permeable pavement using in situ experimentation and numerical simulation with hydrus-2D

Dinâmica do processo de infiltração da água em pavimento permeável utilizando experimentação in situ e simulação numérica com o hydrus-2D

ABSTRACT

This work presents a two-dimensional simulation of infiltration dynamics in a real permeable pavement (PP) structure in the city of Recife, representing more realistically the geometry of the infiltration bulb and the dynamics of water redistribution processes in the PP. Sixteen infiltration tests were carried out on the PP using the Beerkan method. The hydrodynamic parameters of the PP surface were determined by applying the inverse method to the infiltration data. Simulations of water transfer processes were carried out with Hydrus-2D using the hydrodynamic properties corresponding to the highest and lowest saturated hydraulic conductivity observed on the surface. Satisfactory infiltration characteristics were observed in the PP. The inverse method showed good adjustment capacity to the accumulated infiltration curves and estimation of hydrodynamic properties. Simulations using Hydrus-2D demonstrated that the infiltration process and water redistribution in the subgrade depend on the hydrodynamic properties of the coating.

Keywords:  Hydrus-2D; Infiltration; Compensatory technique; Beerkan Method

RESUMO

Esse trabalho apresenta uma simulação bidimensional da dinâmica da infiltração numa estrutura real de um pavimento permeável (PP) na cidade do Recife, representando de maneira mais realística a geometria do bulbo de infiltração e a dinâmica dos processos de redistribuição de água no PP. Foram realizados dezesseis ensaios de infiltração na superfície do PP utilizando o método Beerkan. Os parâmetros hidrodinâmicos da superfície do PP foram determinados aplicando o método inverso nos dados de infiltração. Simulações dos processos de transferência de água foram efetuadas com o Hydrus-2D utilizando as propriedades hidrodinâmicas correspondentes à maior e à menor condutividade hidráulica saturada observadas superficialmente. Observou-se características de infiltração satisfatórias no PP. O método inverso apresentou boa capacidade de ajuste às curvas de infiltração acumulada e de estimativa das propriedades hidrodinâmicas. As simulações usando o Hydrus-2D demonstraram que o processo de infiltração e redistribuição da água no subleito dependem das propriedades hidrodinâmicas do revestimento.

Palavras-chave:  Hydrus-2D; Infiltração; Técnica compensatória, Método Beerkan

INTRODUCTION

Urban occupation has caused changes in the components of the hydrological cycle, mainly favouring surface runoff to the detriment of water infiltration into the soil and aquifer recharge. Compensatory techniques for urban drainage are being used to reestablish the natural hydrological conditions existing in pre-urbanised basins, rescuing natural processes in river basins and reducing impacts in urban areas through valorising water infiltration and storage processes (Dong et al., 2017).

Permeable paving, infiltration trenches, green roof, rain gardens, bioretention and infiltration wells are some examples of compensatory techniques based on the phenomenon of infiltration and water storage in the soil (Ferreira et al., 2019; Marinho et al., 2020; Costa et al., 2020; Justino et al., 2021; Arboit et al., 2021; Lopes Bezerra et al., 2022). In particular, surfaces composed of coatings such as porous concrete, porous asphalt and interlocking blocks (hollow or non-hollow) are alternatives contained in the concepts of Water Sensitive Urban Design (WSUD) in Australia, Sustainable Urban Drainage System (SUDS) in the United Kingdom, Low Impact Development (LID), Best Management Practices (BMP) and Green Infrastructure (GI) in the USA, or Sponge City in China (Fletcher et al., 2015; Li et al., 2019; Nguyen et al., 2019).

Permeable pavement is an infiltration device in which surface runoff is diverted to a reservoir layer of granular material (gravel, stones) beneath the land's surface. Its use in urban areas aims to reduce effective precipitation (Rodriguez et al., 2024), improve water quality during the infiltration process with the retention of pollutants (Zhao et al., 2023; Ma et al., 2024; Huang et al., 2016) contribute to increased groundwater recharge (Ma et al., 2021; Barnes & Welty, 2019) consequently reduce the diameter of rainwater drainage conduits and this system's costs.

Efficiency analysis studies on permeable surfaces to reduce surface runoff have been widely reported in the Brazilian technical scientific literature (Araújo et al., 2000; Castro et al., 2013; Jabur et al., 2015; Marinho et al., 2020; Martins Vaz et al., 2021). In particular, the characterization of the infiltration capacity and hydrodynamic properties of the surface layer of a permeable pavement is essential for assessing the need for maintenance of these structures.

In this sense, several in situ experimental methodologies have been applied to evaluate the infiltration capacity and estimate the hydrodynamic properties in permeable pavements. Coutinho et al. (2016) used the semi-physical method Beerkan, with a seven-and-a-half centimeter infiltrometer, to estimate the parameters of the functions that reflect the retention curve h(θ) and the hydraulic conductivity curve K(θ) on a permeable pavement with interlocking blocks in the city of Recife. Marinho et al. (2020) expanded the scale of estimating infiltration capacity in permeable pavements by using infiltrometers with one meter in diameter, applying the Beerkan methodology and obtaining good performance in estimating hydrodynamic properties. Jabur et al. (2015) evaluated the infiltration capacity of permeable pavements using the Standard Test Method for Infiltration Rate of In Place Pervious Concrete methodology of the American Society for Testing and Materials (ASTM) C1701.

In addition to these methodologies, the physically based model Hydrus-1D has been widely used to estimate the hydrodynamic properties of soils in various contexts using optimisation techniques (Šimůnek et al., 2024; Hilten et al., 2008), where the inverse method stands out (Silva Ribas et al., 2021). The inverse method is a method for calibrating and optimizing unknown hydraulic parameters in porous media. It can be used to estimate hydrodynamic parameters of the hydraulic conductivity function k(h) and hydraulic retention curves θ(h) (Šimůnek et al., 2024). However, as far as the authors know, the use of the inverse method to estimate hydrodynamic properties using the experimental infiltration curve and the use of HYDRUS-2D to evaluate the geometry of the infiltration bulb and the dynamics of the water redistribution process on a real scale, taking into account the contrast of hydraulic properties mainly in the surface layer in permeable pavements has yet to be reported in the literature.

Two-dimensional modeling with Hydrus 2-D provides support for the observation of specific phenomena, such as preferential flows, which arise when there are contrasts in the hydraulic properties between different materials (Coutinho et al., 2015). This contrast is particularly notable in the case of permeable pavements, where the coating and reservoir layers often have superior hydraulic properties than the underlying supporting soil. This disparity creates favorable conditions for the emergence of preferential flows, phenomena that stand out especially in two or three-dimensional simulations.

Furthermore, two-dimensional modeling offers a more intuitive representation of infiltration bulb geometry and dynamics, both in homogeneous and heterogeneous media. This makes it possible to estimate the advance of the moisture front on a broader spatial scale. In summary, the two-dimensional approach not only allows a deeper understanding of preferential flows, but also facilitates the visualization and analysis of infiltration processes in different soil types and pavement configurations.

In this context, the present work proposes the use of the inverse method in solving the Richards equation for the particular case of infiltration with constant load, intending to calibrate the parameters of the retention curve and the conductivity curve with the aid of techniques of numerical simulation, adjusting the experimental curve of accumulated infiltration. The precise estimation of hydrodynamic parameters associated with the geometry of infiltration structures can enable the simulation of water transfer processes and evaluate the phenomenon of internal redistribution of infiltrated water more realistically, taking into account the details of the aspects of the construction of permeable pavements.

MATERIAL AND METHODS

Location and characteristics of the study area

The experimental site is in the parking lot of the School of Engineering of the Federal University of Pernambuco in Recife (Figure 1a). According to the Köppen classification, the region's climate is type Ama (Tropical Monsoon Climate) (Agência Pernambucana de Águas e Clima, 2023), with a rainy season in the winter period, with more significant precipitation from March to August, where 70% of the year's total precipitation occurs.

Figure 1
(a) Location of the study area. (b) Highlighted the experimental site located in the parking lot of the Pernambuco Engineering School – Technology and Geosciences Center. (c) Schematic of the pilot permeable pavement structure (dimensions in meters).

Rainfall data at the Várzea station belonging to the monitoring network of the Pernambucana Water and Climate Agency - APAC, for the period from 1994 to 2010, present an annual average of 2173.8 mm, with a minimum of 1255.4 mm and a maximum of 3482.0 mm. According to Coutinho et al. (2013), for a return time of 10 years, the region has a precipitation intensity of 85 mm/h, considering a rain duration of 30 minutes.

The permeable pavement was built to partially compensate for an impermeable area in the Technology and Geosciences Center (CTG-UFPE) parking lot. Two types of structures were built on site. The “structure 1” comprises a coating layer of interlocking blocks hollow with grass, a layer of sand and the subgrade, composed of urban soil, resulting from the site's earthing processes. The “structure 2” was built to compensate for an impermeable area of 110 m² is made up of a coating layer of interlocking blocks hollow with grass, a layer of sand that works as a filter, a reservoir layer made up of gravel with an average diameter of 19 mm and porosity of 43%, plus a layer of sand and the subgrade, and has 3 meters long (Figure 1b).

Methodology for simulating water transfer processes in permeable pavement

To simulate the water transfer processes in the permeable pavement, three steps were taken: began carrying out infiltration experiments in the field, then the estimating the hydrodynamic properties of the coating layer using the inverse method, and finally, two-dimensional simulation of the water transfer processes in the permeable pavement. Initially, infiltration tests were carried out on the surface of the permeable pavement using simple ring infiltration. For the two-dimensional simulation of water transfer processes in the permeable pavement, the hydrodynamic parameters of the surface layer were determined from the inverse method using Hydrus-1D. For the subsurface sand and subgrade layers, the estimates suggested by Rosetta (Schaap et al., 2001) for the sandy textural class and the hydrodynamic parameters estimated for the subgrade by Coutinho et al. (2020) were used.

Infiltration experiments

The infiltration tests were carried out in duplicate at points on the pavement surface. Infiltration points P2, P3, P4, P5 and P6 represent structure 1 and P1 represent structure 2 (Figure 2a). The development of vegetation was observed both between the hollow blocks and in their voids, forming a heterogeneous integrated system with concrete filled with soil, vegetation and its roots. The infiltration campaigns were carried out in three different months (P1 and P2 in September/2019; P3 and P4 in February/2020; P1, P2, P5 and P6 in March/2020). The Beerkan methodology described in Lassabatère et al. (2006) was used, with a single-ring infiltrometer measuring one meter in diameter (Figure 2b). The Beerkan method is a semi-physical method currently applied in experiments that evaluate infiltration in permeable pavements (Coutinho et al., 2016; Marinho et al., 2020). To carry out the test, the simple ring infiltrometer was inserted into the surface with the aid of bentonite to avoid lateral water losses during the infiltration process. Near the ring, a soil sample was collected and placed in a well-sealed aluminium container for laboratory analysis of the water content conditions in which the soil was found at the initial moment of carrying out the test.

Figure 2
Detail of the infiltration experiments: (a) Sketch (dimensions in meters); (b) Test records.

Defined volumes of water (20 litres) were poured into the cylinder, and the time required for all the water to infiltrate was recorded, repeating the process until infiltration became constant. A new soil sample was quickly collected to determine the final soil moisture.

The basic infiltration velocities were calculated to be compared with the saturated hydraulic conductivity obtained through the inverse method.

Inverse method

To estimate the hydrodynamic parameters using Hydrus-1D, a one-dimensional geometry of 9 cm in length was constructed and discretised into 181 nodes. Hydrus is a computational program that simulates water, heat and solute transport in one, two or three dimensions in saturated and unsaturated porous media (Šimůnek et al., 2016). Hydrus solves the Richards equation numerically, using the finite element method as a mathematical tool. The upper boundary condition was constant pressure with a 25.5 mmH₂O hydraulic head, it corresponds to the division of the volume of water applied by the area of the ring infiltrometer. The lower boundary condition was free drainage. The convergence criteria used were 0.001 for water content and 1 mm for matrix potential.

The objective function F to be minimised during the parameter estimation process is presented in Equation 1 (Šimůnek et al., 1998).

$$\begin{array}{l}F\left(b,q,p\right)={\displaystyle \sum }_{j=1}^{m_q}{v}_j{\displaystyle \sum }_{i=1}^{n_{qj}}{w}_{i,j}{\left[q_j^{*}\left(x,t_i\right)-q_j\left(x,t_i,b\right)\right]}^2+\\ {\displaystyle \sum }_{j=1}^{m_p}\overline{v_j}{\displaystyle \sum }_{i=1}^{n_{pj}}\overline{w_{i,j}}{\left[p_j^{*}\left(x,{\theta }_i\right)-q_j\left(x,{\theta }_i,b\right)\right]}^2+\\ {\displaystyle \sum }_{j=1}^{n_b}\widehat{v_j}{\left[b_j^{*}\left(x\right)-b_j\left(x\right)\right]}^2\end{array}$$ (1)

Where the first term on the right-hand side represents deviations between the measured and calculated space-time variables. In this term, m_q is the number of different sets of measurements, n_qj is the number of measurements in a given set of measurements, q_j* (x, t_i) represents specific measurements at time t_i for the for the j-th measurement set at location x (r, z), q_j (x, t_i, b) are the corresponding model predictions for the optimised parameter vector b (e.g., θr, θs, α, n e Ks), and v_j and w_i,_j are weights associated with a given set or measurement point, respectively. The second term of the objective function F represents the differences between the independently measured and estimated soil hydraulic properties, while the terms m_p, n_pj, p_j* (q_i), p_j (q_i, b), v_j and w_i,j have similar meanings as for the first term, but now for the hydraulic properties of the soil. The last term of F represents a penalty function for deviations between prior knowledge of soil hydraulic parameters, b_j*, and their final estimates, b_j, with n_b being the number of parameters with prior knowledge and v_j representing weights pre-assigned. The estimates which use prior information (such as that used in the third term of F) are known as Bayesian estimates.

The minimization of the objective function F is performed using the Levenberg-Marquardt nonlinear minimization method (Marquardt, 1963). This method combines Newton's method and the steepest methods descend and generates confidence intervals for the optimised parameters. It is a gradient-based local optimization algorithm, which has been shown to be reliable when the dimensionality of the inverse problem is low. Table 1 shows the range considered in the optimization of each parameter. The values in Table 1 were inspired based on the variability for each hydrodynamic parameter demonstrated in Coutinho et al. (2016).

Table 1
Intervals considered for optimization of each hydrodynamic parameter.

Parameter	θs (mm3/mm3)	α (1/mm)	n	Ks (mm/h)
Minimum	0.3	0.001	1.1	10
Maximum	0.5	0.1	4.0	1500

Quality of adjustmens assessment

In order to validate the quality of the model adjustments, five statistical criteria were used (Loague & Green, 1991): the coefficient of determination (R², Equation 2), the deviation ratio (RD, Equation 3), the mass coefficient residual (CMR, Equation 4), the mean squared error (MSE, Equation 5) and the modelling error (EM, Equation 6). For the value of the coefficient of determination R², a tendency towards the value 1 (one) is expected. Such a coefficient determines the proportion of the variance in the experienced values that can be attributed to the observed ones. The RD coefficient describes the ratio between the dispersion of observed values and those calculated theoretically, and its optimal value is one, occurring when there is equality between the observed and calculated values.

The expected value of the CMR tends to be zero in the absence of systematic deviations between the observed and calculated values, which may indicate overestimation (CMR>0) or underestimation (CMR<0) of the estimated values. The optimal values of CMR and RD are 0 and 1, respectively (Willmott et al., 1985). The value of the Mean Square Error (MSE) indicates the degree of deviation between the experimental determinations and the values calculated by the theoretical model, the expected value of the MSE tends to zero. Modeling Efficiency (EM) indicates whether the theoretical model provides a better estimate of the experimental determinations than the average value of these determinations, its expected value tends to 1 (one).

${\text{R}}^2=\frac{{\left[\text{n}.(\sum {\text{M}}_{\text{i}}.{\text{T}}_{\text{i}})-\sum {\text{M}}_{\text{i}}.\sum {\text{T}}_{\text{i}}\right]}^2}{\left[\text{n}.\sum {\text{T}}_{\text{i}}{}^2-{\left(\sum {\text{T}}_{\text{i}}\right)}^2\right]\left[\text{n}.\sum {\text{M}}_{\text{i}}{}^2-{\left(\sum {\text{M}}_{\text{i}}\right)}^2\right]}$ (2)

$\text{RD}=\frac{\sum {\left(\text{Mi}-\overline{M}\right)}^2}{\sum {\left(\text{Ti}-\overline{M}\right)}^2}$ (3)

$\text{CMR}=\left(\frac{\sum {\text{M}}_{\text{i}}-\sum {\text{T}}_{\text{i}}}{\sum {\text{M}}_{\text{i}}}\right)$ (4)

$\text{EQM}={\left[\frac{\sum ({\text{T}}_{\text{i}}-{\text{M}}_{\text{i}})²}{n}\right]}^{\frac{1}{2}}.\frac{100}{\overline{M}}$ (5)

$\text{EM}=\frac{\sum ({\text{M}}_{\text{i}}-\overline{M})²-\sum ({\text{T}}_{\text{i}}-{\text{M}}_{\text{i}})²}{\sum ({\text{M}}_{\text{i}}-\overline{M})²}$ (6)

Where T_i are the values estimated by the model, M_i is the experimental values, and $\overline{M}$ is the average of the experimental values and the number of values compared.

Simulation of water transfer processes using Hydrus-2D

To solve the Richards equation in its two-dimensional format (Equation 7), it is necessary to define the upper, lower and lateral boundary conditions, as well as the hydrodynamic properties related to the functions that express the retention curve θ(h) and hydraulic conductivity K(θ). For the functions related to the retention curve and hydraulic conductivity curve, the models proposed by van Genuchten (1980) were used with the hypothesis of Mualem (1976) (Equations 7, 8, 9, 10 and 11).

$$\frac{\partial \theta \left(h\right)}{\partial t}=\frac{\partial }{\partial z}\left[K_z\left(h\right)\cdot \nabla \left(h+z\right)\right]+\frac{\partial }{\partial x}\left[K_x\left(h\right)\cdot \nabla \left(h+x\right)\right]-S$$ (7)

$\theta \left(h\right)=\left\{\begin{array}{c}{\theta }_r+\frac{{\theta }_s-{\theta }_r}{{\left[1-{\left(\alpha \left|h\right|\right)}^n\right]}^m}ifh\le 0\\ {\theta }_{s}ifh>0\end{array}\right.$ (8)

$m=1-\frac{1}{n}$ (9)

$S_e=\frac{\theta \left(h\right)-{\theta }_r}{{\theta }_s-{\theta }_r}$ (10)

$K\left(h\right)=\left\{\begin{array}{c}{K}_s{S}_e{}^l{\left[1-{\left(1-S_e{}^{1/m}\right)}^m\right]}^{2}ifh\le 0\\ K_{s}ifh>0\end{array}\right.$ (11)

In the equations above, θ is the volumetric soil moisture [ L³ L^-3]; h is the matrix potential, [L]; t is the time [T]; x is the horizontal coordinate [L]; z is the vertical coordinate [L]; θ_r is the residual soil moisture [ L³ L^-3]; θ_s is the saturation soil moisture [ L³ L^-3]; α is the inverse of the capillary length [L ^-1]; n and m are shape parameters; K_s is the saturated hydraulic conductivity [L T^-1]; S_e is the effective saturation.

Numerical modeling was carried out for the points that presented the highest and lowest saturated hydraulic conductivity of the coating layer estimated by the inverse method, which were P6R1 and P2R2* respectively. Therefore, the two-dimensional geometry of structure 2, where the points P6 and P2 were located, was constructed using the Hydrus-2D/3D model. The two-dimensional section presented in Figure 3 is heterogeneous, formed by three materials: a surface layer corresponding to the coating and two subsurface layers corresponding to sand and natural soil thickness, respectively.

Figure 3
Details of the materials of the two-dimensional section of the permeable pavement and the boundary conditions used.

The discretization of the section resulted in 26984 nodes, 1014 one-dimensional elements and 53431 two-dimensional elements. The initial condition adopted in the profile close to saturation was constant and uniform pressure throughout the profile h = - 0.1 m. The convergence criteria for volumetric humidity and matrix potential were 0.001 and 1 mm, respectively.

The hydrodynamic properties of the sand and subgrade layers are presented in Table 2. The hydrodynamic properties of the second layer (sandy layer) were obtained from the Rosetta database for a text class with one hundred percent sand fraction. Regarding the third layer, corresponding to the subbase, average values were used based on the estimates obtained by Coutinho et al. (2020), which respectively characterized the surface and the depth of twenty centimeters of the urban soil where the structure is contained. The properties obtained by the inverse method were considered for the coating layer, considering those corresponding to the tests that led to the maximum and minimum saturated hydraulic conductivity. Therefore, these two cases (corresponding to the points that present the maximum and minimum saturated hydraulic conductivity) are simulated.

Table 2
Summary of the hydrodynamic properties of the coating, sand and subbase layers used in the simulations.

Layer	Hydrodinamic parameters
	θr (mm3/mm3)	θs (mm3/mm3)	α (1/mm)	n	Ks (mm/h)
Coating	Inverse Method	Inverse Method	Inverse Method	Inverse Method	Inverse Method
Sand	0.05	0.37	0.00353	3.18	267.90
Subbase	0.21	0.40	0.02081	2.41	14.40

RESULTS AND DISCUSSION

Figure 4 shows the accumulated infiltration and infiltration rates for the permeable pavement. It is observed that the permeable pavement presented a maximum accumulated infiltrated depth of 382 mm in 23231 seconds for point P6R1 and a minimum of 127 mm in 28355 seconds for point P2R2*. Regarding the infiltration rate, there is a big contrast between the initial infiltration rate of the P6R1 test and the other points. However, the infiltration rate at all points has an average value of 33.8 mm/h, presenting medium variability according to the classification of Warrick & Nielsen (1980), with a coefficient of variation of 25.7%.

Figure 4
(a) Cumulative infiltration and (b) infiltration rates for the permeable pavement at different times.*tests carried out in the first campaign; **tests carried out in the last campaign; R1 first repetition; R2 second repetition.

Table 3 presents the hydrodynamic parameters estimated from the inverse method for various tests on the PP coating layer. It is observed that minimum values of the shape parameter n were obtained in three tests (PIR1**, P2R1* and P2R2**). Values close to unity of the parameter n indicate the presence of the fine soil fraction in the particle size distribution. For other cases, values of n greater than two are in accordance with what is expected for the sand particle size fraction, a material used to fill the hollow blocks of the permeable pavement at the time of its construction. Regarding saturated hydraulic conductivity, the highest value was observed was 62.77 mm/h in the P6R1 test. The minimum value obtained for saturated hydraulic conductivity was 16.15 mm/h in the P2R2** test. In general, medium spatial variability is observed in estimates of saturated hydraulic conductivity (coefficient of variation between 12 and 60% according to Warrick & Nielsen (1980). Such variability can be influenced both by particular characteristics resulting from the construction process such as porosity, arrangement of pores, arrangement of blocks, granulometric distribution, as well as post-construction factors such as continuous deposit of sediments arising from surface runoff, possible formation of clogging zones, influence of microfauna (ants) or development of undergrowth (grass or similar). Figure 5 shows the adjustments of the experimental and estimated accumulated infiltration curves with the values obtained by the inverse method. For the statistical measurements obtained from the analysis of the quality of fit of the inverse method, it is observed that the coefficient of determination and the residual mass coefficient are close to the optimal values (one and zero, respectively) for all points. Regarding RD, the values closest to unity were observed at P1R1, P1R2 and P1R2**. The worst performances regarding the deviation ratio, that is, a significant dispersion between the observed and calculated values, were noted for points P4R1, P5R1 and P6R1. The same was indicated by the EQM, which presented errors bigger than 11% for these points. The modelling error presented values close to the expected optimal values.

Table 3
Hydrodynamic parameters estimated from the inverse method for various tests on the PP coating layer, basic infiltration velocity (BIV), percentage errors (E) and statistics of the adjustments made for the permeable pavement: coefficient of determination (R²), deviation ratio (RD), residual mass coefficient (CMR), mean squared error (MSE) and Modeling Error (EM).

Point	θs (mm3/mm3)	α (1/mm)	n	Ks (mm/h)	BIV (mm/h)	E (%)	R2	RD	CMR	EQM (%)	EM
P1R1*	0.3	0.001	3.67	42.94	41.60	3.22	0.9998	0.9805	0.0028	0.9093	0.9997
P1R2*	0.3	0.001	3.70	30.61	30.63	-0.07	0.9999	0.9595	0.0057	1.3144	0.9994
P1R1**	0.3	0.004	1.10	42.96	40.51	6.05	0.9926	0.8015	0.0434	8.8227	0.9720
P1R2**	0.3	0.001	4.00	40.51	35.46	14.24	0.9995	0.9455	0.0070	1.8854	0.9985
P2R1*	0.3	0.001	1.10	27.45	24.48	12.13	0.9992	0.8000	0.0337	6.8761	0.9811
P2R2*	0.3	0.001	2.69	16.15	16.02	0.81	0.9996	0.9695	0.0036	1.2464	0.9993
P2R1**	0.3	0.001	3.74	48.67	40.51	20.14	0.9981	0.8001	0.0382	7.6360	0.9793
P2R2**	0.3	0.001	1.10	40.51	35.46	14.24	0.9994	0.8067	0.0334	6.7151	0.9826
P3R1	0.31	0.003	4.00	41.00	34.02	20.52	0.9972	0.7547	0.0479	9.4598	0.9664
P3R2	0.3	0.001	3.43	28.85	25.52	13.05	0.9997	0.8163	0.0300	6.1215	0.9850
P4R1	0.3	0.002	4.00	41.40	32.13	28.85	0.9969	0.7011	0.0624	11.8329	0.9460
P4R2	0.3	0.001	3.25	29.78	32.61	-8.68	0.9992	0.7849	0.0438	7.7994	0.9757
P5R1	0.3	0.001	4.00	32.58	21.95	48.43	0.9876	0.7407	0.0518	11.3280	0.9505
P5R2	0.3	0.001	4.00	20.49	35.13	-41.67	0.9997	0.8556	0.0211	4.5236	0.9914
P6R1	0.3	0.001	4.00	62.77	51.55	21.77	0.9963	0.7357	0.0585	11.0499	0.9581
P6R2	0.3	0.003	3.96	41.97	38.86	8.00	0.9985	0.8697	0.0227	4.4718	0.9930
Average	0.3	0.002	3.23	36.79	33.53	10.06	0.9977	0.8326	0.0316	6.3745	0.9799
Standard Deviation	0.0	0.001	1.12	11.35	8.66	19.16	0.0033	0.0890	0.0196	3.6944	0.0175
CV***	0.0	0.644	0.35	0.31	0.26	1.90	0.0033	0.1069	0.6200	0.5796	0.0178

• ^*
  tests carried out in the first campaign.
• ^**
  tests carried out in the last campaign; R1 first repetition; R2 second repetition.
• ^***
  coefficient of variation.

Figure 5
Adjustments made using the inverse method for the three periods analysed: (a) September/2019; (b) February/2020; (c) March/2020.*tests carried out in the first campaign; **tests carried out in the last campaign; R1 first repetition; R2 second repetition.

The values obtained for the saturated hydraulic conductivity and the stabilized values of the infiltration rate allow the permeable pavement to be classified as having a medium permeability level, by the classification proposed by Terzaghi & Peck (1967) apud Lambe & Whitman, 1979). Regarding infiltration rates, the results are in accordance with the results found by Jabur et al. (2015), who obtained infiltration rates greater than 36 mm/h for hollow interlocking concrete blocks.

Figure 6 shows the dynamics of water infiltration processes in the coating layer and redistribution of infiltrated water in the subsurface layers of sand and subgrade, respectively. It is observed that for short times, that is, for times smaller than 0.086h, the infiltration process occurs as a piston effect in the soil between the interlocking blocks. It is noted that the water content propagation occurs following horizontal soil moisture curves until it reaches the total thickness of the coating layer.

Figure 6
Simulation of the water infiltration and redistribution process in the permeable pavement for the coating with (a) higher saturated hydraulic conductivity (b) and lower saturated hydraulic conductivity for different times.

For the time T equal to 0.086 h, the medium with the lowest saturated hydraulic conductivity on the surface does not yet present the wetting front breaking the thickness of the coating layer. In contrast, continuous wetting fronts exist for the medium with the highest hydraulic conductivity and become more evident after a time equal to 0.172 h.

From time 0.258 h onwards, the formation of a saturated layer is observed right after the coating layer for the case with higher saturated hydraulic conductivity. From this moment on, it is observed that the speed of water redistribution in the structure is controlled by the coating layer, causing the medium with the highest hydraulic conductivity on the surface to successively reach greater water redistribution depths than the medium with the lowest hydraulic conductivity on the surface.

For the same time, a difference of 288% in the saturated hydraulic conductivity at the surface, in reference to the lowest value, allowed the depth of the wetting front to be 33.3% greater. This fact demonstrates the influence of the saturated hydraulic conductivity of the surface layer of the permeable pavement on the infiltration and water redistribution processes in the structure. This demonstrates the need for scheduled maintenance measures to allow for a good drainage capacity of the structure, which can influence the speed of infiltration and, in the long term, the speed of groundwater recharge.

In general, it is observed that Hydrus 2D demonstrates the capacity to represent the infiltration bulb throughout the permeable pavement profile, covering both the surface layers, heterogeneous section, and the entire homogeneous section of the subgrade. The presence of preferential flows resulting from the contrast of hydrodynamic properties between the surface layers and the subgrade is not observed. In any case, in studies of hydrological processes in green infrastructures, it is essential to evaluate the need to consider the heterogeneity of the subsoil. These heterogeneities can interfere with the dynamics of water transfer processes on a field scale (Coutinho et al., 2015).

Costa et al. (2020) observed that saturated hydraulic conductivity is the most influent parameter on the infiltration capacity of the permeable pavement object of this study through a sensitivity analysis study using Hydrus 1D. The authors observed that an variation of -50% in the saturated hydraulic conductivity of the coating layer leads to an underestimation of around 30% in the recharge and accumulated infiltration.

For Illgen et al. (2007), the speed of infiltration and redistribution of water are mainly influenced by the coating layer and the thickness of the opening of the interlocking block. Given the spatial variability of saturated hydraulic conductivity observed experimentally, the simulation performed in this study demonstrates that greater hydraulic conductivity at the surface accelerates the advancement of the wetting front to a more significant depth. This can amplify the impact of permeable pavement on other urban hydrological processes, such as water retention in the soil, facilitating groundwater recharge. Barnes & Welty (2019) observed that even in the summer, when evapotranspiration exceeds occurrence, the additional water captured by the area deposited on a permeable pavement increases groundwater recharge. Similarly, Chen et al. (2022) observed that in an area covered with permeable pavement, there were positive demonstrations between the change events and the increase in the water table level, demonstrating positive statements that PP increases groundwater recharge.

In general, to increase the scale of groundwater recharge, the use of permeable pavements on sidewalks, parking lots, parks, or other spaces where infiltration can be prioritized can be encouraged. In addition, not only permeable pavements but other green infrastructures can be encouraged in municipal or regional basic sanitation plans, respecting their feasibility criteria, to contemplate the regeneration capacity of natural hydrological processes in urban basins.

Once the benefit of good hydraulic conductivity values has been observed, the need for periodic permeability checks is reiterated, with a view to planning possible maintenance actions. In this context, even with contestable criteria or physical premises, it is possible to observe the existence of brazilian and international norms regarding the establishment of minimum criteria for the permeability coefficient, based on infiltration or in situ permeability tests, as in the standards: ASTM C1701M17, “A Standard Test Method for Infiltration Rate of In Place Pervious Concrete”, (ASTM International, 2017) in the United States, from BS7533- 13:2009, “Pavements Constructed with Clay, Natural Stone, or Concrete Pavers”, (BSI Standards Institution , 2009) in England, from CJJ/T 188-2012, “Technical Specification for Pavement of Water Permeable Brick”, in China (MOHURD, 2012), “Permeable concrete pavements - Requirements and procedures”, in Brazil (NBR 16416/2015) (Associação Brasileira de Normas Técnicas, 2015).

CONCLUSION

The inverse method showed excellent performance in estimating hydrodynamic properties. In general, the statistical measurements presented values close to their optimal values, indicating good precision of the method in representing the accumulated infiltration curve and presenting accuracy in estimating the hydrodynamic parameters. The saturated hydraulic conductivity showed medium variability throughout the permeable pavement. The maximum and minimum values arising from saturated hydraulic conductivity were used to simulate two infiltration and water redistribution scenarios in the permeable pavement. The two-dimensional simulations with Hydrus-2D demonstrated that the saturated hydraulic conductivity of the coating layer influences the infiltration and redistribution dynamics of water in the permeable pavement structure. In general, the two-dimensional simulation demonstrated that greater saturated hydraulic conductivity on the surface of the permeable pavement accelerates the water redistribution processes in the subsoil. Hydrus 2D was able to represent the infiltration bulb throughout the permeable pavement profile, covering both the heterogeneous surface layers and the subgrade. In the simulation, no preferential flows were observed due to the contrast in hydrodynamic properties between these layers. Furthermore, Hydrus-2D proved to be an excellent computational tool for representing the dynamics of water infiltration and redistribution in permeable pavement.

ACKNOWLEDGEMENTS

The authors would like to thank the PRH-ANP/FINEP project - PRH 48.1/UFPE (ANP Nº48610.201019/2019-38), the FACEPE projects APQ-1535-3.01/22, APQ-1115-3.01/21 and APQ-1767-3.01 /22, the CAPES project 88887.689130/2022-00 and the CNPQ project 406978/2022-0.

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Edited by

• Editor in-Chief:
  Adilson Pinheiro

• Associated Editor:
  Priscilla Macedo Moura

Publication Dates

• Publication in this collection
  25 Nov 2024
• Date of issue
  2024

History

• Received
  26 Sept 2023
• Reviewed
  30 July 2024
• Accepted
  29 Aug 2024