Constant-head Tests Research Articles

Examining the Mid to Long‐Term Variability in Saturated Hydraulic Conductivity of Sandy Soils and Its Influencing Factors Under Constant Head Test in the Laboratory

AbstractSaturated hydraulic conductivity (Ks) is a crucial parameter that influences water flow in saturated soils, with applications in various fields such as surface water runoff, soil erosion, drainage, and solute transport. However, accurate determination of Ks is challenging due to temporal and spatial uncertainties. This study addresses the knowledge gap regarding the long‐term behavior of Ks in sandy soils with less than 10% fine particles. The research investigates the changes in Ks over a long period of constant head tests and examines the factors influencing its variation. Two sandy samples were tested using a hydraulic conductivity cell, and the hydraulic head and discharge were recorded for over 50 days. The results show a general decline in Ks throughout the test, except for brief periods of increase. At the end of both tests, there are noticeable reductions in the saturated hydraulic conductivities of the samples, with one sample being 96% and the other sample 91% less than the maximum recorded saturated hydraulic conductivity during the tests. Furthermore, the relationship between flow rate and hydraulic head gradient does not follow the expected linear correlation from Darcy's law, highlighting the complex nature of sandy soil saturated hydraulic conductivity. The investigation of soil properties in three different sections of the samples before and after the tests revealed a decrease in the percentage of fine particles and a shift in specific gravity from the bottom to the top of the sample, suggesting particle migration along the flow direction. Factors such as clogging by fine particles and pore pressure variation contribute to the changes in Ks. The findings of this research show the importance of considering changes of saturated hydraulic conductivity during constant‐head laboratory tests. Therefore, this study provides evidence for the requirement to further assess the laboratory methods for measurement of the saturated hydraulic conductivity in sandy soil mixtures.

Perencanaan Sumur Resapan Air Hujan dalam Upaya Konservasi Daerah Pesisir

Infiltration wells are engineered construction designed for water conservation to accomodate and absorb surface water. Water conservation in necessary to reduce seawater intrusion in coastal areas. Shallow groundwater in Pohe village, located in a coastal a rea, is affected by seawater intrusion. This research aiams to converse groundwater in the coastal area and to reduce rainwater runoff that flows into drainage channels as well as to reduce seawater intrusion. The research is conducted in a coastal area in Pohe Village that is directly adjacent to Tomini Bay. The data are in the form of infiltration rate and soil permeability as the primary data and in form of rainfall in tensity betweet 2019 and 2020 as the secondary data. Infiltration rate data are obtained by useing a Double Ring Infiltrometer and are analyzed using the Horton method. Fourthermore, soil permeability data are tested using the constant head test. Analysis of rainfall intensity uses the Mononobe method, whereas discharge analysis employs th Rational method. The dimension of infiltration wells uses Sunjoto 1988 method.Findings reveal that the infiltration rate (ft) at the research site is 3.89 cm/hour or 38,90 mm/hour which is classified as moderate criteria. The coefficient of soil permeability (k) is 0.07 cm/second. Rain intensity (I) obtains 38.94 mm/hour. According to the data, the area of Pohe Village (A) is 4.83 km2 and the flow coefficient (C) is 0.21. The discharge analysis (Q) is 10.86 m3/second. The dimension of the infiltration wells is planned to use a cylindrical shape with a diameter of (D) 1 m and a depth of (H) 58.90 m. The are 31 wells with a depth of 1.90 m.

Spatiotemporal variations of sand hydraulic conductivity by microbial application methods

The spatiotemporal distributions of microbes in soil by different methods could affect the efficacy of the microbes to reduce the soil hydraulic conductivity. In this study, the specimens of bio-mediated sands were prepared using three different methods, i.e. injecting, mixing, and pouring a given microbial solution onto compacted sand specimens. The hydraulic conductivity was measured by constant-head tests, while any soil microstructural changes due to addition of the microbes were observed by scanning electron microscope (SEM) and mercury intrusion porosimetry (MIP) tests. The amount of dextran concentration produced by microbes in each type of specimen was quantified by a refractometer. Results show that dextran production increased exponentially after 5–7 d of microbial settling with the supply of culture medium. The injection and mixing methods resulted in a similar amount and uniform distribution of dextran in the specimens. The pouring method, however, produced a nonuniform distribution, with a higher concentration near the specimen surface. As the supply of culture medium discontinued, the dextran content near the surface produced by the pouring method decreased dramatically due to high competition for nutrients with foreign colonies. Average dextran concentration was negatively and correlated with hydraulic conductivity of bio-mediated soils exponentially, due to the clogging of large soil pores by dextran. The hydraulic conductivity of the injection and mixing cases did not change significantly when the supply of culture medium was absent.

Analysis of Soil Absorption Capacity of Rainwater in Biopori Infiltration Holes in Purwoyoso Village Semarang City

Drought and floods that hit Semarang City were caused by problems with water distribution and capacity. The ongoing conversion of land functions in the city of Semarang has resulted in reduced green open space and increased building density. This resulted in reduced infiltration of rainwater so that surface water runoff increased. Thus, causing a flood disaster that hit the city of Semarang in 2022, in which 7 out of 16 sub-districts were affected. This condition is exacerbated when rainfall is high and causes stagnant water because the existing drainage system is not optimal. The application of biopore infiltration holes in an effort to expand the rainwater infiltration area is a form of defense that can be carried out by the people of Semarang City in minimizing the occurrence of floods and groundwater crises. This study aims to analyze the absorption capacity of soil against rainwater in biopori infiltration holes in Purwoyoso Village. The method used is the Constant Head and Falling Head tests. The results of the groundwater absorption test showed that in sample B.1. and B.2. are 8.976.E-05 cm/sec and 9.488.E-05 cm/sec respectively. These results indicate that the absorption capacity of the soil in the biopori infiltration holes for rainwater is low or lacking.

Insight on the application of graphene to sandy soils to improve water holding capacity

In this study, the changes in relevant hydraulic parameters (namely hydraulic conductivity, total and effective porosity, specific retention, and longitudinal dispersivity) induced by the introduction of graphene in a calcareous sandy soil and a siliciclastic riverine soil were monitored and modelled via leaching column experiments. Constant pressure head tests were used to calculate the hydraulic conductivity of each column, while leaching experiments were run to estimate total porosity and specific retention, and for each treatment three replicates were done. Columns were then run under saturated conditions via a low flow peristaltic pump and monitored for chloride concentrations. CXTFIT 2.0 was employed to inversely model the column experiments and retrieve effective porosity and longitudinal dispersivity. Results highlighted small changes of hydraulic conductivity and porosity, induced by graphene addition for both soils. A marked increase of specific retention values was instead recorded in the amended columns respect to control ones. Chloride breakthrough curves modelling showed that graphene doubled dispersivity in the calcareous sandy soil compared to the control, while it halved dispersivity in the siliciclastic riverine soil with respect to the control. The results highlight that graphene induces positive shift in the capacity of sandy soil to retain porewater but at the same time it also alters solute transport parameters, like dispersivity, suggesting that further studies need to focus on using several exposure concentrations, durations and mode of exposure, and apply simulated field conditions or perform experiments in real field conditions, to understand the fate of unwanted compound in soils amended with graphene.

A novel in-situ test method for permeability in saturated sandy porous media

Permeability is a vital parameter for the design and construction of structures involving ocean engineering. Based on the steady-state heat transfer theory and Darcy's law, a novel in-situ test method for permeability in saturated sandy porous media is introduced in this work. This approach aims to obtain permeability through the inversion of the measured temperatures. Temperatures measuring device with a constant heater was installed in an insulating experimental tank filled with sandy sediments of different permeability. Further, a numerical model based on the Finite Element method was simulated to validate the feasibility of the proposed method and accuracy of the experimental data. Besides, the results obtained by the constant head test were compared with those calculated by the novel in-situ test method, considering different surface temperatures of the heater and different sediments’ permeability. It shows that the permeability obtained by in-situ method are reliable and accurate (the accuracy is within one order of magnitude) in both numerical simulations and experimental tests. The effects of different surface temperatures of the heater and permeability of porous media on permeability calculation results were also discussed. The surface temperature was found that has little influence on permeability. And the proposed method is applicable when the permeability is higher than 10−12 m2. The findings can provide some reference to the in-situ measurement of submarine sediments' permeability.

Variation of the hydraulic properties in sandy soils induced by the addition of graphene and classical soil improvers

In this study, for the first time, the changes in relevant hydraulic parameters (e.g., hydraulic conductivity, effective porosity, and dispersivity) induced by the introduction of graphene in a calcareous sandy soil and a siliciclastic riverine soil were monitored and modelled via leaching column experiments. Column experiments were also run with traditional soil improvers (compost, biochar, and zeolite) to compare the changes induced by graphene versus well-studied soil improvers. Constant pressure head tests were used to calculate the hydraulic conductivity of each column, while leaching experiments were run to estimate porosity and specific retention, and for each treatment three replicates were done. Columns were then run in saturated conditions via a low flow peristaltic pump and monitored for electrical conductivity, temperature, and chloride. CXTFIT 2.0 was employed to inversely model the column experiments and retrieve parameters like effective porosity, longitudinal dispersivity, bulk thermal diffusivity, and thermal retardation factor. Results highlighted small changes of hydraulic conductivity, porosity, and effective porosity induced by graphene addition (as well as by the other soil improvers) for both soils. A marked increase (nearly 20 %) of specific retention values was instead recorded in the amended columns with respect to control ones. Chloride breakthrough curves modelling showed that graphene doubled dispersivity in the calcareous sandy soil (5.82 ± 1.4 cm) compared to the control (2.6 ± 0.29 cm), while it halved dispersivity in the siliciclastic riverine soil (0.31 ± 0.05 cm) with respect to the control (0.65 ± 0.06 cm). Thermal retardation factors were decreased by graphene by approximately 20 % for both soils. The model fitting via TDS (derived from the electrical conductivity monitoring) produced unreliable dispersivity values in most of the experiments due to the nonconservative nature of this parameter compared to chloride. The results highlight that graphene affected dispersivity but did not significantly alter other physical parameters relevant for solutes transport in sandy soils in comparison to classical improvers, thus future studies should focus on the graphene’s effects on nutrients and agrochemicals leaching in unsaturated flow conditions.

The modification of the Kozeny-Carman equation through the lattice Boltzmann simulation and experimental verification

In this paper, the numerical simulation based on the lattice Boltzmann method (LBM) and experimental studies are conducted to investigate the permeability of porous media with sphere packing. The accuracy of LBM is verified through the comparison of theoretical solutions and the numerical result of flat channel flows. The resolution and the size of representative element volume used for simulation are evaluated. Then, the effects of porosity and particle size on the permeability of porous media are studied through the combination of LBM and discrete element method, and the factors that affect the fluid flow in porous media are explored. It is found that there are very high linear correlations between n3/(1-n)2 and permeability. Meanwhile, the relationship between the particle size, d, and permeability is also established. The physical constant, Ck, is found closely related to the porosity, n, based on which, the modification of the Kozeny-Carman (K-C) equation is proposed. After that, the constant head test is conducted for the glass beads with different porosity and particle size distribution, and the proposed equation is validated. The experimental results show that the modified K-C equation presents a higher accuracy than the classical K-C equation for the porous media from sphere packing.

Interpretation of a network-scale tracer experiment in fractured rock conducted using open wells

The presence of fractures in bedrock allows for rapid aqueous contaminant transport through complex pathways and for diffusion of solutes between the fractures and the matrix. To better understand transport in these settings, tracer experiments are a commonly used tool. The need for expensive multi-level wells to obtain depth-specific concentrations, however, significantly limits the cost efficiency. The primary objective of this study is to develop a method whereby a discrete fracture network approach can be used to simulate the results of a divergent tracer experiment conducted using open observation boreholes in a well-characterized dolostone over distances of 55 m to 242 m. The experiment was conducted using a fluorescent tracer which allowed for continuous concentration measurement with depth in each open observation well. Two numerical models were employed in the interpretation of the experiment. The first was a 1-D finite difference model focused on flow and transport in the observation wells and the second was a 3-D control-volume finite element model capable of simulating the entire fracture network. Through fitting the experimental data to simulations, the most important fractures for transport in the system were identified. The number of fractures that participated in transport was few relative to the number of fractures observed in core and in constant head test results. Heterogeneous distribution of the fracture apertures was determined to be the likely cause of the highly tortuous transport observed at the site. This study demonstrates that tracer experiments conducted using open observation boreholes and a downhole fluorometer can improve our understanding of large-scale transport in fractured rock, especially when analysed with multiple models, and compared to other measured properties such as matrix porosity, hydraulic aperture, and fracture orientation.

Pore water pressures and hydraulic conductivity in the slip zone of a clayey earthflow: Experimentation and modelling

Rainfall is among the most relevant triggering factors of landslides. With the aim of defining a model of the influence of rainfall on deep landslides, this paper presents data of a long-term monitoring of pore water pressures in a clayey earthflow, and the results of many field permeability tests carried out with several procedures. Pore water pressures are being monitored in the Costa della Gaveta slope since 2005. In the last years, new instruments have been installed and permeability tests have been carried out in the stable formation, in the landslide body and in the slip zone. The hydraulic conductivities of the three different zones of the subsoil have been evaluated by two types of field tests: falling head tests (by Casagrande piezometers and test wells), and localized constant head tests (by a permeameter ad hoc designed). The experimental data show that: a) pore water pressures along the slip zone respond to rain more than in the landslide body and in the stable formation, even at about 25 m depth; b) the hydraulic conductivity ksz of the slip zone is much higher than that of the landslide body, kl, in turn higher than the hydraulic conductivity of the stable formation, kf. The numerical 3D modelling of steady-state reference conditions and of transient processes caused by the historical rainfall series shows that the occurrence of ksz higher than kl and kf determines an overall drainage effect which makes the global limit equilibrium safety factor SF greater than that evaluable for other possible conditions. On the other side, even the lowest measured hydraulic conductivity ksz provides seasonal rain effects on water pressures along the slip surface such to determine significant SF variations in phase with the observed seasonal displacement rates.

Investigation on the Influence of Temperature and Confining Pressure on the Hydraulic Conductivity of the Integrated and Fractured Jurassic Conglomerates

This paper presents an experimental investigation on the properties of hydraulic conductivity and permeability of conglomerates under different temperatures and confining pressures with integrated samples and samples with shear failure. Constant head tests were carried out in a temperature-controlled triaxial cell with samples obtained from the Zhuxianzhuang Coal Mine. Five levels of temperatures (10°C, 20°C, 28°C, 35°C, and 50°C) and three levels of confining pressures (3 MPa, 5 MPa, and 7 MPa) were chosen for the tests. The results show that there is a negative relationship between hydraulic conductivity and confining pressure with both original and shear failure samples. An inflection point of 35°C is found in the relationship between the flow rate and temperature. However, with increasing temperature conditions, hydraulic conductivity first increases and then decreases at 50°C with the intact sample, while hydraulic conductivity first decreases from 20°C and then increases with the shear failure sample. Finally, nonlinear regression equations of hydraulic conductivity and temperature were obtained under different confining pressures.

Experimental Analysis of Hydraulic Characteristics of Coarse-grained Soil Treated with Natural-based Nanomaterials

In the last decades the interest in nanomaterials considerably increased due to the development of new technologies of micronization. The prospect of achieving large amounts of nanomaterials from natural bulk materials allows to evaluate the replacement of cement in low-pressure injection for geotechnical soil stabilization. The aim of the research activities was to point out the effectiveness of the injection of nanomaterials in the decrease of permeability in coarse-grained soils. In this study, nanomaterials from sand, clay and graphene were used to create the mix design. In order to reach the goal, a first step was the characterization of nanomaterials and sand used as matrix, then shape and number of samples were defined and finally constant head test was carried out to provide hydraulic conductivity. The results confirmed that the proper injection of nanoparticles-based mixture could be considered a sustainable solution useful to reduce the permeability of coarse-grained soil.

Allocating transmissivities from constant head tests for the development of DFN models

Constant head tests are commonly used for field measurements of fracture transmissivity. As a bulk transmissivity is measured for each test section, it is frequently unclear how this transmissivity relates to the hydraulic properties of individual fractures. The goal of this study is to determine if constant head tests conducted at scales larger than the average fracture spacing can be used to generate discrete fracture network (DFN) models that describe transport. The methodology involved generating DFNs using measurements from constant head tests conducted at lengths both above and below the average fracture spacing at a site in Ontario, Canada. Transport predictions from DFNs produced from different scales of hydraulic tests were compared to determine if a method for proportioning larger-scale test results to obtain a DFN representative of the smaller-scale tests could be established. The results of this study indicate that the choice of method used to apportion bulk transmissivities has a significant impact on transport simulations, with a difference in mass arrival of over a factor of two at travel distances less than 50 m. While the most appropriate method is case specific, the error resulting from the choice needs to be considered when using DFN models.

COMPARISON OF MEASURED AND ESTIMATED PERMEABILITY FOR ARTIFICIALLY PREPARED COARSE-GRAINED SOIL SAMPLES

Knowledge about soil permeability is important in various scientific fields: hydrology and hydrogeology, geotechnics, environmental geotechnics, and others. Depending on the different goals that need to be achieved by a particular engineering project, the conditions in which the permeability coefficient is determined in terms of applied hydraulic gradients, applied stresses, type of test fluid, etc. are adjusted, as well as the required precision of its determination. In addition, the permeability coefficient is a soil property with the largest range of possible values. It can be determined through various laboratory and field methods, and by applying established empirical correlations using data on the grain-size distribution and empirical coefficients that depend on some factors, such as hydraulic radius (specific surface), curvature, porosity, etc. This paper presents the results of laboratory testing of the permeability coefficient by the constant head test and the use of a permeameter. The results were compared with the permeability coefficient obtained by applying a number of empirical correlations. Artificial samples were prepared in the laboratory by mixing different previously prepared soil fractions in order to determine the influence of particle size and soil gradation on the estimated soil permeability coefficient.

Permeability and setting time of bio-mediated soil under various medium concentrations

The bio-clogging using bacteria can be an eco-friendly and sustainable alternative to conventional grouting methods for seepage control. However, it remains unclear to date how the dilute concentration of bacterium and medium during field installation can affect the setting time of bacterium and its correlation with permeability reduction. In this study, the setting time of bacterium and its effectiveness in permeability reduction were addressed through experimental and theoretical investigations. A series of sand column was cultivated using different concentrations of Leuconostoc mesenteroides and culture medium. The distribution and composition of the bacterial product (i.e. dextran) were observed by refractometer, scanning electron microscope (SEM), and energy dispersive X-ray spectroscopy (EDS). Soil permeability was recorded using a constant head test. The results revealed that bacterium was effective to produce dextran at the setting time of about 5 d after installation. This dextran can reduce the permeability of bio-mediated soil by two orders of magnitude, even without culture medium supply. In general, the dextran production decreased proportionally with increase of bacterium and medium concentration. However, at 50% bacterium and medium concentration by weight, it still has a significant influence on permeability reduction with similar setting time, compared to 100% concentration. • Bacteria became effective to produce dextran with setting time after 5 d of installation. • The bacteria and medium concentration seems to have little influence on the setting time. • Dextran can reduce the permeability of bio-mediated soil by two orders of magnitude, even without culture medium supply. • With 50% of bacteria and medium concentration, the dextran can be accumulated in soil macro-pores and thus remain effective to reduce permeability.

Predicted and measured hydraulic conductivity of sand-sized crushed limestone

The hydraulic conductivity of 54 sand-sized crushed limestone materials was measured by conducting constant head tests in a rigid-wall permeameter and was estimated using six predictive equations requiring easily obtainable parameters. The gradations tested had effective grain size, D10, from 0.079 to 2.15 mm; uniformity coefficient, Cu, from 1.19 to 15.79; and void ratio, e, from 0.42 to 0.76. The measured hydraulic conductivity had a range of about three orders of magnitude (3.4*10−3 to 3.3 cm/s). Four of the predictive equations, based on the square of the effective grain size, D102, yielded closely grouped results differing by not more than a factor of 2. Long existing equations by Terzaghi (1925) and by Hazen (1892), adjusted for void ratio according to Taylor (1948), were found to have a high predictive efficiency with a ratio of predicted to measured values between 1/2 and 2 for 70% of the materials tested. The Kenney et al. (1984) equation, based on D52, was also efficient but underestimated measured values for 63% of all cases. The Kozeny–Carman equation (Taylor 1948; Chapuis 2012), based on specific surface, overestimated measurements for 90% of the tested materials by a factor of up to 3.

Constant-head and variable-head injection tests for determining the hydraulic parameters of an aquitard

Although specific storage (SS) is a crucial parameter for characterizing the dynamic water-release process in an aquitard, the Hvorslev analysis method is only capable of estimating the hydraulic conductivity (K), rather than SS. The Hvorslev method is based on an assumption of steady-state flow and uses the falling-head test. Considering the elastic water-release effect in an aquitard and the actual groundwater flow, two mathematical unsteady-state groundwater flow models (i.e., the constant-head and variable-head models), describing the head distribution are presented for a constant-head injection test (CHIT) and variable-head injection test (VHIT) performed in a multi-layered aquifer-aquitard system. The analytical solutions for the models are derived by Fourier transforms to estimate K and SS. The obtained K and SS values from the CHIT and VHIT were generally consistent, although the VHIT is recommended in practice. For the VHIT, estimating K using the Hvorslev analysis method under steady-state groundwater flow conditions resulted in a small relative error compared to the obtained result from the variable-head model. It was demonstrated that a certain relation existed between the constant-head and variable-head methods when the drawdown rate was lower than 1%, and so the constant-head method was applied to the VHIT data to determine K and SS. The synthetic error in the parameters was smaller than 10%, which indicated that the methods could be used interchangeably under these circumstances, thus simplifying the hydraulic parameter estimation process.

Determination of Hydraulic Conductivity Value by using Sunjoto Shape Factor

Hydraulic conductivity, K value, is important for soil properties determination and there are many equations and method that can be used in this region. In 1951, Hvorslev introduced the shape factor method to determine K value that only depends on geometry of well. The geometry of well or shape factor is mainly focused on the length, screen and base of the groundwater well. Later, many researchers used this method and developed different kind of equations for different geometry of wells. Sunjoto also developed equations and shape factor to determine the K value. This method can be used easily by using iteration method. In this research, the comparison has been performed using constant laboratory test method and Sunjoto method. The experiment test was conducted in the laboratory and it took measurements for three tests. The Sunjoto equation was used for analysis to the experiment test measurements. The hydraulic conductivity value with constant head test is 0.00038 m/sec and with Sunjoto shape factor method is 0.000184 m/sec for test (1), 0.000180 m/sec for test (2) and 0.000119 for test (3). According to this comparison value, the hydraulic conductivity value is more acceptable when it uses shape factor method since the constant laboratory test is using disturb sample. Moreover, according to the result, Sunjoto method can be used as a new method to determine hydraulic conductivity value.

Comparison of methods for measuring infiltration rate of pervious concrete

The infiltration rate of both a pervious concrete material itself and a pervious pavement system are important values for understanding how a pervious concrete pavement will drain water. While there is currently a standard test method to measure the infiltration rate of a pervious concrete pavement system (ASTM C1701), there is no standard test procedure for measuring the infiltration rate of only the pervious concrete material. The goal of this research was to compare various methods for measuring the infiltration rate of pervious concrete in isolation. The constant head, falling head, and a modified ASTM C1701 test were compared along with a horizontal version of the constant head test for multiple pervious concrete cylinders from the same mix. It was found that the sample-to-sample variation in infiltration rate is typically much larger than the experimental uncertainty present in a given test method. The infiltration rate depended non-linearly on head level, demonstrating that flows were in the transition flow regime between laminar and turbulent.Therefore, test results are presented in terms of both infiltration rate and modified Darcy’s law parameters.

Land Gradation Effect Analysis on Permeability and Ponding Time on Repeat Rain Frequency: Laboratory Study with Rainfall Simulator

Analysis of Effect of Land Gradation on Permeability and Ponding Time in Frequency of Repeated Rain (Laboratory Studies with Rainfall Simulator) guided by Darwis Panguriseng and Mahmuddin. That soil permeability is the ability of soil to pass water or air. Soil permeability is usually measured in terms of the speed of water flowing in a certain time specified in units of cm/hour. Ponding time (tp) is the time difference between when it rains and the time when water begins to pool above ground level. The purpose of this study was to determine the effect of soil grading on permeability and inundation time with repeated frequency of rainfall with the same intensity on mixed soil types. This research method is a type of laboratory experimental research, using a rainfall simulator. The soil used in this study is mixed soil types. Furthermore, artificial rain is given with an intensity of I15, each intensity is used five times the frequency of rain and the inundation time readings and inundation height are carried out in the Rainfall Simulator experiment tank and for the permeability test, observation is done with the constant head test. The results showed the value of the permeability coefficient is inversely proportional to the increase in rainfall intensity and frequency of rain. Inundation height and final inundation time are directly proportional to increasing rainfall intensity and rainfall frequency.