Original Article
Irrigation network management
afshin uossef gomrokchi; Nader Abbassi; mohammad hossein hadi tavatori
Abstract
Extended AbstractIntroductionDespite the importance of determining indicators of water consumption management in the agricultural sector for use in national macro-planning, so far, indicators of water consumption management in the production of agricultural and horticultural crops have received less ...
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Extended AbstractIntroductionDespite the importance of determining indicators of water consumption management in the agricultural sector for use in national macro-planning, so far, indicators of water consumption management in the production of agricultural and horticultural crops have received less attention. This matter is of double importance regarding the programs to improve the efficiency of water consumption. In this regard, the determination of the volume of applied water, as one of the important and influential indicators in agricultural planning, should be considered. Therefore, conducting a research that can lead to more accurate information about the volume of water used for various agricultural and horticultural crops in the country is necessary, and its results can be of great help to the decision-making of officials related to water and agriculture.The review of the conducted research showed that the accurate determination and monitoring of the current status of water consumption management indicators, including the volume of water consumed and the efficiency of irrigation water, as part of the important and influential indicators in agricultural planning in different regions of the world. Several studies have been conducted focusing on the analysis of the volume of olive water consumed in different places. Meanwhile, the researches done inside the country are mainly focused on the analysis of water needs, estimation of evapotranspiration, effects of lack of irrigation in different stages of growth and recognition of drought tolerant varieties of olives, and estimation of the amount of water consumed by olives. The monitoring of the current situation of water resources exploitation in olive groves in the country has received less attention. In this research, regardless the amount of water needed for evaporation and transpiration of olive plants, the amount of water consumed by olive growers in Qazvin province during the cropping season of 2017-2018 has been measured.MethodologyQazvin province is one of the main regions of olive production in the country, and the most important olive growing areas of the province are located in Tarom region, the area between Gilan and Zanjan provinces. The area of olive orchards in the province in 2017 was 9,300 hectares, and the area of fertile olive orchards was about 6,500 hectares. Also, the average yield of olives in the province is estimated at 2977 kg/hectare. This research was conducted with the aim of directly measuring the water consumption of olives in the olive production region of Qazvin province (Tarom region). Olive is the main product of gardeners in most villages of this region and is the only source of income for many villagers. So that more than 90% of gardeners' economy depends on the production of olives, and olives are their main product in 45 villages out of 105 villages in the region. In this regard, due to the severe limitation of water resources in the region and the development of new olive orchards, it is necessary to pay attention to the volume of water consumed by the orchards and plan based on the monitoring of the current state of water resources exploitation. In this research, measuring the amount of olive water consumed by considering various factors such as irrigation method, size of garden plots, soil texture, quality of water and soil resources, planting intervals and the level of education of the users were done. For this purpose, gardens for measuring water consumption were chosen in such a way as to cover the diversity of these factors. The volume of water given was measured with WSC flume (depending on the flow rate from type 3 to 5) or ultrasonic flow meter without interfering in the farmers' irrigation program. In the current research, in order to monitor the flow rate of the pumping station in drip irrigation systems, an ultrasonic flow meter device model PERCISION FLOW190PD was used and after the hydraulic test and calibration, the flow rate of the pumping station was measured in the selected gardens. After determining the amount of water entering the garden by carefully monitoring the garden irrigation schedule (watering time, irrigation cycle, irrigation times during the growth period), the amount of water consumed by the olive crop was measured for each of the selected gardens. Also, effective rainfall was estimated by SCS method. The water requirement of the reference plant was prepared and estimated using the Penman-Monteith method using the average data of the last 10 years for the target area from the nearest meteorological station. The water requirement of the reference plant was converted to the net water requirement of the plant by applying the plant coefficient. The yield of the crop at the end of the cropping season was also measured and the efficiency of water consumption was calculated and compared in each of the studied orchards.Results and DiscussionThe results showed that the range of irrigation water depth changes was between 5 and 30 mm with an average of 18 mm and a standard deviation of 17.7 mm. The minimum and maximum times of irrigations were 18 and 90 with an average of 39 and a standard deviation of 19.91. The average volume of applied water in the studied olive orchards in Tarom region was 6006 m3/ha with a standard deviation of 1517 m3/ha in all types of irrigation methods. The average yield of olives in the studied orchards in 2018 was equal to 5.46 tons/ha with a standard deviation of 4.8 tons/ha, which was higher than the average yield of olive in Qazvin province (3 tons/ha). According to the amount of water consumed and the yield, the average irrigation water efficiency in the studied orchards was 1.13 kg/m3 and the irrigation water efficiency and effective rainfall was equal to 0.78 kg/m3. In this regard, the highest index of agricultural water productivity index was recorded in dense olive groves of the region with the amount of 3.58 kg/m3. The most important reasons for the high agricultural water productivity index can be mentioned such as appropriate plant nutrition, proper fertilization of the land, soil texture modification, observance of horticulture principles, low-problem irrigation system, regular and correct irrigation cycle, and trained workers.Conclusions What can be concluded from this study is that water is not the only factor and input influencing the performance of olive product, several factors are also involved. In other words, the yield of the product can be increased even with less water consumption and with the management of other inputs and the technical and management conditions of the garden. This issue is very important in the country's water shortage situation where most of the trustees and operators focus on water management to increase performance. In general, it can be said that the performance of olive product, in addition to water, depends on various other factors, paying attention to each of them can play a more important role in improving performance and increasing productivity. Also, the comparison of the average volume of water consumed and the average water requirement of the olive crop indicates that the average amount of water given to olives (6006 m3/ha) is less than its actual requirement, both based on the recent 10-year meteorological data and it is also based on the information of the National Water Document. So, in general, it can be said that there is a lack of irrigation in the gardens. On the other hand, due to severe climate changes in recent years, there has been a big difference between the calculated values of the water requirement of crops and the information of the National Agricultural Water Document, which shows the need to update the National Agricultural Water Document in different regions of the country.
Original Article
Hydraulic
Hossein Sohrabzadeh-Anzani; Masoud Ghodsian
Abstract
Extended AbstractIntroduction Piano key weirs (PKWs) are a kind of non-linear weirs, initially introduced by Hydrocoop in France (Blanc and Lempérière, 2001). PKWs include the inlet and outlet keys as well as the inclined bottom. Due to their high compatibility with the site and their ...
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Extended AbstractIntroduction Piano key weirs (PKWs) are a kind of non-linear weirs, initially introduced by Hydrocoop in France (Blanc and Lempérière, 2001). PKWs include the inlet and outlet keys as well as the inclined bottom. Due to their high compatibility with the site and their economic and hydraulic performance, PKWs have been used in different countries including North America, Europe, Asia, and Australia (e.g., Malarce Dam, France, Lake Peachtree Dam, GA, USA, Dakmi 2 and Van Phong Barrage, Vietnam). There is a wide range of studies addressing the discharge coefficient of PKWs, but the energy dissipation of rectangular and trapezoidal PKWs has not been compared so far. Hence, in this paper the energy dissipation of these weirs are evaluated and compared.MethodologyTests were conducted in the hydraulic laboratory of Tarbiat Modares University, Tehran to assess the energy dissipation and flow properties downstream of rectangular and trapezoidal PKWs. Tests were performed using a flume with 10 m length, 0.75 m width, and 0.9 m height (Fig. 1). The water was provided by an underground sump. PK weir was installed and sealed at 4 m away from the flume inlet, so the minimum flow turbulence was achieved. The discharge was adjusted by changing the speed of the pumps using a control panel. The upstream and downstream flow depths were measured at (Crookston, 2010) and (Eslinger and Crookston, 2010) away from the weir upstream and downstream, respectively, using digital point gage with an accuracy of ±0.1 mm. The weir specifications are listed in Table 1. Experiments were conducted for various discharges and approach flow depths.Results The flow field upstream of PKWs was almost uniform and no turbulence was observed on the water surface. The flow deviated near the PKW with streamlines along the inlet and outlet keys and over the weir walls. Flow deviation led to an increased unit discharge in the outlet keys. Meanwhile, the local velocity was increased, leading to a positive acceleration. The observations showed that this was accompanied by water level decline, and increased downstream turbulence.The flow jet passing over the crest was accompanied by the interaction of three colliding jets. This interaction was the result of the collision between the flow nappies from lateral crests and the approach flow in the outlet keys (Fig. 4). The resulting interactions led to significant turbulence, and expansion of flow at the downstream. As the head increased, the outlet key discharge was increased, and energy dissipation was decreased. Figure 5 shows variations of the energy dissipation for rectangular and trapezoidal PKWs. The relative energy dissipation by trapezoidal PKW was more than that of rectangular PKW, by average of abbot 3%. Figure 6 shows the residual energy of the PKW versus discharge for rectangular and trapezoidal PKWs. It is clear that as the discharge increased, increased. Furthermore, the ascending rate of was higher for lower discharges. This is due to the local submersion upstream of the weir at higher discharge.ConclusionDespite the length of the used crest of trapezoidal PKW being less than rectangular PKW, energy dissipation of trapezoidal PKW is higher than that of rectangular PKW.The average discharge coefficient for trapezoidal PKWs is higher than that for rectangular PKW.The flow characteristics is different for rectangular and trapezoidal PKWs. For , no aeration is occurred. For , a week hydraulic jump is formed at the end of the weir outlet keys.New equation was obtained for estimation of energy dissipation.
Original Article
Irrigation network management
Nader Heydari
Abstract
Extended AbstractIntroductionIrrigation modernization is the process of updating and improving the existing irrigation plan in order to achieve advanced technical, economical, or social goals. It goes beyond just creating modern physical structures and equipment in the irrigation network, but also includes ...
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Extended AbstractIntroductionIrrigation modernization is the process of updating and improving the existing irrigation plan in order to achieve advanced technical, economical, or social goals. It goes beyond just creating modern physical structures and equipment in the irrigation network, but also includes organizational, institutional, and policy measures and reforms. Based on expert opinions, modernization of irrigation networks in Iran is very important and has many advantages.The activities carried out in the modernization projects that have been carried out in recent years in different countries, mainly include the change of water distribution systems based on open gravity channels to pipe networks under pressure to supply water to irrigation systems, and the implementation of pressurized irrigation methods (mainly drip or sprinkler irrigation methods) and intelligence and automation in irrigation systems in the fields.Modernization of systems has various advantages, including increasing reliability and flexibility, which lead to improved irrigation efficiency and increase crop yield; these two indicators play an important role in terms of durability and sustainability of irrigation projects. MethodologyThis research was carried out with the aim of developing a basic road map for the modernization of irrigation networks and emphasizing the related issues and challenges in the agricultural water sector in three steps. In the first and second steps, by reviewing and analyzing all related local and international scientific literature, issues, challenges, and various components affecting the modernization process were identified and then compiled in the form of a comprehensive questionnaire and expert opinions were obtained. n the third step, by holding a joint brainstorming workshop on the subject and with the necessary facilitations, the answers to the various key questions were obtained. Then, by combining the results of the workshop with the results obtained from the first and second steps, the main and key influencing factors in the basic road map of modernization of irrigation networks related to the following item were identified and compiled (step 4). These includes: expected goals; issues, problems, and obstacles; strategies/solutions (actions); what kind of modernization and where in the network; priority indicators in selecting networks; effectiveness monitoring indicators and the methods; and how the discussion of modernization enters laws, macro-level documents, and development plans. Results and Discussion After some brain storming discussions, some key questions were raised as topics discussed in the workshop, and with necessary facilitation, the related outputs were obtained. In Figures 1 and 2, the main and key components of the road map for the modernization of irrigation networks are presented and displayed according to the various key questions proposed on the subject. Considering the water crisis in the country and the need for optimal use of water in irrigation networks, as well as the results of the review and analysis of the opinions of experts in the field of water management and experts in the subject under discussion, the modernization of irrigation networks in the country is very necessary.When formulating the modernization roadmap, it is crucial to take various aspects of the issue into account. These include identifying effective parameters and necessary criteria for selecting and prioritizing networks for modernization, as well as understanding both internal and external obstacles that may hinder the modernization process. Additionally, it's important to assess the extent to which modernization contributes to real water conservation. The challenges and problems pertaining to the modernization of irrigation networks can be categorized into four main groups: technical, economic-social, institutional-legal, and environmental. Among these, the economic-social and institutional-legal aspects hold particular significance. Notably, some vital issues in these categories involve empowering farmers, addressing problems related to cooperative farming systems, improving farmer engagement and participation, establishing comprehensive farming systems, and enhancing coordination among different executive organizations and stakeholders. To successfully implement the modernization roadmap, it becomes imperative to develop comprehensive exploitation systems and water users associations. Moreover, special attention should be directed towards enhancing the networks' resilience and flexibility to effectively combat the impacts of climate change. Several other critical and challenging points also need consideration when adopting modernization policies and solutions in the country, including: In the process of implementing the modernization roadmap, the entire system, that is, from the water supply source, the conveyance network (both main and secondary canals), to the farm and the irrigation system, should be seen together and integrated, as far as the consensus of opinion is that the title of this integrated process should be called "irrigation modernization" (not irrigation network modernization). The challenge of paying attention to the rehabilitation and its integration and simultaneous implementation with the main activities of modernization.Modernization is one of the requirements of changing the supply-based water distribution system to a water demand-based distribution system. But at the same time, it should be noted that due to the lack of water in the networks due to drought, climate change, the expansion of the cultivated area, etc., and as a result of the increase in water demand, the water requirement of the command areas of the network should be provided by a conjunctive method and modernization should not cause social tensions in the network in this regard. The challenge of creating the platform and hardware and software infrastructures necessary for social and cooperative management of operation and maintenance of networks and in the framework of compiling and establishing a "participatory water exploitation system".The challenge of volume delivery of water and the accurate determination of applied and required water in the farm, considering that water delivery is based solely on traditional and historical concepts and methods, and the existence of previous traditional and outdated water rights is another challenge in the field of implementing modernization. Issues and challenges related to the weaknesses in the training of experts in the field of modernization and required technologies and the lack of related research projects in universities and research institutes.Challenges related to weaknesses in specialized training for extension staff and farmers and overall weaknesses in capacity building and the problem of creating modern farmers.Modernization is a complex and time-consuming process, and it must be implemented with necessary planning, and also the local community and the user should justify and accept it. In the first step, this concept should be explained and mainstreamed in the relevant literature and the expert community, and this term and its related programs should be properly entered into the country's macro-level documents and development plans. The purpose and necessity of modernization should be specified and targeted in such a way as to ensure the sustainability of the land and the satisfaction and the livelihood resilience of the beneficiaries. In the modernization program, the goal, the amount of development, and the method of doing the work should be mentioned and specified, and the required credibility should be taken into consideration, so that the legislator and the budget provider can be justified. The modernization program and the implementation of its plan must first be seen and prepared on a national scale (and even if possible with a basin view). That is, the plans should be seen comprehensively and for the sustainable development of the country and in a national scale. Also, the existence of a comprehensive road map with the necessary details is necessary so that the plans have a guarantee of implementation and are not influenced by the governments and the plans are not changed or deviated by their changes.
Original Article
Irrigation network management
mohamadreza zayeri
Abstract
Extended Abstract
Introduction
The effective use of water for irrigation requires that flow discharge and flow volume be measured carefully. Venturi flumes are widely-used structures for monitoring flow discharges in canal networks (Venturi tubes used in pipelines). Venturi was the first that observed ...
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Extended Abstract
Introduction
The effective use of water for irrigation requires that flow discharge and flow volume be measured carefully. Venturi flumes are widely-used structures for monitoring flow discharges in canal networks (Venturi tubes used in pipelines). Venturi was the first that observed the effect of a local contraction in a conduit on flow velocity distribution. The Venturi flumes have a local constriction. These devices may be built in different shapes and generally are very accurate when operated under free outflow conditions. Longitudinal section of the Venturi flumes has a constant bottom slope, or the bottom has a local sill or hump. The Venturi flume with an arc-shaped inlet is referred to as Khafagi flume. Montana flume is also a flume without diverging downstream wall. The polygonal-shaped flumes are simpler in construction than curve-shaped flumes and are less expensive due to plan shaped elements. The Parshall flume is characterized by a specific shape with variousdegrees of convergence and divergence. Since development of the Parshall flume in 1926, many studies have been made to simplify, reduce construction costs, increase performance and accuracy of the flumes. A review of the literature of the subject shows that the study of hydraulics in flow measurement flumes is mainly based on laboratory research, and although numerical modeling is of interest, due to the complexity of the geometry of the section and the Contraction of the triangular shape, their accuracy is not reported to be acceptable. On the other hand, researchers have tried to develop and use soft computing models to estimate flow characteristics in such sections due to the hydraulic complexity of these types of flumes, which according to published reports, their accuracy has been suitable in all types of sections. Therefore, in this research, the development of data group classification model, support vector machine (SVM) model and random forest algorithm were developed to estimate the Discharge in flumes with triangular contraction.
Methodology
By investigating the hydraulics of flow in flumes, researchers have found that the Discharge depends on the width of the contraction at the location of the structure, the horizontal and vertical slopes of the triangular walls, and the relative depth of the flow. Therefore, in the present study, for the development of GMDH, SVM and RF models, five dimensionless input parameters were considered. GMDH algorithm has been widely used in solving various hydraulic engineering problems. One of the most important applications of this method is the estimation of erosion around the bridge base, downstream of the cup-shaped launcher, and the discharge coefficient of flow measurement structures such as overflows. The SVM model is divided into two main groups a) Support Vector Classification model and b) Support Vector Regression model or SVR for short. The support vector machine classification model is used to solve data classification problems that are placed in different classes, and the support vector machine regression model is used to solve forecasting problems.
Results and Discussion
First, the collected data are divided into two categories, training and testing. It should be noted that the number of collected data is 592, and in this research, 80% of the data was assigned to training and the remaining 20% to testing. The training data is used for calibration and the test data is used for validation. Due to the fact that the collected data do not have a time series nature, they were randomly assigned to each of the training and testing groups. First, the results of the random forest model are presented. The reason for the priority of presenting the results of the random forest model compared to other modes used in this research is the identification of the most important effective parameters in the development process of the random forest model in the modeling and estimation of Discharge.
Conclusions
First, the collected data are divided into two categories, training and testing. It should be noted that the number of collected data is 592, and in this research, 80% of the data was assigned to training and the remaining 20% to testing. The training data is used for calibration and the test data is used for validation. Due to the fact that the collected data do not have a time series nature, they were randomly assigned to each of the training and testing groups. First, the results of the random forest model are presented. The reason for the priority of presenting the results of the random forest model compared to other modes used in this research is the identification of the most important effective parameters in the development process of the random forest model in the modeling and estimation of Discharge.
table 1- Error statistics of the models developed in the training and testing stages
Test
Train
Model
RMSE
RMSE
0.02
0.900
0.02
0.902
Random Forest
0.034
0.805
0.033
0.818
GMDH
0.016
0.951
0.015
0.982
SVM
Original Article
Pressurized Irrigation Systems
Edris Tand; Fariborz Abbasi; Jaman MohammadVali Samani
Abstract
Extended AbstractIntroduction Iran is characterized by a dry and semi-arid climate. The limited irrigated arable land in and the need for increasing food production due to the upward trend in population growth, coupled with water scarcity and Iran's heavy reliance on irrigation, have led to a heightened ...
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Extended AbstractIntroduction Iran is characterized by a dry and semi-arid climate. The limited irrigated arable land in and the need for increasing food production due to the upward trend in population growth, coupled with water scarcity and Iran's heavy reliance on irrigation, have led to a heightened importance of water productivity in agricultural sector. In this regard, for the purpose of identifying and understanding the agricultural potential of farmlands, the analysis and estimation of physical water productivity can be utilized. The main objective of conducting this research is to evaluate various interpolation methods and to select the most appropriate method for estimating the physical water productivity of the sugar beet. Additionally, the study aims to investigate the spatial distribution pattern of sugar beet production in its major cultivation centers across Iran. MethodologyTo accomplish this research, 108 field measured data obtained from selected sugar beet farms across Iran for the agricultural year 2016-2017 were used. Data on crop yield, irrigation water, and a ten-year average effective precipitation were collected, and the water productivity index of sugar beet was calculated for the selected farms. To achieve this goal, initially, the data was analyzed using the capabilities of the SPSS software. Descriptive statistical analysis was conducted, and similar regions were classified into independent and homogeneous groups (by drawing a dendrogram). Additionally, the spatial analysis of the data was carried out using the GS+ software. Furthermore, various interpolation methods were employed to create a classification map using the Geographic Information System (GIS) software. These methods encompass algebraic methods, including weighted inverse distance, radial basis function, global polynomial, and local polynomial methods, as well as geostatistical methods like ordinary kriging, simple kriging, and universal kriging. To assess the different interpolation methods, validation methods were employed, and accuracy index values such as Mean Bias Error (MBE), Mean Absolute Relative Error (MARE), Mean Squared Error (MSE), Mean Absolute Deviation (MAD), and Root Mean Square Error (RMSE) were utilized.Results and DiscussionThe results of the present study revealed that the water productivity index for sugar beet ranged from 2.60 to 13.11 kg/m³, with an average of 6.30 kg/m³. Despite the high standard deviation, the findings indicate a significant potential and high capacity for improving water productivity and crop performance in the sugar beet production hubs in Iran. Among the examined interpolation methods, the Radial Basis Function method with a completely regular spline model (CRS) exhibited acceptable accuracy (MBE=0.009) for generating the water productivity zoning map. The analysis of the generated map suggested that the western regions of the country, especially Kermanshah province, have higher water productivity index values compared to other parts of the country, making them more suitable for sugar beet cultivation. Furthermore, cluster analysis results for influential factors such as variety type, soil salinity, and irrigation water salinity indicated that within the study area, about 5% of the potential sugar beet cultivation areas could be divided into 23 distinct clusters. The minimum and maximum water productivity index were observed in cluster 11 (2.64 kg/m³) and cluster 3 (11.025 kg/m³), respectively.Based on the low level of correlation coefficient according to the results of the Pearson correlation test, the physical productivity of water utilization can be influenced by various factors other than precipitation and climate parameters. These factors include salinity of water, soil salinity, total irrigation water, average effective precipitation (over a ten-year period), and crop yield. It can be concluded that, in addition to precipitation and climatic parameters, other constant factors including management factors have an impact on improving the physical efficiency of water utilization. ConclusionsGiven the high water consumption in agricultural sector and the need for increased production in cultivated lands, evaluating the water productivity of high-water-demand crops such as sugar beet in Iran is essential. Understanding its current state and obtaining comprehensive information from fields, as well as monitoring cultivated fields, are necessary for decision-making and macro-level planning to enhance and improve water productivity of sugar beet cultivation in Iran. However, due to the extensive cultivation area, costs, limited resources, and time constraints, this task is challenging and often unfeasible. To address this, the potential of interpolation tools can be utilized. These tools have the capability to extrapolate point-based information to spatial information (area-wide). Results have shown that the highest and lowest error values were associated with the kriging interpolation method and the radial basis function (completely regularized spline) method, respectively, for creating zoning maps. In conclusion, it can be stated that through interpolation, if there is a strong correlation between the data, a better understanding of the spatial distribution of water productivity can be achieved in the study area.
Original Article
Geotechnic
Amir Malekpour; Nima Sadeghian; Mohammad Javad Farrokhi
Abstract
Extended AbstractIntroductionThe consolidation and the subsequent settlement can lead to the land subsidence, building destruction, pipeline ruptures in water supply networks, and damage to the asphalt pavement. In soil consolidation analyses and many other geotechnical problems, the uncertainty of geotechnical ...
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Extended AbstractIntroductionThe consolidation and the subsequent settlement can lead to the land subsidence, building destruction, pipeline ruptures in water supply networks, and damage to the asphalt pavement. In soil consolidation analyses and many other geotechnical problems, the uncertainty of geotechnical variables and their spatial variations is of significant importance. As a result, the uncertainty-based approaches are currently employed to consider these problems rather than deterministic analyses. In this regard, some researches have demonstrated the considerable influence of the random variables of hydraulic conductivity and volume compressibility on the soil consolidation phenomenon. However, the studies have rarely addressed the correlation between these random variables and its effect on the probabilistic consolidation analysis. The current research aims at investigating the impact of correlation between two random variables of hydraulic conductivity and volume compressibility using copula functions via the development of a computer program in MATLAB. The performance of different copula functions in the bivariate probabilistic analysis of consolidation and the temporal variations of pore water pressure distributions are studied in a case study in Guilan province of Iran.MethodologyIn this research, a computer program was developed in MATLAB to estimate the marginal distributions of two random variables of hydraulic conductivity and soil volume compressibility. Then the bivariate probability distributions of two random variables were obtained using two copula groups of Archimedean (Clayton, Gumbel and Frank) and elliptic (Gaussian and t-student). The bivariate distributions of random variables were applied to estimate the temporal pore water pressure distributions during consolidation in soil depths of 2 and 4 meters. The best joint probability distribution and the corresponding copula function was determined on MvCAT software based on the correlation of random variables and using certain criteria such as AIC, BIC, RMSE, and NSE. As a feature of developed computer program in this research,1000 pair values of hydraulic conductivity and volumetric compressibility were generated by copula functions (from the primary 24 field data) in order to create more accurate results. Then, after numerically solving the governing differential equation of consolidation using the implicit central finite difference method, the probability distributions of pore water pressure over time including the probability density functions (PDFs) and cumulative distribution functions (CDFs) were calculated using different copulas and compared with each other.Results and DiscussionThe results showed that the inverse Gaussian distribution properly fits to the marginal distributions of each single random variable, according to BIC criterion. In this research, Kendall’s correlartion coefficient showed a positive correlation between the random variables of hydraulic conductivity and soil volume compressibility. After 15 days from the beginning of consolidation with an initial loading of 400 kPa, the pore water pressures in the depth of 2 meters were estimated equal to 398.75, 398.9 and 398.95 kPa for Clayton, Gumbel and Clayton copulas, respectively. Whereas the pore pressure in the same depth were obtained equal to 399 and 399.05 kPa for Gaussian and t-student copulas, respectively. In the depth of 4 meters, Clayton, Gumbel and Clayton copulas, estimated the pore pressures equal to 399.54, 399.55, 399.54 kPa, respectively. It shows that Archimedean copulas create almost similar results in deeper regions within a soil layer. For elliptical copulas in the depth of 4 meters, the pore water pressures were calculated equal to 399.8 and 399.75 kPa for Gaussian and t-student copulas, respectively.ConclusionsConsidering the correlation of random variables, it is concluded that Archimedean copulas are more accurate in extreme values than elliptic copulas but elliptic copulas according to AIC, BIC and other evaluation criteria provide better balance between the number of parameters, the accuracy and the complexity of model. Generally, for both Archimedean and elliptic copulas, the temporal variations of pore water distributions show an increase in uncertainty with time via changing from sharp and narrow curves to flat and wide curves. Moreover, the consolidation rate (pore pressure dissipation rate) is slower for elliptic copulas than Archimedean copulas. Gaussian copula was found to be the best copula among all investigated copulas. The error of neglecting the correlation of random variables is bigger when a shallow foundation is to be designed by an engineer. Meanwhile, the consolidation rate is overestimated when the correlation of random variables is ignored. AcknowledgementThe authors express their gratitude to the experts working in technical and soil mechanics laboratory of Guilan province for their collaborations and carrying out the experiments on the soil samples of this research.
