11610414, to the Indian Institute of Technology Guwahati, for the award of the degree of Doctor of Philosophy in Civil Engineering is a record of bonafide research work carried out by him under my supervision and guidance. I must also convey my gratitude to all the faculty members of the Civil Engineering Department for their thoughtful suggestions, help and encouragement.
ABSTRACT
Objectives
Furthermore, it is also shown how the uniformity of leaching associated with a multi-layer pond ditch drainage system, both in terms of water flow and travel time distribution in the flow space, can be improved by adopting a suitable pond distribution at the surface of the flow. the ground. We now proceed to obtain some solutions of Eq. 2.1) using the separation of variables method (Kirkham and Powers 1972).
Mathematical Formulation and Solution
Allowing for the above expressions, we can then represent this by doing a Fourier expansion, as we have. Now, given the above expressions, can then be determined using the expansion of the Fourier series in the range that we thus have.
Estimation of Travel Times
Verification of Proposed Solution
The calculation of discharges using the proposed model is done by considering the hydraulic conductivity of Fukuda's experimental soil as a value obtained using Eq. 2.100) to Fukuda's experimental discharge. A further check of the proposed solution was also performed by plotting a numerical solution of the flow problem of Fig. With the model thus developed, a steady-state MODFLOW run was then performed and hydraulic head contours corresponding to some numerical hydraulic head values were then drawn as shown in Fig.
As can be seen, the analytically obtained hydraulic heads for all the tested heads match closely with the corresponding MODFLOW generated values, which again proves the correctness of the developed solution.
Discussions
Water particle travel times (in days) starting from the ground surface to the ditches when the parameters in fig. 2.6(a), as can be observed, bottom flow accounts for approx. 39% of the total flow to the ditches; the corresponding figure for the flow situation in fig. However, the effect of the variable dam fields can be seen to be much more prominent on the travel time distributions corresponding to the flow situation in fig.
Travel times of water particles (in years) from the ground surface to the ditches when the parameters of Fig.
Conclusions
The study clearly highlights the fact that a significant improvement in streamline distribution and water particle travel times in a multi-layer drainage space can be achieved by constructing a variable pond field at the surface of the soil. This is important because such a system, if installed for leaching a salt-affected soil, will result in better, faster and more uniform cleaning of the drainage space compared to the case where the leaching is carried out with only a constant depth on site of the drainage. surface of a drained ditch system. The study also shows that subsurface drainage in a rice field is a slow process, especially in the presence of muddy and plow sole layers, and that water particles may require long time intervals to reach the drains from the soil surface.
This is because, as mentioned before, most of the soils in nature, including rice paddies, are mostly layered in nature.
List of Notations
This chapter deals with the development of an analytical model for the prediction of time-dependent seepage in a network of culverts partially penetrating a homogeneous and anisotropic soil underlain by an impermeable barrier at a limited distance from the bottom of the culverts, where the seepage feeds from a variable pond distribution on the land surface. The accuracy of the proposed model is checked for some simplified situations by comparing the discharge and travel times of specific water particles for some simplified situations with identical values obtained from analytical and experimental works of others. A numerical check on the accuracy of the proposed model is also performed using the PMWIN platform (Chiang and Kinzelbach 2001).
Furthermore, it is also demonstrated with the help of a few examples how the streamline distribution in a drainage space can be modulated to a desired pattern by imposing a suitable water distribution at the ground surface.
A Few Solutions of the Two-Dimensional Continuity Equation of Groundwater Flow for a Homogeneous and Anisotropic Soil
The model is versatile as it takes into account the final width and final water level of the trenches, the final penetration of runoff into the ground and, as mentioned earlier, also the variable field of ponds on the ground surface. 3.1) on both sides of it and then we introduce the transformation. on the obtained equation, after some simplification, we find one. is the soil anisotropy ratio and. Now we find some solutions to the equation. Then, of course, we also have the equation as a solution.
Since the addition of solutions of a differential equation also leads to another solution of the equation, a solution of Eq. 3.15) where are all arbitrary constants, and are summation indices and and are any positive integers.
Mathematical Formulation and Solution
Now applying the equality of the main hydraulic state (X) at the interface between regions II and III to Eqs. Also applying the flux equality condition (XI) at the interface between regions II and III to Eq. As before, adjusting the bases for the double summation terms in the above equation, we get
Applying conditions (I) to Eq. Now readjust the bases for the double summation terms of Eq. It should be noted that. 3.72), and the one in the above equation is lined with. Now the amount of water seeping through the earth's surface in time T can be expressed by integrating Eq.
Model Verification and Discussions .1 Verification of the proposed solution
- Discussions
Changes and relationships with time for different ratios when the parameters of the flow problem in Fig. Vertical velocity distribution on the ground surface at two different times when the parameters of the flow problem in Fig. 3.7(a) and 3.7(c) ) can further be observed, that the size of the ponding depth on the soil surface of the trench drainage scenario with ponds plays an important role in deciding the velocity distribution (and thus also the time-varying upper discharge function) on the soil surface; change in lake depth from 0 m in the flow situation in fig.
Travel times for water particles (in days) from the ground surface to the ditches when the parameters of Fig.
Conclusions
In reality, if the wet field is not fed by any external water source, the water level in the ground surface lakes would decrease over time and as such the height would then not be constant but would continue to decrease with time. MODFLOW validation of the proposed solution was also performed for a specific problem configuration. This is all the more true if the soil is very thick and the penetration depth of the drainage is relatively high in relation to the thickness of the soil.
The study also clearly shows that the outlet gradients at the boundaries of a ditch are very sensitive to the simulation time of a ditch drainage system as well as to the location of the water level in.
List of Notations
The accuracy of the derived solutions for some simplified situations is verified by comparison with the corresponding analytical and experimental works of others. The proposed models are used to study how the travel times of water particles to runoff from the soil surface are affected by various problem parameters, such as hydraulic conductivity, length, width and thickness of the soil profile, water level elevations in trenches, lake depths, and the presence or absence of a boundary without of the flow on the vertical side of the flow domain. Using these models, the variation of soil surface discharge with time is also investigated for various combinations of hydraulic conductivity, specific storage, soil profile thickness, and the presence or absence of a no-flow boundary in the flow space.
Furthermore, the derived solutions are also used to study the effects of variations of water level heights and surface dam distributions on distribution of the stream surfaces corresponding to some three-dimensional dam ditch drainage scenarios.
A Few Solutions of the Three-Dimensional Continuity Equation of Groundwater Flow for a Homogeneous and Anisotropic Soil
Equating each term on the left side of Eq. Of course, the solution to Eq. where is an arbitrary constant. If we now assume a solution to Eq. where and are functions only and - and we use the same for the equation. 4.9), obtained after separating similar variables. If the second and third terms on the left side of Eq. where and are arbitrary constants - and we solve the differential equations derived from them, then we get and as. where and are arbitrary constants.
Also when the last two terms of Eq. whose solution can be expressed as 4.26) where are any arbitrary constants.
Mathematical Formulation and Solution
- Case 1: Ponded field flanked on four of its vertical faces by ditch drains
The distance of the ith bundle, as measured from the origin O, in the x and y directions is taken as. It should be noted that there will be none. inner bundles on the surface of the soil and the pond depth will then be uniform. The directional conductivity of the soil column along the x, y and z directions is taken as and respectively and indicate the specific storage of the soil column.
Constancy of pond depth in pond belts can be maintained by continuously supplying the soil surface with irrigation water; thus, soil water loss due to infiltration can be balanced at all times.
