In this article, the spectrum trading problem between primary users and secondary networks is
investigated. The secondary network requests multiple channels with the targeted availability to satisfy its
users' demands. Due to the uncertainty about the channels availability, stochastic optimization techniques
are adopted to nd the optimal set of channels for each secondary network for the lowest cost. Two different
constraints on the secondary demand are de ned. The rst one is when the throughput has to be fully satis ed
for a certain percentage of time, and the second one is when the expected value of the throughput has
to exceed a certain percentage of the requested one. Also, the possibility for channel subleasing among
the secondary networks is investigated to reduce the demand shortage. The results show that demanding
simultaneous channels increases the cost as it reaches up to 20% higher than if the same resources were
requested individually. Also, channels subleasing reduces the demand shortage probability and increases
the achieved throughput, especially at low value of requested demand. In this case, the demand satisfaction
probability increases by around 30% while the achieved throughput increases up to 40% compared to the
scenario where channels subleasing is not allowed.
Since more than one-third of dam failures have been attributed to uncontrolled seepage, it is of great importance to investigate the behaviour of this phenomenon in order to achieve the maximum degree of safety for such dams. The present work investigated the influence of the permeability coefficient of the different materials used in zoned earth dams on different seepage parameters. For the modelling and analysis processes, the Seep/w and Seep2D software were employed. The numerical results prove that the optimum relative hydraulic conductivity between the inner and transition shells is about 0.001, and it is better to use filling materials with less hydraulic conductivity in the upstream transition and outer shells than in the downstream ones. A good agreement was noted between the obtained results from Seep/w and those from Seep2D. Reducing the hydraulic conductivity of both the upstream and the downstream shells, or of the downstream shells only, causes the pore water pressure in the dam body to increase significantly, and causes a remarkable reduction in the seeped water quantity and velocity. A moderate reduction in the different seepage parameters is achieved by reducing the hydraulic conductivity of the upstream transition shell, and a small reduction is noticed by reducing the hydraulic conductivity of the upstream outer shell.
One of the most popular tools for dealing with the seepage problem in embankment dams is using different types and shapes of downstream drains. So, the paper presents a comprehensive study of the different drainage systems through such dams. Many earth dam models are investigated through the SEEP/W model representing different dimensions and geometry of downstream drains. A comparison is carried out between the present study and previous experimental and numerical studies and the results of the present study are almost close to the previous studies. The present work concludes that the most influential factor in a horizontal drain is the length, and the thickness has a negligible effect. The reasonable length ratio of a horizontal drain (L/B) is about 0.34 according to the minimum seepage. The angle of toe drains has a slight effect on the different seepage parameters. The performance of the inclined chimney drain is better than the vertical drain to control the seepage.
The seepage study through earth dams is very essential for the design and construction processes of such dams to ensure the needed safety and efficient performance. The present study focuses on the seepage flow through zoned embankment dams by introducing a numerical analysis using the Seep/w numerical model. The main objective of the study is to investigate the different effects of the dam zones' thickness and side slopes on seepage through such dams to achieve the most suitable dimensions and geometry of the different zones. First, the Seep/w is used to analyze the problem of seepage through earth dams with an internal core. The present obtained results and the results of other previous experimental and analytical studies are almost close to each other. The present work proves that the best relative thickness of the inner, transition, and outer zones (t1:t2:t3) according to the minimum seepage and cost of the used materials is 2:1.5:1.5 respectively. At the same time, it is proven that the reasonable optimum side slopes (H:V) of the inner, transition, and outer zones are 1:1.75, 1.25:1, and 3.75:1 respectively.
