No abstract

The technique of sand or stone columns is widely used to improve the load carrying capacity and reduce the settlement of soft soils. The technique consists of excavating holes of specific dimensions and arrangement in the soft soil and backfilling them with either stone or sand particles. The efficiency of the technique depends primarily on the type of the backfill material (sand or stone) and gradation as well as the placement relative density. In the present research, holes 50 mm in diameter and 300 mm in length were excavated in a bed of soft soil, 400 mm in thickness, of undrained shear strength between 16-19 kPa. The holes were backfilled with either sand or stone particles at loose and dense states. Each column was loaded gradually through a circular rigid footing 64.6 mm in diameter up to failure with continuous monitoring of the settlement. The outcomes of the model tests revealed that for both floating and end bearing types, the sand columns at low relative density exhibited higher bearing improvement ratios and lower settlement reduction ratios compared to stone columns. On the other hand, a reverse behavior was noticed, when the backfill material was placed at "dense state". The results shed the light on the importance of placement relative density of both backfill materials. The results are thoroughly analyzed in terms of the stress concentration ratio and stiffness ratio.

Sand and stone columns are used to improve bearing capacity of soft clayey soils… because of their stiffness which is higher than the soil was replaced, the compacted columns… produce shearing resistances which provide vertical support… for overlying structures… or embankments. Also the sand… and stone columns… accelerate the settlement… in the native surrounding soil… and improve the load settlement… characteristics… of foundation. The technique… consists of excavating… holes of specific… dimensions and arrangement… in the soft soil… and backfilling… them with either… sand or… stone particles.The present work investigates the behavior of soft soil reinforced with group of stone columns, sand columns and sand columns stabilized with lime or cement. The percentage of lime and cement used in this research, were determined previously in papers of single sand column stabilized with lime and cement, 11% by weight lime and 9% by weight cement. The model tests were carried out on a soil with undrained shear strength ranging between 16-18 kPa. The models consist of eight… columns at area replacement ratio of (0.196) in square pattern, the holes 50 mm in… diameter and 300 mm… in length were excavated… in a bed… of soft soil. The holes… were backfilled… with stone, sand and sand… stabilized with lime or cement particles. Each group… of columns was loaded… gradually through… a rectangular… rigid footing, its dimensions… 400×200 mm with 50 mm thickness, up to failure… with continuous… monitoring of the settlement. The test… results are analyzed… in terms… of bearing improvement… ratio… and settlement reduction… ratio for all… columns… and in terms… of the stress… concentration… ratio and… stiffness ratio.The results show that the improvement in bearing capacity was about 70% and 62% for sand columns stabilized by lime and cement respectively, and the improvement in bearing capacity was about 42% and 34% for sand columns stabilized by lime and cement compared with stone columns respectively.

Stone or sand columns are most widely used to improve the engineering properties of soft saturated soils. In principles, sand columns technique is very close to the well-known stone columns technique and the only difference is the backfill materials.The present work focuses on implementing sand columns in soft soil of different diameters, different relative densities considering both floating and end bearing types.The model tests were performed inside a steel container (600mm x 600mm and 500mm in height). Sand columns of diameters ranging between 22mm to 50mm were constructed in beds of soil of undrained shear strength ranging between (15-20) kPa. Each individual sand column was loaded vertically through a rigid circular footing of diameters between 28.6mm to 64.7mm provided an area replacement ratio (a s ) of (0.6),the ratio of column depth to the column diameter (L/D) was (6). The model test results revealed good improvements of the load carrying capacity of the columns ranging between (1.3 to 1.9) and significant reduction in the settlement over the untreated soil ranging between (0.18 to 0.47). End bearing columns exhibited better results than floating columns and the diameter of column has no effect on bearing capacity as the (a s ) and (L/D) are constants.

Graphs provide a useful mathematical tool for modeling various real world phenomenons.Dense graphs arise in many places of interest, for instance the internet and social networks to name just two. The density of a graph should be a real number reflecting just how many edges it contains. Many networks found in the real world share the so-called "small world" property that is organized into communities. These organizations rely on close relationships of people belonging to a same subgroup.The term "network" is used to denote the real world entity that usually maps to a graph after it is modeled. Therefore, there is greater need to propose more efficient graph and subgraph match methods to decide if their structures are identical.Reduce the search space in these networks motivate many researchers to give generously persevering attempt to propose a new efficient algorithm for that purpose.According to theoretical and practical interest in graph isomorphism, a new algorithm for determining graph isomorphism between two dense graphs is proposed.Furthermore, a new algorithm for determining an induced subgraph isomorphism between pattern and target graphs is proposed also.Those algorithms are analyzed from complexity point of view to demonstrate its effectiveness after applying it to several types of graphs. It is demonstrated that subgraph isomorphism is an improvement over the use of graph isomorphism in the zero knowledge protocol. The improvement comes from subgraph isomorphism being an NPcomplete problem, and therefore, more difficult for anunauthorized user to solve. Whereas, the graph isomorphism problem has been solved therefore, is vulnerable to attacks by malicious users. The algorithms have been applied using VB-language, with two easy to use interfaces to be helpful for the beneficiary.