This study presents the results of in-situ field stabilization of clay soil using Lime, Dolerite and Quartzite powders. The rock samples were collected from Oghi village and Misri Banda village of Mansehra District of Khyber Pakhtunkhwa Province, Pakistan. A 415m2site comprised of loose clay in village of Haripur district of Khyber Pakhtunkhwa was selected for field stabilization. In order to implement the experimental plan, eight test pits were dug and soil samples were collected from each pit to determine their major geotechnical properties. The raw soil contained Kaolinite, Illite and Montmorillonite and hence characterized as CH type according to the Unified Classification System. Later, different amounts of Lime were added to the retrieved samples and it was found that an addition of 6% Lime causes significant impact on soil properties. Following a steady augment by 10%, a maximum of 30% Dolerite and Quartzite powder were separately mixed with each of the 6% Lime-added soil samples. The resulting mixed soils were placed back into their respective pits and compacted slightly using compaction vibrator. and Standard penetration, field density and plate load tests were performed on each test pit. Finally, soil samples were extracted from all the test pits and the values of their direct shear box and Atterberg limits were measured. The results demonstrate that the addition of Dolerite and Quartzite leads to a significant increase in the bearing capacity, dry density, penetration resistance and angle of internal friction and thus improves the performance of the formerly Lime-stabilized soil by drastically decreasing its compressibility. The resulting improvement is mainly due to the denser and less hydrophilic character of the constituents of the added rock powders as compared with the Lime and raw soil. It has also been found that the magnitude of impact on the soil properties by Dolerite and Quartzite is notably different owing to the difference in mineralogical composition and physical characteristics of individual minerals present both rock types. This study would help construction engineers for better soil treatment.
We consider the Robin eigenvalue problem ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω where Ω ⊂ R n , n > 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λk(α) of this problem as functions of the parameter α. We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ ′ 1 (α). Assuming that the boundary ∂Ω is of class C 2 we obtain estimates to the difference λ D k −λk(α) between the k-th eigenvalue of the Laplace operator with Dirichlet boundary condition in Ω and the corresponding Robin eigenvalue for positive values of α for every k = 1, 2, . . ..