ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT

We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained

CSEM IMAGING OF THE NEAR SURFACE DYNAMICS AND ITS IMPACT FOR FOUNDATION STABILITY AT QUARTER 27, 15th OF MAY CITY, HELWAN, EGYPT

In the present work, we involve the Control Source Electromagnetic (CSEM) Technique to image the dynamic migration center of the near surface fractures, fissures, and cracks in a new dwelling area at 15th of May city close to Cairo. This area forms the center of the zonal weakness of the subsoil, which in turn, interact with the weight center of the construction leading to catastrophiccollapses.The control source electromagnetic technique has been developed recently to monitor the migration of the weakness center represented as the accumulative fissures and cracks in thenear surface. Three composite profiles of wide and planshet mesh data have been collected in 2008. This survey has been followed by performing two profiles in 2010; one of these profiles has been repeated to observe the situation changes, and the second profile has been measured between the other two profiles of2008. The last profile had been performed to study the mutual relation between the measurements of the two cycles. The objectives of the whole process are to validate the capability of the technique to pick the minor changes of the weakness center, consequently, study its relation to the weight center of the adjacent construction to produce a recommended procedure to minimizethe destruction resources at the site of investigation.The measured data has been interpreted and represented in graphs showing the distribution of the heterogeneity of the geoelectric parameters in the subsoil, furthermore, in a series of geoelectric cross section representing the applied frequencies used during the survey. The study concludes that (1) the center of the cracked zone is moving upward closer to the surface of the ground and heaver, (2) the water content is moving downward producing soil dryness at the shallow depths, and (3) the site became more stable in 2010 than 2008, however, the destruction resources remain warning with collapse events. Furthermore, the situation reflects the relation between the water content and the changes in the weakness center

Csem imaging of the near surface dynamics and its impact for foundation stability at quarter 27, 15th of may city, helwan, egypt

In the present work, we involve the Control Source Electromagnetic (CSEM) Technique to image the dynamic migration center of the near surface fractures, fissures, and cracks in a new dwelling area at 15th of May city close to Cairo. This area forms the center of the zonal weakness of the subsoil, which in turn, interact with the weight center of the construction leading to catastrophiccollapses.The control source electromagnetic technique has been developed recently to monitor the migration of the weakness center represented as the accumulative fissures and cracks in thenear surface. Three composite profiles of wide and planshet mesh data have been collected in 2008. This survey has been followed by performing two profiles in 2010; one of these profiles has been repeated to observe the situation changes, and the second profile has been measured between the other two profiles of2008. The last profile had been performed to study the mutual relation between the measurements of the two cycles. The objectives of the whole process are to validate the capability of the technique to pick the minor changes of the weakness center, consequently, study its relation to the weight center of the adjacent construction to produce a recommended procedure to minimizethe destruction resources at the site of investigation.The measured data has been interpreted and represented in graphs showing the distribution of the heterogeneity of the geoelectric parameters in the subsoil, furthermore, in a series of geoelectric cross section representing the applied frequencies used during the survey. The study concludes that (1) the center of the cracked zone is moving upward closer to the surface of the ground and heaver, (2) the water content is moving downward producing soil dryness at the shallow depths, and (3) the site became more stable in 2010 than 2008, however, the destruction resources remain warning with collapse events. Furthermore, the situation reflects the relation between the water content and the changes in the weakness center