الفهرس 
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Abstract
This research deals with the Rigid Inclusions improvement technique considering the installation effects. The cavity expansion approach is utilized to estimate the improvement in the surrounding soil properties and enhance the accuracy of estimating the deformations and the straining actions. Two case studies will be extensively analyzed to gain insight into dealing with such soil improvement techniques by studying full-scale tests conducted in Venette City and New Mansoura City. Results of the study showed that considering the improved soil parameters results in a better prediction of the settlement values of footings resting on the improved soil compared to the measured values. The average error in the settlement values is reduced from about 74% to about 24% after considering the enhancement in the soil parameters due to the installation effect.
In addition to that, the behaviour of rigid inclusions under seismic loading is then studied to ensure that no problems arise as a result of overstressed rigid inclusion elements under significant seismic loads. Thus, the straining actions of rigid inclusions must be determined to detect the need for reinforcement in rigid inclusions, mainly when soft soils exist between two stiff layers. The current research aims to develop a reliable approach to consider seismic loads, considering the installation effect of rigid inclusions by utilizing the cavity expansion theory to estimate the improvement in the surrounding soil properties and thereby enhance the accuracy of estimating the deformations and the straining actions.
Finally, a parametric study is carried out using numerical modelling to predict the variation in the improvement factor with the variation of the treated soil stiffness and geometry of the RI system. The analyses use the verified numerical model for the zone loading test case study conducted at New Mansoura city in Egypt, employing the finite element software (PLAXIS 3D). This research aims to develop simple and user-friendly charts to estimate the settlement improvement factor (N) that correlates the settlement values without soil improvement to the settlement values after improvement, considering the installation effect of the rigid inclusions in soft clay formations. The settlement associated with loading both the improved and unimproved soils is then compared for each studied condition in the parametric study to determine the improvement factor (N). The performed analyses clearly showed the high effect of the rigid inclusions in reducing the settlement associated with the construction on the improved soft clay. Based on the conducted parametric study, design charts are developed to provide a simple tool for predicting the settlement values associated with construction on improved soft clay formations with rigid inclusions under different conditions.
7.2 Conclusions
The results from the numerical analyses have pointed to the importance of considering the installation effects of the rigid inclusions to achieve a reliable estimate of the induced deformations and a better evaluation of the straining actions acting on the rigid inclusions. Three-dimensional finite element analyses have been performed through this research to compare the estimated behaviour of a loaded footing on soft clay formations, either ignoring or considering the installation effects of the rigid inclusions used to improve the soft clay properties. Due to the limitations of the 3D FEM in dealing with the large strain problems, axisymmetric FEM was developed to define the enhancement in the soil parameters due to installing the rigid inclusion by applying the cavity expansion theory. The enhanced soil parameters resulting from the axisymmetric model were then adopted in the 3D FEM to consider the installation effect of the rigid inclusions. from the performed analyses, the following conclusions can be drawn:
1. Two-dimensional axisymmetric finite element analysis is suitable for simulating the installation effect by applying the lateral displacement occurring during rigid inclusion installation.
2. The hardening stress soil model can capture the ground constitutive behaviour while constructing rigid inclusions.
3. Three-dimensional finite element analysis has proved to be an effective method for estimating the settlement associated with the foundation on the soil-rigid inclusion system.
4. The applied displacement in the axisymmetric model generally shows significantly improved parameters where the improvement ratio depends on the initially defined radius and the applied lateral displacement.
5. The error calculated in the case of the applied radial displacement of 0.20m is the minimum error in all the performed analyses. A theoretical minimum error that tends to zero is most likely to be found when applying a radial displacement equal to the rigid inclusion’s radius. However, due to the limitations of finite element analysis, the ability to simulate an initial radius value of zero and consequently apply a radial displacement equivalent to the radius of the rigid inclusion is not applicable.
6. The unloading behaviour revealed from the numerical analysis is relatively linear and may be attributed to the utilized soil constitutive model (i.e., hardening soil model), which adopts a constant stiffness value during the unloading stage.
7. The analyses show that the commonly applied approach of neglecting the effect of rigid inclusion installation leads to overestimating the predicted settlement.
8. The estimated settlement trends are in good agreement with the measured ones, where the best is for applying a radial deformation of 0.20m. The maximum measured settlement in the field at a stress of 300 kPa is 5.12mm, while the estimated settlement is 8.67mm, 6.75mm, 6.21mm, and 5.91mm in the cases of neglecting the installation effect and applying a radial deformation of 0.05m, 0.15, and 0.20m, respectively.
9. The error in estimating the settlement associated with the loading test on the improved soil is found to be 74%, 46%, 30%, and 24% in the cases of neglecting the installation effect and applying a radial deformation of 0.05m, 0.15m, and 0.20m, respectively.
10. The bending moments are significantly increased after considering the seismic loading, which reaches about six times the bending moment in case of ignoring seismic loading as per the applied seismic intensity in the study.
11. Because of the significantly increased bending moments, the resulting stresses could cause the rigid inclusions to break suddenly if the stresses are too high compared to the structural & geotechnical capacities of the reinforced inclusions.
12. It is evident after studying the case study in the case of ignoring the installation effect and considering it that the values of the maximum straining actions acting on the rigid inclusions are very close. At the same time, there is a significant difference in the distribution along the inclusion shaft. Also, it is clear from both cases that resulting stresses could cause the rigid inclusions to break suddenly.
13. For the proposed approaches to simulate the sudden break in the inclusions due to the seismic loading, ignoring the existence of rigid inclusions in the soil-inclusion matrix is proved to be too conservative.
14. The simulation of horizontal sets of interfaces every 1.0m deep of the rigid inclusions has shown almost the same results as that of inclined sets of interfaces every 1.0m deep of the rigid inclusions with minor changes.
15. The simulation of weak horizontal/inclined interfaces has indicated minor changes in the settlement values compared to the normal condition where no crack is applied on the inclusion that the designer of the superstructure elements may ignore. The minor changes in the settlement are reduced due to the confinement of the rigid inclusions, even in the case of weak interfaces, and minor friction occurs on the interface surface of the inclusion.
16. Considering horizontal sets of interfaces with a dummy material every 1.0m deep of the rigid inclusions has indicated that the settlement increase is about 65%, which is a significant increase that the designer of the superstructure elements shall consider.
17. The failure approaches have indicated a significant variation in the results, whereas the two conservative approaches have shown a dramatic increase in the settlement value. In comparison, the other three approaches have indicated a minor change in the settlement value. These findings shall be carefully studied, and further analyses shall be carried out depending on an accurate failure simulation in the inclusions. A trial loading zone is to be performed where these various simulations shall be applied to detect the most reliable simulation approach for failure that occurs in the inclusion due to seismic loading.
18. The maximum allowable stress in the case of simulating weak horizontal/inclined interfaces is the same compared to the normal condition where no crack is applied on the inclusion. On the other hand, the worst simulation for failure was the ignorance of the inclusion’s existence, where the system efficiency reached about 52%.
19. The ratio of the improved deformation modulus to the initial deformation modulus in the case of the rigid inclusions bearing in the clay deposits ranges between 1.78 and 3.34, with an average value of 2.46, while in the case of the rigid inclusions bearing in the sand deposits with the same clay layer thickness, the ratio of the improved deformation modulus to the initial deformation modulus ranges between 2.55 and 3.94, with an average value of 3.19, with an increase of about 30% over that in the case of the rigid inclusions bearing in the clay.
20. The ratio between the improved deformation modulus and the initial undrained shear strength in the case of the rigid inclusions bearing in the clay ranges between 356 and 668, with an average value of 492, while in the case of the rigid inclusions bearing in the sand deposits with the same clay layer thickness, the ratio between the improved deformation modulus and the initial undrained shear strength ranges between 510 and 788, with an average value of 638, with an increase of about 30% over that in the case of the rigid inclusions bearing in the clay.
21. Results of the analyses have shown that increasing the diameter of the rigid inclusion increases the value of the improved soil deformation modulus. Rigid inclusions of 0.60m in diameter resulted in increasing the deformation modulus by an average value of about 16.6% compared to 0.40m in diameter inclusions.
22. In the case of the rigid inclusions bearing in the clay, the improvement factor decreases as the undrained shear strength decreases. The improvement factor considering the different values of the undrained shear strengths in the current study (i.e., cu = 10, 17.5, 25 kPa) ranges between 2.23 and 8.74, with an average value of about 4.68. On the other hand, in the case of rigid inclusions bearing in the sand for the same clay layer thickness, the improvement factor ranges between 11.80 and 58.10, with an average value of about 25.60 (i.e., 5.50 times that in the case of the rigid inclusions bearing in the clay).
23. In the case of the rigid inclusions bearing in the clay, the ratio (S/D) is inversely proportional to the improvement factor, where the improvement factor for (S/D = 2) ranges between 3.13 to 8.74, with an average value of 5.73. In contrast, for (S/D = 3), the improvement factor ranges between 2.61 to 7.23 with an average value of 4.62, while for (S/D = 4), the improvement factor ranges between 2.23 to 5.62 with an average value of 3.69.
7.3 Recommendations for Future Studies
1. More case studies for rigid inclusions improvement technique need to be analyzed using 3D and 2D models to ensure the research findings where an extensive instrumentation program shall be performed.
2. Considering the proposed failure approaches, the seismic loading effect on the soil-rigid inclusions matrix shall be widely studied. The analyses of the various failure approaches are to be compared relative to the measurements of an actual case study where rigid inclusion shall be broken to simulate the overstressing that occurs during seismic loading.
3. The developed simplified charts shall be verified by comparing the estimated preliminary settlement utilizing the chart with the measured settlement through various projects to enhance the reliability of such charts.
4. Simple software shall be developed to facilitate the preliminary estimate of the number, lengths, and reinforcement needed for the rigid inclusion system based on the findings of this research.
5. Methods for improving the rigidity of the soil-rigid inclusion matrix, especially at the top part of inclusion, shall be studied to increase the capability of this technique to resist the high lateral loads that can be transferred when applying such improvement in structures like bridges.