Effect of Embedment on Generated Bending Moment in Raft Foundation under Seismic Load

This research shows the experimental results of the bending moment in a flexible and rigid raft foundation rested on dense sandy soil with different embedded depth throughout 24 tests. A physical model of dimensions (200mm*200mm) and (320) mm in height was constructed with raft foundation of (10) mm thickness for flexible raft and (23) mm for rigid raft made of reinforced concrete. To imitate the seismic excitation shaking table skill was applied, the shaker was adjusted to three frequencies equal to (1Hz,2Hz, and 3Hz) and displacement magnitude of (13) mm, the foundation was located at four different embedment depths (0,0.25B = 50mm,0.5B = 100mm, and B = 200mm), where B is the raft width. Generally, the maximum bending moment decreased with increasing the embedment depth from zero to B, by (75%,41%, and 43%) for the flexible raft under (1, 2 and 3) Hz respectively, for the rigid raft the maximum bending moment decreased by (62%, and 37%) under (1and 2) Hz respectively, for 3Hz excitation frequency, the direction of behavior wasn't the same for the case of the rigid raft foundation as the maximum bending moment increased with increasing the embedment depth from zero to (0.25B,0.5B and B) by (142% , 268% and 5%) compared with the surface raft foundation.


INTRODUCTION
For a safe design of the shallow foundation, it must have the ability to resist the dynamic loads; this subject has taken considerable attention in recent years. Embedment has a significant effect on the response of the foundation and must be careful when evaluated, (Chowdhury and Dasgupta, 2008). In practice, foundations are located at a certain depth under the soil surface to transmit the structural loads to the soil, this procedure leads to increase the foundation stiffness, (Al-Azawi, 2006). Moreover, the energy is dissipated by radiation damping under and along the sides of the foundation, (Prakash and Puri, 2006). In this study the foundation was placed at four different depths to investigate the embedment effect on the generated bending moment during seismic loading. Flexible and rigid raft foundations were used for that reason. The foundations were subjected to three frequencies (1, 2, and 3) Hz, which appointed to minor, intermediate, and substantial earthquakes.

MODEL PREPARATION AND EXPERIMENTAL WORK
The soil response is greatly affected by the method of preparation (Albusoda and Salem, 2012). Twenty-four model loading tests were carried out in a rigid steel cylindrical container of (700) mm in diameter and (600) mm in height, the inside walls of the container were covered by styropor sheets to avert the reflection wave during seismic loading which results in extra stresses and intercepts friction of container face and soil. To create a physical model a small scale concrete raft foundation of size (200 × 200 × 10) mm for the flexible raft and (200*200*23) mm for the rigid raft is used. The relative stiffness factor (K) method was applied to determine the thickness that separates flexible raft and rigid by Eq. (1), it was equal to (16) mm, (Gupta, 1997). The foundation was reinforced by 30*30 mm steel mesh of 2 mm diameter which represents approximately (1%) of the section area of raft foundation. Fig.1 shows the modeling of raft foundation. A steel frame of (320) mm in height was firmed on the raft foundation to constitute the building and to carry the additional mass of (40) kg. This mass was determined based on the total allowable settlement of the raft foundation. The building height and the soil layer thickness underlying the raft foundation were fixed to (320) mm and (450) mm, respectively. The used soil was dry dense sandy soil of (70٪) relative density passing through sieve No.10 (2.0) mm and retained on sieve No. (200), properties of the used sand are listed in Table 1 with the standards of the test, hygroscopic water content (≈0.5-3.0%) was added to the sand prior to compaction to ensure small cementation of soil. The soil was placed in the container in layers and then compacted to the needed density, which equals (16.86) KN/m³ using a steel hammer of (4.5) kg. The height of falling was approximately between (150) and (200) mm, and the number of blows was (4) for each layer, which was decided by fabricating a relation between the number of drops and the resulting dry density. The sand-cone method was used according to (ASTM-D7698-11a, 1998) to make sure the required density is achieved. To simulate the earthquake loading, shaking table technique was used, the table was fitted to a fixed displacement equals to 13 mm and (1,2, and3) Hz frequency in x-direction for 10 secs (the Where: E = Modulus of compressibility of the foundation in kg/cm 2 E, = Modulus of compressibility of the foundation soil in kg/cm 2 b = Length of the section in the bending axis in cm d = Thickness of the raft or beam in cm K= The relative stiffness factor (for K>5 the raft foundation is flexible)

INSTRUMENTATION AND MEASUREMENT OF DYNAMIC RESPONSE
To measure the response of the raft foundation the following devices were used:

Strain Gauges
To measure the generated bending moment three pairs of PFL-20 strain gauges were used. Every pair consist of two gauges fixed at the top and bottom of the foundation and connected by halfbridge technique; these pairs were placed at the raft edges and center.

Data Logger
All the testing devices were calibrated and connected to the data logger unit which provides a connection of these devices with the computer laptop. The data logger consisted of five channels, three of them for half-bridge connection of strain gauges, and two for LVDTs readings.
The overall description of test components and measuring devices is shown in Fig.3.

RESULTS AND DISCUSSION
Bending moment in raft foundation was measured by using three pairs of strain gages located at the edges and the center of the raft; in general, the maximum bending moment was generated at the edge close to the excitation source.  Figure 3. General view of the testing model and instruments.

Effect of embedment depth
To study the influence of embedment depth of the raft foundation on the generated bending moment under seismic loading the foundation was located at four different depths (0, 0.25B = 50 mm, 0.5 B = 100 mm, and B = 200 mm). Fig. 4, Fig. 5, and Fig. 6 show the results of variation bending moment with embedment depth. It was clear from results that the bending moment was reduced with increasing the embedment depth for all excitation frequencies, and for both flexible and rigid foundation except one case, it will be explained later. Table 3 shows the percentages of bending moment reduction for raft foundation embedded at (0.25 B, 0.5 B, and B) comparing with surface foundation. Increasing the embedment depth means increasing confinement of raft by sidewalls of the basement and surrounding soil which led to reduce the generated bending moment, this trend of behavior wasn't the same for the case of the rigid raft foundation under (3 Hz) which behaved in a different way as in Fig. 6. It is explained in the following points: 4.1.1 The maximum bending moment increased with increasing the embedment depth from zero to (0.25 B, and 0.5 B) by (142% and 268%), respectively, compared with surface embedded raft. 4.1.2 The maximum bending moment decreased with increasing the embedment depth from 0.5 B to B by (71%), but it is still more than that of surface embedded raft by (5%). This behavior may be caused by the influence of the additional inertia resulting from embedment, which was more than that provided by increasing the side friction forces when the embedment depth was increased. When the embedment depth became B the influence of increasing side frictional forces became more than the influence of increasing the inertia forces, and accordingly, the bending moment decreased.

Effect of raft thickness (rigid and flexible)
The bending moment-time history was recorded for all tests. Fig.7, Fig.8 and Fig.9 show the momenttime history for 0.5B embedment depth and (1, 2, and 3) Hz, respectively, which have been chosen to represent the effect of raft thickness on generated bending moment with time. For all tests the maximum bending moment generated in rigid foundation was most larger than recorded in the flexible foundation, this result agrees with (Aung, and Tun, 2012) who conclude that the maximum bending moment in raft foundation increases with increasing raft thickness.       Table 4. summaries the ratio of maximum bending moment generated in the rigid raft to that of the flexible raft foundation. The higher stiffness for the rigid raft means more resistance to the shape change when subjected to seismic loading, and that led to higher internal forces and bending moment generated in the raft foundation (the moment is a function of the force).  Table 4. Summary of the maximum bending moment generated in the rigid raft to that generated in flexible raft.

The effect of excitation frequency on bending moment
The raft foundation was subjected to three different excitation frequencies (1, 2, and 3) Hz, for both flexible and rigid raft foundation, and for all embedment depths, the variation of bending moment was as shown in Fig.10, and Fig.11. From figures, it's clear that higher frequency led to generate higher bending moment in the flexible and rigid raft foundation because higher frequency means higher applied forces, which leads to higher bending moment as the moment is a function of loading. Table 5 summarizes the ratio of maximum bending moment generated in raft foundation excited by (2 and 3) Hz to excited by (1Hz). Generally, the ratios related to flexible raft were higher than those of rigid rafts because the higher ability of vibration damping of rigid raft foundation.

CONCLUSIONS
 Generally, the maximum bending moment decreased with increasing embedment depth. With increasing the embedment depth from zero to B, the maximum bending moment decreased by (75%, 41%, and 43%) for flexible raft under (1, 2, and 3) Hz respectively, for rigid raft the maximum bending moment decreased by (62%, and 37%) under (1 and 2) Hz respectively.    3.3 1.8 Rigid  For 3Hz excitation frequency, the trend of behavior wasn't the same for the case of rigid raft foundation as the maximum bending moment increased with increasing the embedment depth from zero to 0.25B and 0.5B by (143% and 268%) respectively, compared with raft foundation of zero embedment depth, however, as the foundation embedded at B, the maximum bending moment decreased by (71%) compared with raft foundation of 0.5B though it still higher than that of zero embedment depth by (5%).  Increasing the excitation frequency increases the maximum bending moment of flexible and rigid raft foundation.
 Generally, the maximum moment is measured at the edge close to the direction of starting the dynamic excitation of the foundation. Also, significantly higher maximum moment values were measured in rigid raft foundation comparing to the flexible one.
 The maximum bending moment is significantly affected by raft thickness; very high readings were recorded for the rigid raft foundation comparing with the flexible raft foundation.
 The ratio of the maximum bending moment generated in the rigid raft foundation to that generated in flexible raft foundation ranged between (1.6 to 6.9).