Structural Behavior of Tall Building Raft Foundations in Earthquake Zones

The paper studies the behavior of reinforced concrete raft foundations for multi-story buildings. It also develops a reliability assessment tool for multi-story building raft foundations subjected to earthquake loading. Several multi-story buildings with various configurations, heights, and soil profiles, were subjected to several ACI code combinations of gravity and earthquake loads from different seismic zones. The reliability of the raft foundations of these buildings was assessed using the reliability index approach based on their resistance to the applied loads. Also, the responses of the multi-story buildings under these loading combinations were studied and analyzed in order to draw recommendations and guidelines for the preliminary design of structurally efficient and reliable raft foundations in earthquake zones.


Introduction
Most multi-story buildings use raft foundations as structural elements to resist applied loads and transfer safely to the soil.The reliability and response of raft foundations were studied using the reliability index β and finite element analysis, respectively [1] [2].The reliability index β measures the reliability level of raft foundations based on their response to applied loads and according to their design codes.The reliability index chart is very useful for determining the raft foundation strength capacity for a desired level of reliability [3].3D finite element models were developed for multi-story building raft foundations to analyze their safety, stability, deformation, and crack formation based on the ACI code [4] [5] [6] [7].First, the commercial finite element software, STAAD-Pro, was

Reliability Formulation
A raft foundation fails when its resistance is less than the action caused by the applied loads.The raft foundation resistance and action are computed using the design strength M c and the external bending moment M e , respectively.Raft foundations fail when the resistance of the raft is less than the action caused by the applied load.The raft resistance is measured using the design moment strength M c while the raft action is measured by the external bending moments M e as shown in Figure 1.
The raft limit state function is given by the following equation: The raft limit state function is given by the following equation: ( ) where: φ = bending strength reduction factor, μ fy = mean value of f y ; Figure 1.Rectangular reinforced concrete raft cross section.
Because the limit state function is nonlinear, a Taylor series expansion was used to linearize it and obtain an approximate answer [9].The Taylor expansion about the mean value yields the following equation: The reliability index β of the linear function is given by the following equation: , , , where: σ AS = standard deviation of AS, σ fy = standard deviation of f y , f ′ ; and σ Me = standard deviation of M e .The parameters a 1 , a 2 , a 3 , and a 4 are computed using the following equations: The standard deviation σ is equal to the product of the mean value μ and the coefficient of variation V.The formulation estimates the reliability index β of reinforced concrete raft foundations when subjected to flexural loads, based on their resistance to applied loads as shown in Table 1 and Figure 2

Finite Element Analysis
Figure 1 shows the layout and steel detailing of a raft foundation for a high-rise building.The raft foundations are designed in earthquake zones to transmit building gravity and earthquake loads to the supporting soil without failure or large settlement (1 -4).The buildings considered herein had various heights and shapes (i.e., square, rectangular, tube, and circular) and included reinforced concrete shear walls (Figures 3-9).They were subjected to earthquake loads with a drift index of 0.002 [5] [6] [7] for different seismic zones and soil profiles as defined by the Uniform building Code (UBC) and the International Building Code (IBC), as shown in Table 2.The building responses and reactions were obtained using the finite element software STAAD-Pro [10].
A nonlinear finite element analysis was conducted using the commercial software STAAD-PRO to obtain the building drifts and reactions [8] [9] [11].
The buildings reactions were then used as point loads for the design of the raft foundations using STAAD-Foundation [12].As shown in Table 3, several parameters were used in the design, namely, concrete unit weight, c γ ; soil density, S γ ; allowable soil pressure, Q s ; reinforcing steel bar yield strength, y f ; concrete compressive strength, c f ′ ; and settlement ∆.

Results and Discussion
Reinforced concrete raft foundations for various structural buildings models were simulated, analyzed, and optimally designed optimally as per ACI design code.Figure 10 summarizes the design procedure for raft foundations.
The square, rectangular, tube, and circular buildings were subjected to earthquake loads defined by UBC and IBC codes, for different seismic zones and soil profiles.The building support reactions were obtained using the finite element         The results in Table 4 shows that the 7-story building raft foundation in zone 1 on soil profile 1 could be used in zone 5 on soil profile 5 with a small increase y = reinforcing steel yield strength, and c f ′ = concrete compressive strength.
c f ′ , μ As = mean value of A S , and μ Me = mean value of M e .

Figure 5 .
Figure 5. Square building plan and elevation.

Figure 6 .
Figure 6.Circular building plan and elevation.

Figure 7 .
Figure 7. Tube building plan and elevation.

Figure 8 .
Figure 8. Rectangular building plan and elevation.

Figure 9 .
Figure 9. Circular building floor plan and elevation.

Table 2 .
Soil profile and seismic factors.

Table 4 .
Raft dimensions and settlements.