Linear Dynamic Analysis and Design of Raft Foundation considering Long-Term Deflection and Uplift Check

. The Mat or Raft Foundations are widely used these days because we cannot use isolated footings and combined footings everywhere. As the spacing of the column is not uniform in the actual structures it may result in large uneven settlements at the base of the high-rise buildings. In a Mat foundation load from the superstructure is distributed evenly on the soil and uneven deflection is eliminated. Mat or raft foundation can be used with drops or without drops and with beams or without beams. For structures built on low-bearing capacity soil raft foundations, it is a good alternative as it reduces the settlement by distributing loads from super-structure to very large. In this study, the analysis and design of Mat Foundation for a G+7 story building are done by considering long-term deflection and uplift pressure accounts. For this study, Etabs v19.1.0 and Safe v20.0.0 software is used. The analysis is done by performing Response Spectrum Analysis or Linear Dynamic Analysis. After the analysis, results are collected in terms of short-term deflection, Uplift Pressure, long-term deflection, and punching shear and compared with permissible limits specified by the code IS 1904 (Part-1):1986. Results show that all values like deflection, uplift pressure and punching shear are under the permissible limits.


Introduction
The foundations are provided to support the load from the super-structure and to transfer it to the ground safely without causing excessive shear failure and excessive settlement failure [1].A foundation, the lowest element of a building, is in direct touch with the soil and situated below the earth level [2].A raft foundation is a monolithic foundation that is cast for the whole floor area and carries the loads from all the columns and walls [3].It is generally provided when the total area covered by the column is greater than 75%.[4].The raft slab is provided with the reinforcement bars running perpendicular to each other in which there is one layer at the top and the other provided at the bottom forming a mesh.It may also be used with beams provided invertedly on both sides of the raft foundation and termed as Main and Secondary beams.These beams are cast monolithically with the raft foundation.The raft foundations are used for soils that have small soil-bearing capacities, but the soil has to support heavy loads from columns or walls [5].As the foundation is the lowest part of the structure and it is in direct contact with the soil below.And whenever there is an earthquake there is shaking at the base of the structure.So, a Dynamic analysis of the foundation should be performed to ascertain the behavior of footing under earthquake loading.Raft Foundations are used when there are large settlements or differential settlements are anticipated [6].Raft foundations are used for buildings on compressible ground such as very soft clays, alluvial deposits, and compressible fill material [7].When the bearing capacity of soil is low then the raft foundation is used as it results in a decrease in an uneven settlement and reduces the further cracking in the walls of the superstructure.Whenever we provide a raft foundation, due to heavy loads from the columns results in very high uplift pressure.This Uplift is counteracted by the weight of the raft.If the thickness of the raft is not adequate to counteract the uplift pressure, then the footing will fail [10][11][12][13].
The thickness of the raft foundation is also governed by the Punching shear criteria.In this study, the Dynamic analysis of the raft foundation is performed by the Linear dynamic analysis using SAFE software.Joshna Manjrekar et al., (2018) did a study on "Analysis and Design of Mat Foundation using Safe" [1].In this study, they have designed a raft for a G+5 story building for low-bearing capacity soil.They have done the analysis by static analysis and dynamic analysis.Results have been compared from both analyses.They found that the results are within the permissible limits.Also, they concluded that the steel requirement for the dynamic analysis is 37.6% more than the static analysis.Sunesra Shakira et al., (2017) did a study on "Analysis of Raft & Pile Raft Foundation using Safe Software" [4].In this paper, they have designed the foundation for the G+22-story residential building.Their main objective was to reduce the settlement and to keep the bearing pressure within limits.For that, they have provided piles under the raft at a spacing of 6m.They have concluded that the Pile-Raft foundation proved to be very effective in reducing the settlement and settlement reduced by 57.16% and SBC requirements were also reduced by 57.18%.Ziaabe Deen.S. Punekar et al., (2014) did a study on "Analysis and Design of Raft Foundation" [2].In this paper, they have designed the raft footing for the 12-story building and performed the dynamic analysis using safe v12.They have compared the parameters like moment, punching shear, and deflection of the footing.After analysis, they concluded that the moments and punching shear and deflection are within the limit.And also, found that detailing and casting of rafts is very simple as excavation can be done on go.Suman M. Sharma et al., (2020) did the study "Comparison of Raft foundation and Beam & Slab Raft Foundation for High Rise Building" [3].In this study, they have done the analysis in staad pro software.Analysis was performed by considering three SBCs of soils viz.180 kN/m2, 220 kN/m2, 250 kN/m2.The analysis they have found that concrete requirement is more in the case of raft foundations and steel requirement is more in the case of beam and slab raft foundations [14][15].But the overall cost of materials in raft foundation is more.So, they concluded that beam and slab raft foundation is more economical than raft foundation.Omer Mughieda et al., (2017) did a study on the "Effect of soil subgrade modulus on raft foundation behavior" [5].In this paper raft foundation for a 10-story building is considered and the effect of soil subgrade modulus on the bending moment, shear, and deformation of the raft foundation is studied using safe software.After analysis, they found that Bending moment and shear are independent of the value of the soil subgrade modulus [16][17][18].As the soil subgrade modulus increases deflection values decrease due to more support from the soil.Yuwen Ju and Honggang Lei (2019) did the study "Actual Temperature Evolution of Thick Raft Concrete Foundations and Cracking Risk Analysis" [6].In this study, they have taken an actual construction of a raft for analysis.In the analysis, they have fitted the temperature sensors at the top and bottom of the raft foundation and the temperature gradient is noted and found that the difference between the temperature at the surface and at the core after 9 days is 35℃.They have concluded that thermal cracking occurs when the raft thickness is more than 2.5m which results in a temperature gradient of more than 25℃.So, the temperature control measure should be used [19][20].The objective of this study is to analyze the behavior of raft foundations under dynamic loading using response spectrum analysis.The various responses of raft foundations were investigated in terms of uplift pressure, settlement, and punching shear.Further, the long-term deflection was evaluated using CSI Safe software in raft footing due to creep and shrinkage.

Methodology
In this study, we have taken a G+7 story building for which a raft foundation is to be designed.Support reactions are imported from Etabs to Safe software.The Building Plan dimensions are 20x20m.and story height is 3m.Following is the configuration of the model for which Raft is to be designed.

Modeling
Modeling of the raft foundation is done in the Safe software.The concrete grade used for the Raft is M25.Cover to reinforcement is considered 50mm.The thickness of the raft is taken as 1000mm.The raft slab is modeled without providing drops.All the response spectrum load cases are imported directly from the Etabs software.

Analysis
The analysis is performed in CSI Safe software.For uplift check, uplift combinations are defined in load combination.Also, for the check of long-term deflection load cases and load combinations have been defined.No extra load is considered on the raft as all the reactions are considered by Safe software from Etabs itself.Thickness is basically designed on the basis of punching shear criteria and the area of the raft is decided by soil pressure from below.

Load combinations For Uplift check
Load Combinations for uplift checks are selected from ACI 318-08, "Building Code Requirements for Structural Concrete and Commentary" [7].Load Combinations are listed below: In these combinations, we have used response spectrum load case instead of static earthquake loading to take care of linear dynamic analysis.

Load combinations For Long-Term Deflection
Long-Term Deflection is due to the effect of creep and shrinkage.The following load combination has been used for long-term deflection: −    +     In the above combination for long-term sustained loading only 25% live load is considered to be sustained for the life of the structure.And the other 75% is considered an immediate deflection.

Results and Discussions
After performing the analysis in software, we finalized the thickness of the raft as 1000mm and the area of the raft as 22m x 22m.The following observations have been done from the analysis:

Punching Shear
It governs the design the thickness of the footing.It is also called a two-way shear.The thickness of the Footing/Foundation should be enough to resist the penetration effect of the column loading otherwise it results in the failure of the foundation.In Safe, the punching shear values are shown for each column and all values should be less than 1.In our case, as the thickness is 1000mm so it is much on the safer side.The punching shear result is shown in Fig. 2. We can see that all values are quite less than 1.So, it means our thickness is much safe, but to make it economical we can decrease the thickness and by trials, we can finalize the thickness of the footing.N/C in Fig. 2 shows that in these areas punching shear cannot take place as there is no column and shear wall provided there.So, the load is distributed on the large area and perimeter to resist the punching is also more.

Soil Pressure
Basically, soil pressure from below the footing governs the area to be provided for the foundation.The area should be enough to reduce the soil pressure such that it does not exceed the soil bearing capacity otherwise slope failure of soil occurs results in failure of the foundation.If soil pressure increases more than the bearing capacity of the soil then we have to increase the area of the footing.Our design area provided is 22m x 22m which results in soil pressure less than the bearing capacity of the soil.The soil pressure result is shown in Fig. 3.This figure shows values of soil pressure in colored contours.As we can see from the figure soil pressure is maximum at the corners because the area provided there is less.So, to further reduce this pressure we can provide more offset from the outer columns (In our case 1m offset is provided.

Deformation
Deformation of the footing also governs the area of the footing.Deformation should be limited as given by IS 1904 (Part-1):1986.If it exceeds the limiting value then we have to increase the area or depth of footing.In our case, the deformation values are less than the permissible values.The deformation result is shown in fig. 4. We can see from the distribution of contours that the deformation is maximum at the corners and minimum at the center.The maximum value is 67.88mm which is less than the permissible limit specified in the IS 1904 (Part-1):1986 [11].At the corners because of the presence of shear walls load intensity is more there so resulting in large deformation than the center of the raft foundation.

Uplift Check
Uplift of the foundation is a very serious problem, as it causes tension at the base of the footing which may cause cracking in the structure or sometimes additional moments due to overturning at one edge.This uplift effect usually results from lateral forces like wind or earthquake.In our case, as we are doing linear dynamic analysis of the foundation so here the lateral forces are seismic forces.In this study, we have checked all combinations of uplift as per ACI 318-08.ACI has given these load combinations for static earthquake loading.In this study, we have replaced them with response spectrum load cases as we are doing response spectrum analysis.Fig. 5 shows the uplift pressure values for the (DL+LL) load combination and the maximum value of pressure under this load combination is -201.28kN/m 2 which is compressive in nature.Fig. 6 shows the uplift pressure values for the (DL±0.7Eqxor DL±0.7Eqy) load combination and the maximum value of pressure is -172.17kN/m 2 which is again compressive in nature.Fig. 7 shows the uplift pressure values for the (DL+0.7LL±0.525Eqxor DL+0.7LL±0.525Eqy)load combination and the maximum value of pressure under this load combination is -192.55kN/m 2 which is also compressive in nature.As in all the cases, we get negative soil pressure at the base of the raft which indicates that there is only compressive pressure at the base and no tension is there.So, our raft foundation is safe against uplift forces.

Long-Term Deflection
Long-term deflection is also important in the design of footing and it should be within limits prescribed by the IS 1904 (Part 1)-1986.Long-term deflection occurs because of the sustained loading and mainly due to the creep and shrinkage of concrete.It depends on time, as time increases, it goes on increasing.Long-term deflection occurs due to sustained loading which includes mainly dead load and superimposed load.But the code specifies take effect of live load also up to 25% and the rest 75% is considered in the immediate deflection case.Fig. 8 shows the deflection for an immediate sustained loading case in which a non-linear cracked section is taken and only 25% of the live load is considered.The maximum deflection, in this case, is 61.57mm which is under the permissible limit.Fig. 9 shows long-term deflection under load case similar to immediate sustained but in this effect of creep and shrinkage is also considered.The value of the creep coefficient is taken as 2 and the shrinkage strain is taken as 0.0005 [9].The maximum deflection was found to be 89.50 mm which is less than the permissible limit  240 given by ACI 318-14 [8].The design of the Safe software is very simple.As it draws the column strip and middle strip by itself and calculates the area of steel required.Fig. 10 (a) shows the area of steel for the column and middle strip both along the x-direction.And Fig. 10 (b) shows the reinforced steel values for the column and the middle strip along the ydirection.As we have performed the dynamic analysis, the area of reinforcement required is very high.Safe software gives us the freedom to specify the bar dia.and spacing and we can find which dia. or spacing is suitable.We can see from both these figures that at the position column steel required is at the bottom and at other positions top steel is governing.

Conclusion
• Dynamic analysis results in a large thickness of raft and a large area of steel reinforcement than the static analysis.
• Software shows the punching shear values on each location of the column and should be less than 1.
• Deformation of raft should be within permissible limit specified by the IS 1904 (Part-1):1986.
• For lateral loadings uplift check must be applied at the base of the foundation and there should not be any tension at the base to prevent any overturning failure.• During the design of the foundation, we have to take care of the long-term deflection also as the foundation is below the ground and it is always under sustained loading.
(a) Plan of G+7 building (b) Plan of Raft Foundation 22m x 22m Fig. 1 Plan of building and foundation

Fig. 8
Fig. 8 Immediate deflection (Non-Linear cracked section) Fig. 9 Long-term deflection due to creep and shrinkage3.6 Design of Raft Foundation (a) X-direction (b) Y-direction Fig. 10 Area of steel reinforcement required

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For the Different ages of concrete IS 456:2000 has specified the values of creep coefficient and the choice depends on at what age we are going to check long-term deflection.• CSI Safe makes the foundation design very simple and it gives the reinforcement design based on strip design or on basis of the finite element method.• In our study we concluded that the weight of the foundation should be enough to balance the uplift pressure.• To keep long-term deflection within limits we have to increase the area or thickness.• In the areas with high severity of earthquakes we have to do dynamic analysis and consider uplift pressure and long-term deflection.
).The maximum pressure is -226.28kN/m 2 and the minimum pressure is -146.46kN/m 2 .As both pressures are negative and within our soil bearing capacity i.e., 250 kN/m 2 .Hence the area of footing is safe.