A Geotechnical and Structural Analysis and Design of Transformer Foundation Using Finite Element

The main parameters of a typical transformer foundation design are: Identifying requirements of transformer, soil investigation, geotechnical design of foundation, calculation the loads and check settlements and finite element modelling.

Analysis and design methodology of transformer foundation contains various stages which is explained by the flowchart shown in Figure 1.

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Figure 1. Schematic diagram of a transformer foundation

2.1 Principal requirements of transformer foundation

Many of manufactured companies attach some civil instruments to operate and maintain the transformers in good performance. One of these guides are the distance between the railway of the transformer and the dimension of the pit under transformer. Almost, the distance between the railways is 1.505m and the height of pit from the foundation to mesh of gravel is minimum 1 m. So, depending on the pervious requirement, the foundation is drawing as shown in Figure 2.

Transformer has length=5.10 m, width=4.5 m and the height=5.00 m. The total calculated weight of unique transformer (including oil)=800 kN. A fire wall is constructed to avoid spate from the two transformers and also it used to protect each transformer of other. The transformer is installed on pedestals 0.6 cm in thickness and 0.9 m height, these pedestals carry iron railway to move the transformer in one way. On the two sides of the transformers iron meshes are putted on concrete pits and covered with suitable stone. This system needs to be constructed on raft foundation to prevent the differential settlement which may be cause damage for the electrical cables. The soil beneath the foundation was enhanced by replacing the weak soil and some layers of crushed stone, sub base and concrete layer were implemented according to recommendation of soil investigation reports.

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Figure 2. Principal requirement for transformer foundation

2.2 Site investigation

To recognize the soil strata a soil investigation was planned and executed. Two boreholes at a depth of 10 m each one was conducted in the field and many required tests were done. Standard penetration test, SPT, is considered one of the famous tests, so it was done during progressing of boring. This test is performed according to ASTM D 1586-99 [9].

Figure 3 shows the characteristics of subsoil profile for two bore holes and S.P.T diagrams.

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Figure 3. Soil profile and SPT numbers with depth

The profiles of two bore holes explain the following:

1. A grey organic fill material, loose sand soil, this layer extends from 0 to 1.5 meters.
2. Layer of inorganic gray silty sand soil (SM) to clayey sand (SC), of medium plasticity. Loose to medium density and this layer extended from 1.5.0 to 6.0 m.

A layer of inorganic gray SM, of medium plasticity. Medium density and this layer extended from 6.0 to 10.0 m.

Based on field investigation and results of laboratories test, the bearing capacity using static Terzaghi’ formulas were estimated.

Using test data from field tests, the allowable bearing capacity and settlement of footings on coarse-grained soils are often determined on empirical methods. SPT “N” values at various depths using the dynamic method to estimate the bearing capacity for cohesion less soil in 25 mm of settlement was considered as field test [10, 11].

Accordingly, the bearing capacity of the soil under the foundation depending on SPT blows number is summarized in Table 1.

Table 1. Allowable bearing capacity according to SPT test

The direct shear tests were used to guess the bearing capacity using static method because most soil consisted of sand with some silts. Terzaghi equations with Meyerhof’s modification were used to calculate the bearing capacity values [12].

Table 2 shows the bearing capacity values for the soil beneath foundation using shear strength parameters.

Table 2. The allowable bearing capacity from direct shear

From the results Table 1 of SPT and direct shear tests, there are weak layers for all investigated depth; the failure of soil is of punching shear.

Gathering information of SPT and laboratories tests and relying on accepted engineering practices, 45 Kpa allowable capacities can be used in the design of raft foundation. From the results of SPT and direct shear tests, there are weak layers for all investigated depth; the failure of soil is of punching shear. So, the designer should choose suitable footing with safety factor more than 3 and that does not exceed the allowable bearing capacities

During the soil investigation, the level of underground water was measured at end of boring which was 1.5m underground surface and the average unite weight of soil about 18 kN/m³.

2.3 Geotechnical design of footing

The electrical transformer footing is basically designed depending on conventional method. Depending on the applied loads the geometry of the foundation will be considered and the foundation will be embedded to 1.5 m depth. According to the manufacture details of transformer as the dimensions and weight, the primary dimensions of raft is 13 m as length and 5.5 m as width. The thickness of raft foundation was assumed 0.5 m to resist the punching and wide bean shear. The dimension of foundation was selected depending on two criteria; the first is the requirement of electric standard designs for transformer and the second bearing capacity of the soil under foundation. This primary dimension will be checked later to overcome the elastic and differential settlement and then is modified if it doesn’t comply the bearing capacity.

2.3.1 Calculation the static loads

Length of transformer (L)=5.1 meters.

Width of transformer (B)=4.5 meters.

Height of transformer above top of Pedestal (H)=5.00 meters.

Each transformer has total weight (including oil)=800 kN.

So, the total load of the pad foundation and inverted beams with fire wall=1423 kN.

The total load of two transformers and foundation=1600 + 1238=3023 kN.

2.3.2 Calculation the wind load

The effect of the wind load will be considered in this article, so maximum wind velocity (Vb) will be taken=170.0 km/hr.

The velocity of wind was considered depend on the previous record of winds in city.

The design wind pressure (Fz) is calculated according to the following equation [13].

$F=A \times P \times C d.$    (1)

where, F=load of wind (N).

$P= pressure~of~wind =0.00256 {~V}^2$    (2)

- The speed of the wind (V) is 170 km/hr=47.2 m/s.

= 0.613×(47.2)²=1365.67 N/m².

A=the area of the facade=6.80 m (height)×5.50 m (width)=37.4 m².

Cd= factor =1.2.

F_z=37.4×1365.67×1.2=61291.26 N=61.3 kN.

This equation considers the location of the transformer whether in open or closed area, so the Cd factor was taken according this criterion.

2.3.3 Soil stability check

In several cases, any foundations are generally subjected to the vertical load in addition moments, so, the pressure distribution from foundation on soil is not uniform. The pressure is distributed off on the soil as [10]:

${{q}_{\max ,\min }}=\frac{\sum{p}}{BL}\left( 1\pm \frac{6e}{L} \right)$    (3)

where,

P=the total applied load.

B and L represent length and width of the foundation.

E=eccentricity of the footing.

The total load of two transformer and foundation=3023 kN.

Maximum moment at the base due to maximum horizontal force=61.3 kN ×3.5=214.6 kN.m.

Eccentricity for the footing=214.6/3023=0.071 m.

Eq. (3) with related data produce two values of pressure beneath footing on soil one represents the maximum and other minimum as following:

q_max=43.6 kN/m² which less than the allowable bearing capacity of soil.

q_min=40.8 kN/m²

2.3.4 Settlement check

Under all loads, any soil will suffer consolidation or settlement leading damage of structures stablished on it. If this settlement is not stayed to allowable value, the favorite use of this structure may be weakened and next structure’s life may be reduced. settlement of structures may be uniform or some time nonuniform which is named differential settlement [11].

The loads from any structure cause stress to the soil that happen when a structure is constructed on a foundation consisting of soil. The stability and safety of the structure depend on two most important requirements which are:

(1) The vertical deformation which is known settlement of the soil must be within permissible values;

(2) The shear strength of soil beneath foundation should be safe to resist the stresses induced [14].

Because all the soil profile illustrates that soil is sand, so the elastic settlement is considered to check the settlement under foundation.

Theoretically, if the foundation is perfectly flexible, the settlement may be expressed as [10]:

$S c=\Delta \sigma\left(\alpha B^{\prime}\right) \frac{1-\mu^2 s}{E s} I s I f$    (4)

where,

∆σ=net calculated pressure on the foundation, for two transformer and footing=2814/66.3 =42.28 kN/m².

μ_s=Poisson’s ratio for soil=0.3.

E_s=average modulus of elasticity for soil beneath the foundation which is measured from z=0 to z=5B=9000 kN/m².

B´=B/2 for foundation center. Where the width of footing (B) is 5.5 m, so B= 5.5/2 = 2.75 m.

Is=shape factor which depend on the length, width and depth of footing underground=0.0871.

α=factor that relates on the foundation settlement which is wanted to calculate. At the center of the foundation for calculation of settlement =4.

I_f=depth factor which depend on the Poisson’s ratio of soil, length, width and depth of footing underground=0.83.

Accordingly, the elastic settlement from data above=3.39 mm which is within the permissible settlement.

The value of settlement is considered acceptable and less than the allowable settlement under certain structures which is 25 mm [10, 11, 15].

2.4 Finite element modeling

FEM is one of the excellent-established techniques to solve of complex problems using the computer in various fields of civil engineering.

The foundation material and the concrete are modelled in finite elements as linear elastic materials with specified young’s moduli and poison’s ratio [16].

To perform structural analysis and design for concrete foundation, CSI-SAP 2000 software V14 was selected and some assumptions should be assumed to create the numerical model as illustrated in Tables 3 and 4.

Table 3. Material data

Table 4. Structural elements data

To simulate the soil under the foundation, the spring elements are developed and distributed under the foundation after dividing it to regulator small elements. The raft was divided to 0.5×0.5 m size of elements and a spring will be attached under center of each element.

The contestant stiffness of spring is in vertical direction (Z-direction) and the required unit is in kN/m³.

Bowles [15] has suggested the following for approximation calculation to k_sdepending on the allowable bearing capacity q_a:

k_s=40 (SF) q_a (kN/m³)    (5)

where:

q_a=the allowable bearing capacity of soil furnished in kPa.

SF=safety factor which almost equal to 3.

This equation is founded on q_a=q_ult/SF at a settlement ∆H=0.0254 m in ultimate soil pressure.

The subgrade modulus is taken calculated k_s=5400 kN/m³.

The elasticity modulus of footing concrete was taken as following equation [17]:

E_c=4700 (fc´)^1/2       (6)

where:

fc´=the compression strength of the concrete.

The raft foundation and fire wall are a shell element with related thickness, compressive strength and the unite weight.

After inputting the data required in Tables 3 and 4 which represent properties of the structural parts, a real dimension and size were created in the SAP 2000 model. To simplify inputting the structural parts many grids were created in three dimensions and the distance between grids represents size of footing and fire wall [18].

A distinctive agreement was obtained between the FEM with the use of the developed programs software and theoretical load–deflection results [19-21].

The FE analysis seemed a reasonably good coincidence with the results of laboratory experimental; a discrepancy of within 11 to 25% when nonlinear finite element analysis was performed to study the geotechnical behavior to shell footings [16, 22, 23].

According to the obtained results, Table 5 shows the results of design of foundation and fire wall. From this table it is clear to see the closer results between the analytical and these obtained from numerical model. This convergence in the results is due to the correct input of the properties and analysis the model by FEM which depend mainly on same ACI-code requirements.

Table 5. Results of the analytic ad FEM

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Figure 12. The whole design of transformers foundation

After conducting all steps, the analysis and the design of raft foundation, beams under the transformer and the fire wall. It is desire to explain the full sketch of the reinforcement for all parts in details.

Using the finite elements analysis using structural software for structural analysis and design of structures is considerable safe to in finding the reinforcements and structural requirement.

The whole design of the raft foundation and the beams with retaining walls are shown in Figure 12.