Finite Elements Analysis On Weak Foundation Of Oil Storage Tank

Yang Xiujuan College of Civil Engineering, China University of Petroleum, Dongying 257061,

China Jia Shanpo

College of Civil Engineering, China University of Petroleum, Dongying 257061, China

Yan Xiangzhen College of Civil Engineering, China University of Petroleum, Dongying 257061,

China Abstract

In this paper, the distribution of extra stress and distortion of homogeneous soil is studied by using ANSYS and comparing the result with the result by formula of criterion. Then, according to the geological references of Cangzhou refinery in Hebei province, several methods on how to deal with foundation and minimum compound modulus of elasticity and Poisson’s ratio that are required in order to control the settlement in some magnitude are concluded by using finite element analysis to simulate the extra stress distribution of the single oil storage tank whose volume is 15×105 m3 on the basis of preceding conclusions. The result illustrates that finite element analysis is dependable for analyzing extra stress and distortion of the foundation of an oil storage tank. This method can provide reference for the analysis of elasticity and plasticity of foundations and dependability for engineering design.

Introduction Because of the new policy reformation and opening, China Petroleum & Chemical Corporation wants to set up several oil storage tanks, considering the need for energy storage in Shanghai and Zhejiang province, and that the volume of a single oil storage tank is up to 15×105 m3. The construction of oversized oil storage tanks not only puts forward stricter requirement for the design of equipment and techniques, but also increases the difficulty for the reconnaissance of geotechnical engineering and the construction of oil storage tanks. At present, many experts in soil mechanics have made many attempts to design a foundation for this kind of oversized oil storage tank by engineering examples of other countries and their experiences about how to construct an oil storage tank whose volume being 15×105 m3 in China. Because there are no criteria to consult on how to construct this type of oil storage tank, designing the tank is very difficult. Many references provide the coefficient tables of additional stress with the even, circular plane load on an infinite homogeneous foundation, but in fact, the actual foundation is inhomogeneous and additional stress and settlement changes with the influence of physical soil parameters. So there are many errors when using the criterion formula to calculate stress and settlement.

In this paper, the distribution of extra stress and distortion of homogeneous soil is studied by using ANSYS and comparing the result with the result by formula of criterion. Then, according to the geological references of Cangzhou refinery in Hebei province, several methods on how to deal with foundation and minimum compound modulus of elasticity and Poisson’s ratio that are required in order to control the settlement in some magnitude are concluded by using finite element analysis to simulate the extra stress distribution of the single oil storage tank whose volume is 15×105 m3 on the basis of preceding conclusions.

Foundation model and reliability of computational method The direction of soil particles important because of different characteristics exhibited by horizontally- versus vertically-oriented soil in a soil deposit that is anisotropic. But, compared with the difference

between different soil layers, the vertical inhomogeneity of soil in the same layer is smaller. So it is necessary to assume that soil in the same layer of earth is isotropic in this study. It is generally understood that soil is made of loose particles and cannot withstand pull. After soil layers suffer pressing, the distortion of soil consists of elastic distortion and plastic distortion, of which plastic distortion is larger than elastic distortion. According to the working condition of the foundation, it mainly suffers pressing and at the same time, the load-bearing capacity of foundation is limited in the course of foundation design, so plastic distortion only happens at very small areas and it can be ignored in engineering. As a consequence, soil can be assumed to be an elastic solid.

The methods on how to calculate the additional stress and settlement in Chinese criterion are the foundation the following hypothesis: the soil of the foundation is a homogeneous, continuous, isotropic, and elastic semi-infinite body. So, the finite, compressed layer foundation model is applied in this paper.

Numerical analysis of homogeneous soil In this paper, the volume and radius of the oil storage tank are 15×105 m3 and 50 meters, respectively. When the oil storage tank is filled with oil, the maximal additional pressure on the foundation is assumed up to 250 KN/m2. In fact, the contact status of soil and tank foundation is between viscous contact and slick contact, but if the tank foundation only supports vertical force and the soil of foundation is cohesive soil, the contact status of soil and tank foundation tends to viscous contact. Also, dynamic effect and horizontal lateral force of tank foundation are ignored in this work. According to the symmetry of oil tank and foundation, a one-quarter model of the foundation is applied in this paper. The finite element model is shown in Figure 1. Considering the influence areas of displacement and stress of soil whose modulus of deformation is 2.8 N/mm2 and Poisson’s ratio, 0.42, the length, width, and depth of the finite element model are 500 meters, 500 meters, and 150 meters, respectively.

Figure 1. Finite Element Model of Foundation

Result of additional stress The contour line of additional stress in the vertical direction is shown in Figure 2. It can be seen that maximal stress does not appear at the center of tank foundation, but appears at the areas between 15 and 25 meters away from the center, and this maximal stress is also higher than the pressure that the foundation is loaded when the tank is filled with oil. For the areas that appear to have a concentration of stress, the soil moves into plastic status from elastic status. Moreover, the soil mass suffers from upward force if the soil is very far from the center of tank foundation.

Figure 2. Contour Line of Additional Stress in Vertical Direction

A comparison of the results obtained using the finite element analysis method and the criteria method for additional stress are presented in Table 1. It can be seen that the error of additional stress between finite element analysis results and criteria results is less than 5% in the soil layer whose depth is no more than 70 meters. When the depth of soil layer is more than 70 meters, additional stress errors are more than 5%, which is because the finite element meshes are more and more sparse with the increase of soil depth. In fact, that the errors when the depth of soil layer is more than 70 meters are more than 5% doesn’t influence the study and use of finite element analysis, because the soil body is rock when the depth is greater than 70 meters, and rock has different mechanical properties than soil, moreover, during the course of foundation treatment, pile foundation cannot reach this depth and the bearing capacity of rock in this depth is very large.

Table 1. Comparison of finite element method and criteria method for additional stress

Depth

(m)

Criteria results (KN/m2)

Finite element analysis results (KN/m2)

Criteria coefficient

Corrected coefficient

Error (%)

(KN/m2)

0 250 250.041 1 1 0.0

10 248 242.678 0.992 0.971 -2.1

20 237.25 229.111 0.949 0.916 -3.4

30 216 208.791 0.864 0.853 -1.2

40 189 184.857 0.756 0.739 -2.2

50 161.5 163.868 0.646 0.655 +1.3

60 136.75 137.73 0.547 0.551 +0.7

70 115.25 117.635 0.461 0.47 +1.9

80 97.6 105.0 0.390 0.42 +7.1

90 83 90.506 0.332 0.362 +8.2

100 71.25 72.815 0.285 0.291 +2.1

Figure 3 shows additional stress using both the criteria method and the finite method with the soil in the center of the tank foundation. It can be seen from Fig.3 that criteria results are larger than finite element results when the depth of soil layer is less than 50 meters, which is acceptable from the point of design and the aim for safety, whereas criteria results are lower than finite element results when the depth of soil layer is more than 50 meters. It is generally understood that the bearing capacity of a layer is higher than a soil layer when there exists rocks in a given depth and it can contend to the requirement of design, which is often ignored in engineering. As a whole, compared with criteria method, the finite element analysis method also is safe and reliable.

Figure 3. Comparison of stress with different methods (radius =0)

Analysis of foundation settlement The summated method of divided layers in foundation design criteria is a prevalent method that can calculate the settlement of foundations in China, and it can obtain reliable results in average base engineering. But this method does not give satisfactory conclusions if it is applied in the foundation engineering of a good-sized oil storage tank because the diameter of the oilcan is so large. There is no unanimous agreement in engineering literature for the settlement calculation of an oversized oil storage tank, and some authors (Xu Zhijun and Shen Zhujiang) think the divided layer summation method is not fit for the settlement calculation of an oversized oil storage tank foundation, so they recommend a better computing method called the three-dimensional settlement method. In order to prove the feasibility of the finite element analysis method, the three-dimensional settlement method is compared with finite element analysis method for the foundation settlement in this paper.

The contour line of foundation settlement in homogeneous soil is shown in Figure 4. It can be seen that the maximal settlement in the center of tank foundation is 5.291 meters and, if the meshes of this model are divided more coarsely, the maximal settlement in the center of tank foundation is up to 5.497 m. The settlement result obtained using three-dimensional settlement method is 5.553 meters, and the difference between the previous methods is almost 6 centimeters. Figure 5 shows the compared results using the three-dimensional settlement method and finite element analysis method. It can be seen that the trend of settlement curves is consistent.

Figure 4. Settlement contour line of homogeneous soil

Some literatures indicates that the results obtained using the three-dimensional settlement method is a little larger than the measured settlement of foundation, whereas the results using finite element analysis method are lower than those of the three-dimensional settlement method. So results obtained using finite element are closer to the measured settlement. Therefore, finite element analysis is a reliable and reasonable way to calculate the settlement of the foundation of an oversized tank.

Figure 5. Settlement comparison with different methods

Example of engineering China Petroleum & Chemical Corporation, which is the largest engineering firm in China, is going to build an oil storage tank whose volume approximately 15×105 m3 in the Baisha gulf. In this paper, the geologic conditions at Cangzhou refinery are selected for the engineering example, because the geologic conditions at the refinery are similar to that at the Baisha gulf, but the latter geologic conditions are worse than the former. From the previous analysis, finite element analysis is reliable; this method can provide engineering references for the Baisha gulf engineering. Geologic data from Cangzhou refinery are shown in Table 2.

Table 2. Geologic data of CangZhou refinery

Soil layer Name

Average thickness

(m)

Surface thickness

(m)

Poisson’s ratio

Modulus of Compression

(GPa)

Modulus of deformation

(GPa)

Bearing capability (KPa)

1 Silty 1.85 0 0.3 4.5 3.34 110

2 Clay 1.35 1.85 0.35 5.0 3.15 120

3 Silty 2.4 3.2 0.3 4.5 3.34 110

4 Silty 4.35 5.6 0.3 6.0 4.45 130

5 Silt 5.25 9.95 0.25 6.5 5.43 130

6 Silty 1.75 15.2 0.28 7.5 6.03 150

7 Silty 1.9 16.95 0.32 4.5 3.4 100

8 Silty 2 18.85 0.25 12 10.02 210

9 Silt 6.55 20.85 0.25 19 15.87 300

10 Silty 7.7 27.4 0.3 7 5.19 140

11 Silt 6.2 35.1 0.25 16.5 13.78 280

12 Silty 9.8 41.3 0.28 12 9.45 200

13 Silty 8 51.1 0.25 13 10.86 220

14 Decayed rock Infinite 59.1 — — — —

The magnitude of seismic intensity is six in this area and the liquefaction of saturated sands caused by earthquake is ignored in this paper. Moreover, the water table of this refinery changes with the rainfall of different seasons, but water table is steady between 0.9 and 1.15 meters. For the soil compressibility of this area, layers 1, 2, 3, 4, and 7 belong to moderately- to highly-constrictive soil layer, and layers 5 and 6 are moderately-constrictive soil layers, but these moderately- or highly-constrictive soil layers have a lower bearing capacity and cannot be the natural foundation of the tank. Layers 8 and 9 show a state of rigidity and are less constrictive soil layers, with soil particles in tight contact and has a higher bearing capacity, consequently, these layers are the perfect choice for a supporting layer for piles. Layers 10 and 11 show that the state of plasticity belongs to a moderately constrictive soil layer; whereas layers 12 and 13 are moderately, or even less, constrictive soil layers that are ideal layers for a tank foundation.

According to the analysis of geologic data, the foundation must be no more than 20 meters deep in order to make the settlement and stress meet the requirements of bearing capacity and deformation necessary for an oversized tank.

Additional stress Analysis of natural foundation The contour line of additional stress in the vertical direction is shown in Figure 6. It can be seen that the distribution of additional stress is more uneven when the soil of the tank foundation is inhomogeneous than when the soil is homogeneous.

Figure 6. Contour line of additional stress

A comparison of the results obtained using the finite element analysis method and the criteria method for additional stress is presented in Table 3. It can be seen that the calculated difference in additional stress with the changes of layers is very large between the finite element analysis and criteria results. The more changes in rigidity between two adjacent layers, the greater the difference in additional stress. The error of additional stress between finite element analysis results and criteria results is nearly 30% near the interface of soft soil layer and rock. But when the depth of soil layer is less than 27 meters, the errors are no more than 3%, and this precision fits the requirements of engineering the foundation. So, the previous errors should be considered carefully in order to analyze precisely.

Table 3. Comparison of finite element analysis and criteria methods for additional stress

Depth

(m)

Criteria coefficient

Criteria results (KN/m2)

Finite element analysis results (KN/m2)

Corrected coefficient

Error (%)

0 1 250 250.72 1.003 0.29

1.85 0.999 249.75 248.506 0.994 -0.5

3.2 0.999 249.75 249.646 0.999 0 5.6 0.999 249.75 249.039 0.996 -0.3

9.95 0.998 249.5 249.455 0.998 0

15.2 0.974 243.5 248.861 0.995 2.11

16.95 0.967 241.75 248.024 0.992 2.52

18.85 0.955 238.75 246.006 0.984 2.95

20.84 0.948 237 240.963 0.964 1.66

27.4 0.885 213.75 235.411 0.942 6.05

35.1 0.809 202.25 225.904 0.904 10.51

41.3 0.742 185.5 212.467 0.850 12.71

51.1 0.645 161.25 195.123 0.78 17.3

59.1 0.550 137.5 192.789 0.771 28.68

Settlement analysis of natural foundation The displacement contour line obtained using finite element analysis is shown in Figure 7. It can be seen from this figure that the maximal settlement in the center of the tank foundation is 1.683 meters, which exceeds the maximal allowed settlement according to China’s criteria for controlling oil storage tanks. Much literature indicates that it is advisable that the foundation settlement of an oversized oilcan be kept to less than one meter. Therefore, the natural foundation cannot meet the settlement requirements and the foundation needs to be altered.

Figure 7. Contour line of settlement

Figures 8 and 9 show the vertical settlement curve in the center of tank foundation and the horizontal settlement curve on the surface of tank foundation, respectively. It can be seen from Figure 9 that the settlement difference between the center and the edge of tank on the surface of tank foundation is 0.912 m, but some literature proposes that the maximal allowed settlement difference between the center and the edge of tank is 0.37 m. So the natural foundation cannot meet the requirements. The settlement at the center of the tank, being larger than that at the edge of the tank, causes the bottom board of the tank to experience the greatest amount of deformation, which will make the bottom board rupture by the pull force and it will leak oil at the end. Compared with the bearing capacity, the results of layers 9, 11, and 13 using finite element analysis can meet the requirement of bearing capacity, but the layers above layer 9 cannot meet the need of bearing capacity.

Figure 8. Vertical settlement curve

Figure 9. Horizontal settlement curve

Numerical analysis of complex foundation According to the previous example of engineering at the Cangzhou Refinery, a natural foundation cannot meet the bearing capacity requirements of an oil storage tank, so the natural foundation must be made into a complex foundation that can meet the bearing capacity needs. A geology institution can measure the converted deformation modulus and the converted Poisson’s ratio for a complex foundation. In this study, the general strategy adopted for finding the optional parameters for a complex foundation that control the settlement is divided into five cases. The following are these cases.

1. The depth, radius, converted deformation modulus, and Poisson’s ratio of complex foundation are 20.85 m, 60 m, 8 MPa, and 0.25, respectively;

2. The depth, radius, converted deformation modulus, and Poisson’s ratio of complex foundation are 20.85 m, 55 m, 8 MPa, and 0.25, respectively;

3. The depth, radius, converted deformation modulus, and Poisson’s ratio of inner complex foundation are 20.85 m, 30 m, 10 MPa, and 0.25 respectively, whereas, the depth, inner radius, outer radius, converted deformation modulus, and Poisson’s ratio of outer complex foundation are 20.85 m, 30 m, 60 m, 8 MPa, and 0.25, respectively;

4. The depth, radius, converted deformation modulus, and Poisson’s ratio of inner complex foundation are 20.85 m, 30 m, 15 MPa, and 0.3 respectively, whereas, the depth, inner radius, outer radius, converted deformation modulus, and Poisson’s ratio of outer complex foundation are 20.85 m, 30 m, 60 m, 10 MPa, and 0.3, respectively;

5. The depth, radius, converted deformation modulus, and Poisson’s ratio of inner complex foundation are 20.85 m, 30 m, 18 MPa, and 0.3 respectively, whereas, the depth, inner radius, outer radius, converted deformation modulus, and Poisson’s ratio of outer complex foundation are 20.85 m, 30 m, 60 m, 10 MPa, and 0.3, respectively.

Table 4. Additional stresses in the center of tank foundation

Vertical additional stresses (KPa) Depth

(m) Case1 Case2 Case3 Case4 Case5

0 252.601 250.384 250.23 251.467 249.27

4.17 245.965 251.019 — 248.717 —

8.34 249.127 254.779 250.281 247.779 247.023

12.51 261.005 257.669 — 246.667 —

16.68 292.247 265.136 — 243.461 —

20.85 338.659 252.448 244.848 239.331 234.242

27.4 308.866 254.008 237.72 232.758 232.66

35.1 286.133 214.761 228.363 223.35 223.76

41.3 -2.156 202.623 219.875 209.745 210.516

51.1 — 199.605 197.341 192.214 193.05

It can be seen from Table 4 that there is obvious stress concentration after the tank foundation becomes a complex foundation. In Case1, stress concentration mainly occurs at the contact interface of layers 8 and 9 and the maximal stress comes to 378.2 KPa. That is larger than the force loaded on the foundation. Moreover, the soil near the areas of natural foundation that are in contact suffer from the upward force. In Case2, stress concentration is not more serious than that of Case1, but the stress concentration is more serious than that of a homogeneous foundation. In Case3, stress concentration mainly occurs at the areas of contact between the inner and outer complex foundation and the distribution of stress in the inner foundation, which is the main area resisting force, is even, moreover, there is obvious stress concentration at the contact interface of layers 8 and 9. Case4 is similar to Case5; stress concentration appears in both at the areas of contact between the inner and outer complex foundation.

Table 5. Additional stresses on the surface of tank foundation

Vertical additional stresses (KPa) Radius

(m) Case1 Case2 Case3 Case4 Case5

0 252.601 250.83 250.23 251.467 249.278

10 254.288 253.12 250.12 250.12 249.72

20 249.949 251.02 254.315 261.402 259.42

30 237.064 254.49 226.96 281.607 288.63

40 214.968 225.16 224.385 225.839 220.088

50 108.993 164.16 123.05 120.56 123.0

60 -2.601 -2.5(Radius =55) -2.371 -1.5 -1.471

Additional stresses on the surface of the tank foundation with variable radius are shown in Table 5. The results indicate that there is obvious stress concentration after the foundation of tank is modified to become a complex foundation. For cases 3, 4, and 5, the position of stress concentration is affected by the differences between the deformation modulus of the inner and outer complex foundation. It occurs in the inner complex foundation when the deformation modulus difference is small (Case3) and it occurs at the interface of the inner and outer complex foundation when the deformation modulus difference is small (cases 4 and 5). Moreover, stress concentration is more and more serious with increasing difference of deformation modulus. As for cases 1 and 2, the stress concentration is more and more serious with the increase of distance between the edge of the complex foundation and the edge of the oil storage tank. Stress concentration happens primarily at the interface of the complex foundation and the contacting layer. Also, the soil near the areas of natural foundation in contact suffer from the upward force.

Table 6. Settlements on the surface of tank foundation

Settlement (m) Radius (m)

Case1 Case2 Case3 Case4 Case5

0 1.102 1.338 1.232 1.05 1.006

10 0.989 1.330 1.22 1.038 0.995

20 0.908 1.291 1.178 1.000 0.962

30 0.821 1.195 1.131 0.966 0.939

40 0.686 1.039 1.000 0.870 0.865

50 0.402 0.678 0.627 0.557 0.557

60 0.095 0.393(radius=55) 0.253 0.236 0.230

70 0.015 0.161(radius=65) 0.109 0.209 0.109

Differences (cm) 70 66 60.5 49.3 44.9

Radial settlement curves are shown in Figures 10 and 11. It can be seen from Figure 10 that the settlement difference is small when the distance between the edge of complex foundation and the edge of tank is between 5 and 20 m and that the foundation settlement is more even when the edge of foundation is closer to the edge of tank. It can be seen from Fig.11 that the settlement difference is small when the difference of deformation modulus between the inner and outer complex foundation is larger than 5.

Figure 10. Radial settlement curve of case1 and case2

Figure 11. Radial settlement curve of case3, case4 and case5

Comparisons of cases 1 and 2 are shown in tables 4, 5, and 6 and in Figure 10. It can be seen from Table 5 that the addition stress of Case1 is higher than that of Case2 in the center of tank foundation, but that the additional stress of Case1 is lower than that of Case2 at the edge of tank. It can be seen from Table 6 that the settlement of Case1 is 70 cm and the settlement of Case2 is 66 cm. Figure 10 shows the settlement curve of Case1 is sharper than that of Case2. Therefore the radius of complex foundation should be selected by trying to meet the conformation requirement of a complex foundation during the course of creating a tank foundation.

Comparisons of cases 1 and 3 are shown in tables 4, 5, and 6. It can be found that the stress distribution of a complex foundation is more even after the middle complex foundation is strengthened, with increased rigidity. Table4 shows that the additional stress of Case1 is higher than that of Case2 in the center of tank

foundation, but the additional stress of Case1 is lower than that of Case2 at the edge of the tank. Therefore the settlement difference at the center of the tank and at the edge of tank is lessened after the middle of the complex foundation is strengthened.

Comparisons of cases 3, 4, and 5 are shown in Table 6 and Figure 10. It can be seen from Table 6 that the settlement at the center of tank becomes small when the rigidity of the inner complex foundation is strengthened. But depending only on enhancing the rigidity of the inner complex foundation is not a good idea, because it also decreases the settlement difference of the center of the tank and the edge of the tank. After the maximal settlement is settled by the criteria result, changing the rigidity of the outer complex foundation can also decrease the settlement difference of the center of tank and the edge of the tank.

According to the previous analysis, in order to make the oversized tank with volume 15×105 m3 meet the requirement of settlement and bearing capacity, the following complex foundation is proposed:

The radius of the inner complex foundation is 30 m and the deformation modulus should be not less than 18 MPa in order to limit the maximal settlement to less than 1 m.

The outer radius of the outer complex foundation is 55 meters and the deformation modulus should be not more than 10 MPa in order to limit the settlement difference between the center and edge of the tank to less than 40 cm.

Results and discussion Based the previous analysis, several conclusions can be drawn. For inhomogeneous soil with changing rigidity between layers, the criteria results are not accurate. The calculation of additional stress should be based on the actual layers of the foundation and the errors are more and more serious when the difference in rigidity for layers in contact increases. After the foundation of the oil storage tank is made into a complex foundation, stress concentration is inevitable.

The finite element analysis method for analyzing and studying the stress and settlement distribution of a tank foundation is provided and proposed in this paper, which may offer some aid for designing a tank foundation. The results indicate that this method can simulate the settlement of a tank foundation reliably. The operation of finite element analysis is convenient and needs less equipment than the traditional method of experiment; the result of this method is identical to that of the traditional method. It is a practical and valuable method for analyzing and studying the stress and settlement distribution of a tank foundation, which can also be used to study other foundation types.

References [1] Xu Zhijun, Xu Chaoquan and Shen Zhujiang. Foundation design of oil tank and foundation treatment, china petrochemical press, Beijing.

[2] Gao Dazhao. Soil mechanics and foundation engineering, china construction industry press, Beijing.

About the author:

1Associate Professor, College of Civil Engineering, China University of Petroleum, Dongying 257061, China.

2Graduate student, College of Civil Engineering, China University of Petroleum, Dongying 257061, China.

3Professor, College of Civil Engineering, China University of Petroleum, Dongying 257061, China.