Advances in Civil Engineering
Volume 2018 (2018), Article ID 3672868, 16 pages
https://doi.org/10.1155/2018/3672868

Research Article

Uplift Test and Design Method for Bearing Capacity of Isolated Spread Concrete Foundation Slab with Large Width-to-Height Ratio

Yuanqi Li,¹ Xiaoliang Qin,¹ Jinhui Luo,¹ Meng Xiao,² and Cong Hua²

¹Department of Structural Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
²State Grid Sichuan Economic Research Institute, Chengdu 610041, China

Correspondence should be addressed to Yuanqi Li; liyq@tongji.edu.cn

Received 10 April 2018; Revised 12 September 2018; Accepted 15 October 2018; Published 15 November 2018

Academic Editor: Cumaraswamy Vipulanandan

Copyright © 2018 Yuanqi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

This paper is focused on the experimental study and numerical simulation of isolated spread concrete foundation slab with a large width-to-height ratio (in short ISCFS-LWR) to investigate the failure modes and uplift bearing capacity, as well as the design method of uplift capacity. First, a total of 16 isolated spread concrete foundation slabs with the width-to-height ratio varied from 1.5 to 4 and the hypotenuse slope varied from 10° to 30° were tested under uplift load. Based on the test results, effects of the width-to-height ratio and the hypotenuse slope on uplift bearing capacity of ISCFS-LWR were analyzed and discussed. Then, several numerical models were built using the finite element software ABAQUS and the results of numerical analysis agreed well with the test results. Furthermore, the cross-sectional performance of ISCFS-LWR was studied, and the coefficients of internal force arm were also evaluated further using previous validated numerical models. To obtain the suggested design method of uplift capacity for the foundation slab, effective width correction coefficient k and slope correction coefficient j were introduced to propose a design formula. Finally, the proposed design method was applied to a practical engineering, and the economic indicators obtained from the suggested design method were compared with that from the original design method. The results of this paper showed that the correction coefficient jsks based on numerical analysis agreed well with the recommended correction coefficient jk, and the error was between 1% and 3.4%, by which the reasonability of the proposed design method of uplift capacity for ISCFS-LWR has been proved. It can also be found that the economic benefits of the practical engineering in this paper were obvious due to the suggested design method, and this paper can provide a reference for other engineering practices and the further research work on ISCFS-LWR.

1. Introduction

As one of the main forms of transmission tower foundations, isolated spread concrete foundation has been widely used in transmission lines recently because of its efficiency and economy. The foundation in transmission lines not only can be subjected to the downward load but also can be affected by the uplift load, so it is necessary to consider double-layer reinforcement for the foundation slab.

Many successful researches on foundations, which subjected to the uplift load, have been reported. Several scholars performed tests and finite element studies to analyze the uplift mechanism of foundation [1, 2], uplift bearing capacity of foundation [3–5], and uplift load-displacement behavior of foundation [6, 7]. Furthermore, many relevant studies have been performed to explore the deformation characteristics and failure modes of the reinforced sand [8–11]. Uplift tests were also conducted to study the law of crack expansion and deformation characteristics of spread foundations under a combination action of uplift and horizontal loads [12]. For the transmission line tower, a site test [13] and a laboratory test [14] were carried out to evaluate the uplift bearing capacity of fabricated foundation. However, the previous researches mainly focused on the behavior of upper covered soil of the uplift foundation. Failure modes and bearing capacity of the concrete foundation slab itself under the uplift load have rarely been developed, especially the research on the design method of uplift capacity for the isolated spread concrete foundation slab with large width-to-height ratio (in short ISCFS-LWR).

At present, the Chinese power industry standard DL/T5219-2014 [15] stipulates that the upper steel reinforcement is the same as the lower reinforcement, as shown in Equation (1). Moreover, there is no relevant explanation for the uplift foundation slab in the Chinese standard GB50007-2011 [16] and the following Equation (2) can be used for the design of the normal foundation slab:

where , M, h₀, fy, x, and As is the coefficient of the internal force arm, bending moment of the section, effective height, tensile strength of steel reinforcement, concrete depth of the compression zone, and area of steel reinforcement, respectively.

From the comparison between Equations (1) and (2), it showed that the coefficient of the internal force arm, , is 1 − (x/2h₀) in DL/T5219-2014 [15], while it is equal to 0.9 in GB50007-2011 [16]. It is not clear if the equations in standards [15, 16] can be used for the design of ISCFS-LWR, as both of them ignore the effects of the width-to-height ratio and the hypotenuse slope on for the uplift foundation slab. Therefore, experimental study and design method research on ISCFS-LWR are critical.

The purpose of this paper is to explore the uplift bearing capacity and design method of ISCFS-LWR through the experimental study and numerical simulation. Several isolated spread concrete foundation slabs with different width-to-height ratios and hypotenuse slopes were tested under the uplift load firstly. Then, 8 numerical models were created using finite element software ABAQUS, and the numerical results and experimental results were also compared in this paper. In addition, the cross-sectional performance of ISCFS-LWR was studied further by validated numerical models. Based on the Chinese standard GB50007-2011 [16], the effective width correction coefficient, k, and the slope correction coefficient, j, were introduced to propose the suggested design method of uplift capacity for ISCFS-LWR. Finally, an engineering case in China using the suggested design method was described and the economic indicators were also analyzed.

2. Experimental Investigation

2.1. Experimental Program

In previous researches, many kinds of tests were conducted to study the mechanical properties of uplift foundation, in which the uplift load was applied to the top surface of foundation with the constraint of soil covered on the hypotenuse of foundation. However, this article aims to investigate the failure mode of uplift foundation and find the reinforcement design method to resist the section bending moment when subjected to the uplift load. So instead of the above loading method, the top surface of the foundation was fixed in this paper, and the four oil cylinders with distributive girders were raised to simulate the uplift load. This loading mode is reasonable, and it can also achieve the effect of simulating the uplift load.

2.1.1. Test Specimens

The typical configuration of the test specimen is shown in Figure 1, in which 1 represents the steel connector, and 2 represents the raised concrete platform, L is the length of the foundation, B is the width of the foundation, h is the height of the foundation slab, b is the distance from the edge of the short column to the outer edge of the foundation, h₁ is the height of the edge of the foundation slab, and h₂ is the height of the raised platform; then the width-to-height ratio is defined as b/h.

Figure 1: Configuration of foundation.

The specimens were designed according to DL/T5219-2014 [15]. The steel reinforcement of NJ1 is shown in Figure 2. The detailed information of all specimens are shown in Table 1, where 6@200 expresses that the diameter of steel reinforcement is 6 mm with the spacing of 200 mm and C30 expresses that the standard value of the cube compressive strength is 30 MPa. In order to avoid the test error, the test specimens NJ1∼NJ8 were identical to the specimens NJ9∼NJ16, respectively.

Figure 2: Steel reinforcement of NJ1.

Table 1: Details of specimens.

Specimen
Width-to-height ratio
Hypotenuse slope (°)
Dimension (L × B × h × h₁ × h₂) (mm)
Upper reinforcement HRB400
Lower reinforcement HRB400
Strength of the concrete

NJ1
1.5
10
1000 × 1000 × 266 × 200 × 35
6@200
6@200
C30

NJ2
1.5
20
1000 × 1000 × 266 × 128 × 73
6@200
6@200
C30

NJ3
1.5
30
1000 × 1000 × 266 × 47 × 115
6@200
6@200
C30

NJ4
2.0
10
1000 × 1000 × 200 × 132 × 35
6@200
6@200
C30

NJ5
2.0
20
1000 × 1000 × 200 × 62 × 73
6@200
6@200
C30

NJ6
2.5
10
1000 × 1000 × 160 × 93 × 35
6@160
6@160
C30

NJ7
3.0
10
1000 × 1000 × 133 × 66 × 35
6@160
6@160
C30

NJ8
4.0
10
1000 × 1000 × 100 × 33 × 35
6@160
6@160
C30

NJ9
1.5
10
1000 × 1000 × 266 × 200 × 35
6@200
6@200
C30

NJ10
1.5
20
1000 × 1000 × 266 × 128 × 73
6@200
6@200
C30

NJ11
1.5
30
1000 × 1000 × 266 × 47 × 115
6@200
6@200
C30

NJ12
2.0
10
1000 × 1000 × 200 × 132 × 35
6@200
6@200
C30

NJ13
2.0
20
1000 × 1000 × 200 × 62 × 73
6@200
6@200
C30

NJ14
2.5
10
1000 × 1000 × 160 × 93 × 35
6@160
6@160
C30

NJ15
3.0
10
1000 × 1000 × 133 × 66 × 35
6@160
6@160
C30

NJ16
4.0
10
1000 × 1000 × 100 × 33 × 35
6@160
6@160
C30

2.1.2. Material Properties

The concrete sample with the same material as the test specimens was poured by 150 × 150 × 150 in millimeter. The test strengths of the concrete samples are reported in Table 2. The age of the concrete sample remains the same as the specimens for 42 days and 37 days, respectively.

Table 2: Strengths of concrete samples.

Samples
Curing condition
Designed concrete strength
Curing time (d)
Bearing area (mm²)
Compressive strength (MPa)

Single sample
Average

NJ1∼NJ8
Same with specimen
C30
42
22500
31.1
29.7

27.5

30.4

NJ9∼NJ16
Same with specimen
C30
37
22500
28.6
28.3

28.6

27.8

A group of coupons with three samples for each kind of diameters of steel reinforcement were tested at first. The mechanical properties of steel reinforcements are reported in Table 3.

Table 3: Indices of mechanical properties of steel reinforcement.

Type
Nominal diameter (mm)
Area (mm²)
Tensile test

Yield strength (MPa)
Tensile strength (MPa)

HRB400
6
28.27
461.9
456.5
760.4
767.3

6
28.27
468.3
778.4

6
28.27
439.3
763.2

2.1.3. Test Setup

The uplift tests were conducted at the structural laboratory in the West Campus of Tongji University. The specimen was inverted and fixed to the base, which was also fixed to the subplate and test platform. The uplift load was simulated by the four oil cylinders, whose measuring range is 200 kN. The test setup includes the oil cylinder, the pressure sensor, and the distributive girder, which is shown in Figure 3.

Figure 3: Test setup.

The strain gauges were pasted on the upper steel reinforcement to study the development of stress, as shown in Figure 4, where 1-1 represents the no. 1 strain gauge which was pasted along the length of steel reinforcement.

Figure 4: Typical strain gauges arrangement of steel reinforcement for the specimens.

The deformation of the specimen was measured by the 9 displacement meters arranged at the bottom of the foundation slab, which is shown in Figure 5(a). The measuring points of deformation are shown in Figure 5(b), in which displacement meters are uniformly distributed on the central axis of the foundation slab. The distance between points 1∼5 is 240 mm, and the distance between points 6, 7, 3, 8, and 9 is also 240 mm, respectively.

(a)

(b)

Figure 5: Arrangement of the displacement meters for the specimen. (a) Displacement meters. (b) Measuring point of deformation.

2.2. Experimental Results

The failure characteristics of the specimens are summarized in Table 4, where N is the number of cracks observed during the test and Pu is the ultimate load that each specimen can bear during a test. The failure mode of the specimens NJ1∼NJ8 was basically the same as that of the corresponding repeat specimens NJ9∼NJ16, and the actual failure mode for the specimens NJ1∼NJ8 is shown in Figure 6. For all the specimens, as the load increased gradually, the cracks extended to the side of the foundation slab with an obvious width. After the peak load, the load dropped sharply and the deflection of the foundation slab was large. Concrete in the compressive zone of the foundation slab was crushed along the direction of main cracks. Sometimes, the foundation slab was divided into two parts by the main cracks, as shown in Figure 6(i).

Table 4: Failure characteristics of the test specimens.

Specimen
N
Pu (kN)
Failure mode

NJ1
4
260
C

NJ2
4
192
C

NJ3
5
155
C

NJ4
8
192
G

NJ5
8
138
G

NJ6
The cracks appear circular and dense
160
I

NJ7
8
107
G

NJ8
The cracks appear dense
92
I

NJ9
4
242
C

NJ10
4
210
C

NJ11
5
155
C

NJ12
5
180
G

NJ13
7
150
G

NJ14
The cracks appear circular and dense
124
I

NJ15
The cracks appear circular and dense
124
I

NJ16
5 main cracks
86
C

C: cross-shaped bending failure; G: grid-shaped bending failure; I: incomplete bending failure.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Figure 6: Failure modes for the specimens. (a) NJ1. (b) NJ2. (c) NJ3. (d) NJ4. (e) NJ5. (f) NJ6. (g) NJ7. (h) NJ8. (i) Deformation of the specimen NJ2.

The typical load-strain relationships of the specimen NJ1(NJ9) and the specimen NJ8(NJ16) are shown in Figure 7. The strain of upper steel reinforcement was obtained from the strain gauge 1-2, as shown in Figure 4. The uplift load is the total force of four oil cylinders. From the comparative results of Figure 7, it can be seen that the load-strain relationship of the specimen NJ1 and the specimen NJ8 agree well basically with the results of the corresponding repeat specimen NJ9 and specimen NJ16.

(a)

(b)

Figure 7: Typical load-strain curve for the test specimens. (a) NJ1(NJ9). (b) NJ8(NJ16).

For the specimen NJ1, upper steel reinforcement and upper concrete of the foundation slab bore the tensile stress together at the first stage. So, the stress of the upper steel reinforcement was small, and the curve was nearly vertical when the load was less than 150 kN. As the load increased, the cracks began to appear in the foundation slab and the concrete in the tensile zone of the foundation slab withdrew from work gradually. At this stage, the strain of steel reinforcement became bigger and bigger. The strain of steel reinforcement showed a large increase when the load reached 234 kN, which marks the yielding of the steel reinforcement. After that, the curve remained still until the the specimen NJ1 was damaged. The curve characteristic of the specimen NJ9 was similar to that of the specimen NJ1, which was almost vertical before 150 kN and then the change happened suddenly at about 236 kN. The load-strain results of the specimen NJ8 are in good agreement with the results of the specimen NJ16, which is shown in Figure 7(b), and the steel reinforcement yielded at about 60 kN.

The displacement difference between measuring point 1 and measuring point 3, as shown in Figure 5, was extracted as the deformation of the foundation slab in this paper. The typical load-deformation curves of the specimen NJ1(NJ9) and the specimen NJ8(NJ16) are shown in Figure 8, in which the load-deformation relationships of the specimen NJ1 and the specimen NJ8 agree well basically with the results of the corresponding repeat specimen NJ9 and specimen NJ16.

(a)

(b)

Figure 8: Typical load-deformation curve for the test specimens. (a) NJ1(NJ9). (b) NJ8(NJ16).

For the specimen NJ1, no cracks were observed before 150 kN and the overall stiffness of the foundation slab was large enough, so there was almost no deformation in the foundation slab at this stage. As the load increased, cracks appeared in the hypotenuse of the foundation slab and concrete in the tensile zone was losing efficiency gradually, so the stiffness of the foundation slab dropped sharply with the largest deformation of 3 mm. The deformation of the foundation slab increased rapidly at about 234 kN, as shown in Figure 8(a). The difference of the curves between specimen NJ9 and specimen NJ1 is small. For the specimen NJ9, there was almost no deformation in the foundation slab before 175 kN, and then the deformation increased rapidly at about 236 kN. Figure 8(b) shows the load-deformation relationship of the specimen NJ8(NJ16), in which the two curves were in good agreement with those in the early stage, and the difference between them was larger after 40 kN.

The uplift bearing capacity, Ft, was the load that each specimen sustained when the upper steel reinforcement was yielding. In accordance with the condition of crack expansion, development of strain, and deformation characteristics, the uplift bearing capacities are concluded in Table 5, where Fave is the average value of the uplift bearing capacity. It could be seen that the uplift bearing capacities of the specimens NJ1∼NJ8 were quite close to the corresponding repeated specimens NJ9∼NJ16, and the relative errors of each specimen were less than 5% when compared with the average value Fave.

Table 5: Comparison of the uplift bearing capacity for the test specimens.

Specimen
Width-to-height ratio
Hypotenuse slope (°)
Ft (kN)
(%)
Specimen
Width-to-height ratio
Hypotenuse slope (°)
Ft (kN)
(%)
Fave (kN)

NJ1
1.5
10
234
0.4
NJ9
1.5
10
236
0.4
235

NJ2
1.5
20
174
0.6
NJ10
1.5
20
175
0
175

NJ3
1.5
30
145
1.4
NJ11
1.5
30
140
2.1
143

NJ4
2
10
144
2
NJ12
2
10
150
2
147

NJ5
2
20
118
3.5
NJ13
2
20
110
3.5
114

NJ6
2.5
10
95
3.1
NJ14
2.5
10
100
2
98

NJ7
3
10
80
3.6
NJ15
3
10
85
2.4
83

NJ8
4
10
63
1.6
NJ16
4
10
60
3.2
62

3. Discussion

As is described above, the failure modes were almost bending failure, including cross-shaped bending failure, grid-shaped bending failure, and incomplete bending failure with circumferential cracks. The characteristic of the bending failure was that it had sufficient deformation when it came to failure, as well as the yielding of upper steel reinforcement in the foundation slab. The failure section of the foundation slab was at the section which is close to the edge of the short column, and this section is also called the most dangerous section.

From the comparison of the average value Fave between the specimens NJ1(NJ9), NJ2(NJ10), NJ3(NJ11) and the specimens NJ4(NJ12), NJ5(NJ13), it showed that the uplift bearing capacity reduced gradually with the increase of the hypotenuse slope when the width-to-height ratio, the size of the foundation slab, and the steel reinforcement were the same. Compared with the average bearing capacity of specimen NJ1(NJ9), the average bearing capacity of NJ2(NJ10) and NJ3(NJ11) decreased by 25.5% and 39.1%, respectively. Compared with the average bearing capacity of the specimen NJ4(NJ12), the average bearing capacity of NJ5(NJ13) decreased by 22.4%.

It also showed that with the increase of the width-to-height ratio, the uplift bearing capacity reduced obviously when the hypotenuse slope and the size of foundation slab kept consistent, according to the comparison of the average value Fave between the specimens NJ1(NJ9), NJ4(NJ12), NJ6(NJ14), NJ7(NJ15), NJ8(NJ16) and the specimens NJ2(NJ10), NJ5(NJ13). Compared with the average bearing capacity of the specimen NJ1(NJ9), the bearing capacity of the specimens NJ4(NJ12), NJ6(NJ14), NJ7(NJ15), and NJ8(NJ16) decreased by 37.4%, 58.3%, 64.7%, and 73.6%, respectively. Compared with the average bearing capacity of the specimen NJ2(NJ10), the bearing capacity of NJ5(NJ13) reduced by 34.9%.

Based on the above analysis, it is indicated that the influence of the hypotenuse slope and the width-to-height ratio on the uplift bearing capacity of the foundation slab should be considered. Specially, the width-to-height ratio should not be too large and the hypotenuse slope needs to be limited. When the foundation is subjected to the uplift load, it may not be suitable to apply the concrete foundation with the large hypotenuse slope to the engineering practice.

4. Finite Element Analysis

4.1. Numerical Modeling

In this section, eight numerical models of the foundation slab were built using the finite element software ABAQUS to validate the test results. These analytical models had the same size as the test specimens NJ1∼NJ8, respectively, as shown in Table 1. To simplify the analysis, it was assumed that there is no slip between steel reinforcement and concrete. The typical finite element model of the steel reinforcement and the concrete foundation slab are shown in Figure 9, respectively.

(a)

(b)

Figure 9: Finite element model for the spread foundation slab. (a) Steel reinforcement. (b) Concrete foundation slab.

In this study, three-dimensional eight-node hexahedral linear element with reduced integration (C3D8R) was used to simulate the concrete, and two-node linear three-dimensional truss element (T3D2) was adopted to simulate the steel reinforcement. By using structured mesh technology, the complex model was divided into simple shapes through the partition tool. In addition, the loading condition and the boundary condition, which is shown in Figure 10, were also the same as those of the specimen in the uplift test. The concrete was coupled with steel reinforcement through “Embedded” technology in ABAQUS to simulate the contact behavior between concrete and steel reinforcement. The concrete damaged plasticity model in ABAQUS was used to study the damage process of concrete, with the standard value of the cube compressive strength fcu,k of 29.7 MPa, Young’s modulus Ec of 30 GPa, Poisson’s ratio μ of 0.2, and other parameters can be determined based on fcu,k according to the Chinese standard GB50010-2010 [17]. Meanwhile, this paper adopted the ideal elastic-plastic model as the constitutive model for steel reinforcement, with Young’s modulus Es of 200 GPa, Poisson’s ratio μ of 0.3, and yield strength fy of 456.5 MPa.

Figure 10: Loading condition and boundary condition for the numerical model.

4.2. Comparison of Numerical Results with Experimental Results

The strain of upper steel reinforcement obtained from the numerical analysis was studied in this paper, which is extracted from the most dangerous section corresponding to the test. The comparisons of load-strain relationship between the simulated model and the tested specimen are presented in Figure 11, in which only the typical models NJ1 and NJ8 are shown. From the comparison of Figure 11, it can be seen that the numerical results agreed well with the experimental results basically.

(a)

(b)

Figure 11: Comparison of the load-strain curve between numerical result and experimental result for the typical model. (a) NJ1. (b) NJ8.

To validate the test results, the deformation of the foundation slab obtained from the numerical analysis was also studied. As before, the displacement difference between measuring point 1 and measuring point 3 was extracted as the deformation of the foundation slab. The comparative results of the load-deformation curve between numerical analysis and experimental study for the typical models NJ1 and NJ8 are presented in Figure 12. From the comparison of Figure 12, it can be seen that the numerical results had a good agreement with the the experimental results basically.

(a)

(b)

Figure 12: Comparison of the load-deformation curve between numerical result and experimental result for the typical model. (a) NJ1. (b) NJ8.

The comparison of the uplift bearing capacity between numerical results and tested results is summarized in Table 6, in which Ft is the bearing capacity obtained from uplift test and Fs is the uplift bearing capacity based on the ABAQUS analysis. It showed that the numerical results had a good agreement with the test results, and the error is between 0 and 15.3% when compared with the test result.

Table 6: Comparison of the uplift bearing capacities between the tested and the simulated results.

Model
Width-to-height ratio
Hypotenuse slope (°)
Ft (kN)
Fs (kN)
(%)

NJ1
1.5
10
234
235
0.4

NJ2
1.5
20
174
200
14.9

NJ3
1.5
30
145
150
3

NJ4
2
10
144
150
4.2

NJ5
2
20
118
100
15.3

NJ6
2.5
10
95
105
10.5

NJ7
3
10
80
80
0

NJ8
4
10
63
57
9.5

It can be seen from the comparison of the models NJ1, NJ2, NJ3 and the models NJ4, NJ5, when the width-to-height ratio, the size of foundation slab, and the reinforcement were the same, the uplift bearing capacity based on ABAQUS reduced gradually with the increase of the hypotenuse slope. Compared with model NJ1, the bearing capacities of NJ2 and NJ3 decreased by 14.9% and 36.2%, respectively. Compared with the model NJ4, the bearing capacity of NJ5 decreased by 33.3%.

On the basis of comparison between models NJ1, NJ4, NJ6, NJ7, NJ8 and models NJ2, NJ5, it also showed that, with the increase of width-to-height ratio, the uplift bearing capacity based on ABAQUS reduced obviously when the hypotenuse slope and the size of foundation slab kept consistent. Compared with model NJ1, the bearing capacities of NJ4, NJ6, NJ7, and NJ8 decreased by 36.2%, 55.3%, 66%, and 75.7%, respectively. Compared with the model NJ2, the bearing capacity of NJ5 reduced by 50%.

From the comparative results of Figures 11 and 12 and Table 6, it can be seen that the numerical results agreed well with the experimental results, which verified the reliability of the finite element analysis, and the numerical model can be used to study the cross-sectional performance of this type of the foundation slab further.

5. Design Method of Uplift Capacity for ISCFS-LWR

5.1. Calculation of Coefficient of Internal Force Arm

Based on the above numerical model and the reasonable finite element analysis method, the further analysis was conducted to study the effect of the width-to-height ratio and the hypotenuse slope on the cross-sectional performance of the ISCFS-LWR under the uplift load.

Figure 13 shows the typical stress nephogram of steel reinforcement, where the stress distribution of upper steel reinforcement is large near the edge of short column and the phenomena are similar to those of the uplift tests with the main cracks appearing along the edge of the short column. So the section of the foundation slab which is near the edge of the short column is called the most dangerous section.

Figure 13: Typical stress nephogram of steel reinforcement.

Figure 14 shows the typical stress distribution of concrete in the most dangerous section. It showed that the upper part of the section was under tension, and the lower part of the section was under compression. The stress distribution was nonuniform as the load changed. When the working load was small, the central stress of the compression zone is greater. As the load increased, the stress of the compression zone was gradually transferred from the middle to both sides of the foundation slab. The numerical analysis also showed that the above phenomenon was more obvious when the width-to-height ratio was larger, and the stress of the compressive zone was more likely to be concentrated on the side of the foundation slab. Meanwhile, the average height between tensile steel reinforcement and compressive concrete was changing continuously with the increase of the hypotenuse slope, especially when the cross section of the foundation slab is nonrectangular. So, it is necessary to calculate the coefficient of the internal force arm accurately instead of taking it as 0.9 simply [16], and the effect of the hypotenuse slope and the width-to-height ratio on has to be analyzed according to the finite element analysis.

(a)

(b)

(c)

Figure 14: Typical stress distribution of concrete in the most dangerous section. (a) Partial plasticity. (b) Development of plasticity. (c) Whole section plasticity.

When the upper tensile steel reinforcement was yielding, the stress value of concrete in the most dangerous section was extracted for the calculation of the coefficient of the internal force arm . It was considered that if the density of the selected points is high enough, the actual stress condition of the cross section can be reflected. Because the area of the compressive steel reinforcement was relatively small compared to that of compressive concrete in the calculating section, the stress of the compressive steel reinforcement can be ignored for improving the efficiency.

Based on the selected points, the coefficient of the internal force arm could be estimated by the following approximate equation:

where S, n, , and hi are the area of the cross section, the number of element, normal compressive stress of the concrete in the ith element, and the height of the ith element relative to the upper tensile steel reinforcement, respectively.

The coefficients of the internal force arm calculated by Equation (3) are reported in Table 7, where is the coefficient of the internal force arm based on ABAQUS analysis and is the value of 0.9 proposed in the Chinese standard GB50007-2011 [16].

Table 7: Comparison of the coefficients of the internal force arm.

Model
Width-to-height ratio
Hypotenuse slope (°)

NJ1
1.5
10
0.9
0.88

NJ2
1.5
20
0.9
0.78

NJ3
1.5
30
0.9
0.62

NJ4
2
10
0.9
0.91

NJ5
2
20
0.9
0.79

NJ6
2.5
10
0.9
0.88

NJ7
3
10
0.9
0.83

NJ8
4
10
0.9
0.76

5.2. Effect of Width-to-Height Ratio and Hypotenuse Slope

By comparing the results of the models NJ1, NJ4, NJ6, NJ7, and NJ8 from Table 7, it can be concluded that the coefficient of the internal force arm showed a trend of decrease with the increase of the width-to-height ratio, as shown in Figure 15(a). It also showed that, with the increase of the hypotenuse slope, the coefficient of the internal force arm reduced obviously according to the comparison of models NJ1∼NJ5, which is shown in Figure 15(b).

(a)

(b)

Figure 15: Analysis of the coefficients of the internal force arm. (a) Influence of the width-to-height ratio. (b) Influence of the hypotenuse slope.

From Figure 15(a), it can be seen that when the width-to-height ratio was not more than 2.5, the coefficient of the internal force arm remained steady roughly at about 0.9 with the hypotenuse slope of 10°. When the width-to-height ratio exceeded 2.5, the coefficient of the internal force arm decreased with the increase of the width-to-height ratio. Because of the increase of the width-to-height ratio, the foundation slab became thinner and thinner, and the compressive stress of concrete transferred to both sides and central area gradually. Based on this, the effective width of the compressive zone had the tendency to decrease, leading to a reduction in working efficiency of the concrete. Therefore, it is necessary to evaluate the effect of the width-to-height ratio on the coefficient of the internal force arm. In order to keep the coefficient unchanged as in GB50007-2011 [16], the effective width correction coefficient k was introduced to consider the influence based on the concept of effective width. According to both study [18] and Figure 15(a), the effective width correction coefficient k was assumed first. When the width-to-height ratio is not more than 2.5, k is equal to 1; k is equal to 0.85 when the width-to-height ratio is 4; and when the width-to-height ratio is in the range of 2.5∼4, k should be determined by linear interpolation.

Figure 15(b) showed that, with the increase of the hypotenuse slope, the coefficient of the internal force arm decreased obviously, which indicated that the hypotenuse slope has a significant influence on the coefficient of the internal force arm. In this paper, the slope correction coefficient j was introduced to consider this influence. It is assumed that when the hypotenuse slope is not more than 10°, j is equal to 1; j is equal to 0.90 when the hypotenuse slope is 20°; j is 0.70 when the hypotenuse slope is 30°; and when the hypotenuse slope is in the range of 10°∼30°, j should be determined by linear interpolation.

5.3. Suggested Design Formula

In order to maintain the original coefficient of 0.9, the above correction coefficients j and k were both introduced to consider the effect of the hypotenuse slope and the width-to-height ratio on the coefficient of the internal force arm. Based on the Chinese standard GB50007-2011 [16], the suggested formula of the uplift capacity for the design of ISCFS-LWR is defined as follows:

where = 0.9 and M, h₀, fy, j, k, and As are the bending moment of the section, the effective height of the foundation slab, the design value of the tensile strength of the steel reinforcement, the slope correction coefficient, the effective width correction coefficient, and the area of the tensile steel reinforcement, respectively.

The comparison between numerical correction coefficients jsks and recommended correction coefficients jk is summarized in Table 8, in which .

Table 8: Comparison of the correction coefficients between the numerical and the recommended results.

Model
Width-to-height ratio
Hypotenuse slope (°)

jsks
jk
(%)

NJ1
1.5
10
0.88
0.98
1.00
2

NJ2
1.5
20
0.78
0.87
0.90
3.4

NJ3
1.5
30
0.62
0.69
0.70
1.4

NJ4
2
10
0.91
1.01
1.00
1

NJ5
2
20
0.79
0.88
0.90
2.3

NJ6
2.5
10
0.88
0.98
1.00
2

NJ7
3
10
0.83
0.92
0.95
3.3

NJ8
4
10
0.76
0.84
0.85
1.2

From the comparative results of Table 8, it showed that the numerical correction coefficients jsks agreed well with the recommended correction coefficients jk, and the relative error is only between 1% and 3.4%, which proves the suitability and accuracy of the suggested design method proposed in this paper.

6. Engineering Case

6.1. Background of the Project

The name of this engineering is 500 kV wild peach line relocation project, which is located in the southeast edge of Chengdu Plain in China. The landform and geomorphological features mainly include the accumulation ridge platform, strip-shaped denudation shallow hill, low mountain, gentle slope platform, and other landforms, as shown in Figure 16. The form of the foundation adopts the universal design module of the State Grid.

Figure 16: Landform of the engineering case.

There are three types of towers in this project, and the acting forces of the foundations are shown in Table 9, where Tmax is the maximum uplift load of the foundation, Tx is the horizontal force along the direction X when subjected to the uplift load, Ty is the horizontal force along the direction Y when subjected to the uplift load, Nmax is the maximum downward pressure of the foundation, Nx is the horizontal force along the direction X when subjected to downward pressure, and Ny is the horizontal force along the direction Y when subjected to downward pressure.

Table 9: Acting forces of the foundations.

Number
Type of tower
Rotation degree of high-voltage line (°)
Acting forces (ultimate value) (unit: kN)

Tmax
Tx
Ty
Nmax
Nx
Ny

1
5D1-SJC3-30
50–60
3847.1
702.1
658.1
4485.4
815.1
717.1

2
5D1-SJC4-36
70–80
4161.4
813.5
788.0
4851.7
959.6
874.6

3
SJ164-45
50–60
4533.0
848.3
848.2
5168.3
1024.4
924.5

The geological parameters selected for the design of the foundations are shown in Table 10, in which γ is the gravity of soil, fak is the eigen value of the bearing capacity for the base, c is the cohesive force of the soil, and Φ is the angle of the internal friction.

Table 10: Geological parameters for the design of the foundations.

Depth of the soil (m)
Name of the soil
Geological parameters
Depth of the ground water (m)

γ (kN/m³)
fak (kPa)
c (kPa)
Φ (°)

0.00∼0.80
Silty clay with the characteristic of molliplast
16
90
10
5
1.0

0.80∼1.60
Silty clay with the characteristic of waxiness
17
170
20
15

1.60∼6.70
Clay
21
300
30
15

>6.70
Mudstone
22
500
80
20

6.2. Design Results by Original Method and Suggested Method

The spread foundation slab with the large width-to-height ratio was applied in this engineering practice combining with engineering geology and meteorological characteristics of this project. To compare the economic benefits of this project, both original design method and suggested design method were used to design the foundation slabs. All of the foundations were exposed to 0.5 m.

For the original design method, the design process and the design formula can be found in the Chinese power industry standard DL/T5219-2014 [15]. The drawings of the foundation designed by the original method are shown in Figure 17 and the design results are presented in Table 11, where B is the width of the foundation slab, H is the whole height of the foundation, and h₁ is the thickness of the edge of the foundation slab, respectively.

(a)

(b)

Figure 17: Drawings of the foundation designed by the original method. (a) Elevation of foundation. (b) Plan of foundation.

Table 11: Design results by the original method.

Number
Type of tower
Geometric parameters
Dosages of concrete (m³)
Dosages of steel reinforcement (kg)

B (m)
H (m)
h₁ (m)

1
5D1-SJC3-30
10.0
5.5
0.9
139.14
7785.92

2
5D1-SJC4-36
10.4
5.6
0.9
145.73
8335.2

3
SJ164-45
10.6
5.9
1.0
166.10
9560.5

For the suggested design method, the design process and design formula are similar to those of the original design method. The differences between them were that the optimization design formula proposed by Li et al. [18] was used for the calculation of lower steel reinforcement, and Equation (4) proposed in this paper was used for the calculation of upper steel reinforcement. The drawings of the foundation designed by the suggested method are shown in Figure 18 and the design results are also presented in Table 12, where B is the width of the foundation slab, H is the whole height of the foundation, h₁ is the thickness of the edge of the foundation slab, h₂ is the thickness of the foundation slab, hb is the height of the rigid step, and b is the width of the rigid step, respectively.

(a)

(b)

Figure 18: Drawing of the foundation designed by the suggested method. (a) Elevation of foundation. (b) Plan of foundation.

Table 12: Design results by the suggested method.

Number
Type of tower
Geometric parameters
Width-to-height ratio
Dosages of concrete (m³)
Dosages of steel reinforcement (kg)

B (m)
H (m)
h₁ (m)
h₂ (m)
hb (m)
B (m)

1
5D1-SJC3-30
10.2
5.6
0.4
0.9
0.8
1.6
3.89
84.28
8124.6

2
5D1-SJC4-36
10.5
5.8
0.4
0.9
1.0
1.8
3.83
91.88
10160.2

3
SJ164-45
10.7
6.0
0.4
0.9
1.1
1.975
3.75
100.79
9790.6

6.3. Comparison of Economic Indicators

The dosages of concrete, the dosages of steel reinforcement, and the construction cost of this project were analyzed as the economic indicators to compare the economic benefits of these two design methods. According to the actual conditions of this project, the concrete was priced at 1200 RMB per cubic meter and the steel reinforcement was priced at 5 RMB per kilogram. The comparative results of the economic indicators are presented in Table 13, in which C₁ is the dosage of concrete when using the original design method, S₁ is the dosage of steel reinforcement when using the original design method, CC₁ is the construction cost of this project when using the original design method, C₂ is the dosage of concrete when using the suggested design method, S₂ is the dosage of steel reinforcement when using the suggested design method, and CC₂ is the construction cost of this project when using the suggested design method, respectively.

Table 13: Comparison of economic indicators between the original design method and the suggested design method.

Number
Type of tower
Economic indicators of the original design method
Economic indicators of the suggested design method
Comparison of indicators

C₁ (m³)
S₁ (kg)
CC₁ (RMB)
C₂ (m³)
S₂ (kg)
CC₂ (RMB)
C₂/C₁
S₂/S₁
CC₂/CC₁

1
5D1-SJC3-30
139.14
7785.92
205897.6
84.28
8124.6
141759.0
0.61
1.04
0.69

2
5D1-SJC4-36
145.73
8335.2
216552.0
91.88
10160.2
161057.0
0.63
1.22
0.74

3
SJ164-45
166.1
9560.5
247122.5
100.79
9790.6
169901.0
0.61
1.02
0.69

Note. CC₁ = 1200 × C₁ + 5 × S₁; CC₂ = 1200 × C₂ + 5 × S₂.

The results from Table 13 showed that when compared with the foundation in the original design method, the dosage of concrete designed by the suggested method can be reduced by 37∼39% and the dosage of steel reinforcement should be increased by 2∼22%. However, the construction cost can be saved by 26∼31%, which indicated that the economic benefits of this project were quite obvious.

Figures 19(a)–19(c) show the construction process of this engineering case, and the typical foundation of this project designed by the suggested method is shown in Figure 19(d). The achievement of this project can provide a reference for other relevant engineering cases.

(a)

(b)

(c)

(d)

Figure 19: Construction process of the engineering case. (a) Ground construction. (b) Reinforcement construction. (c) Concrete construction. (d) Foundation after stripping.

7. Conclusions

This paper presents the uplift test and the numerical simulation of the isolated spread concrete foundation slab with the large width-to-height ratio. The failure modes, uplift bearing capacity, and design method of uplift capacity for the foundation slab were summarized. The following points should be emphasized:

(1)The failure modes in the uplift test are almost bending failure, including cross-shaped bending failure, grid-shaped bending failure, and incomplete bending failure with circumferential cracks. Meanwhile, the test results of the specimens NJ1∼NJ8 agree well basically with the results of the corresponding repeated specimens NJ9∼NJ16, respectively, and the numerical results also have good agreement with the test results. Thus, the accuracy of the numerical simulation is proved.(2)Uplift bearing capacity reduces gradually with the increase of the hypotenuse slope, and the uplift bearing capacity also decreases obviously as the width-to-height ratio increases. So, the significant influence of the hypotenuse slope and the width-to-height ratio on the uplift bearing capacity of the foundation slab should be considered.(3)The effective width correction coefficient k is introduced to consider the influence of the width-to-height ratio on the coefficient of the internal force arm. When the width-to-height ratio is not more than 2.5, k is equal to 1; k is equal to 0.85 when the width-to-height ratio is 4; and when the width-to-height ratio is in the range of 2.5∼4, k should be determined by linear interpolation.(4)The slope correction coefficient j is also introduced to consider the influence of the hypotenuse slope on the coefficient of the internal force arm. It is assumed that when the hypotenuse slope is not more than 10°, j is equal to 1; j is equal to 0.90 when the hypotenuse slope is 20°; j is 0.70 when the hypotenuse slope is 30°, and when the hypotenuse slope is in the range of 10°∼30°, j should be determined by linear interpolation.(5)Based on the Chinese standard GB50007-2011, the effective width correction coefficient k and the slope correction coefficient j are introduced to propose the suggested design formula for the design of the isolated spread concrete foundation slab. The recommended correction coefficients jk proposed in this paper can match well with the numerical correction coefficients jsks, and the relative error is only between 1% and 3.4%, which proves the suitability of the suggested design method.(6)In this paper, an engineering case which used the suggested design method is presented, and the construction cost of this project can be saved by 26∼31% when compared with the economic indicators of the original design method, which shows that the economic benefits of this project are quite obvious. The achievement of this project can provide a reference for other relevant engineering cases.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported by the Science and Technology Project of the State Grid Corporation of China (Grant No. 52199915002M).

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