中国与美国规范混凝土基础设计对比

Concrete foundation design comparison between Chinese and American codes

1. Basic design parameters

In this comparison calculation, a large equipment foundation of a foreign project was selected as the design object. In order to make the comparison result more intuitive, a unified regulation was made:

(1) Both the Chinese and US standard calculation examples use the same upper load

standard value, and consider only the horizontal load in the Y direction, but the load combination uses their respective coefficients.

(2) There are differences in the test method, the guarantee rate and the design value of

concrete strength between China and the United States. When designed according to the standard of China, the strength design value of steel and concrete is used. The yield strength is used in the design and calculation of the steel bar according to the American manual, and the experimental value of the concrete is adopted.

(3) The same foundation size and characteristic value of foundation bearing capacity are

adopted.

(4) The specific parameters are as follows: according to the estimation, the basic size is

shown in figure 1 (unit mm).

Thickness of protective layer: 75 mm, Average bulk density of foundation and soil: 20

kN/m3,Characteristic value of foundation bearing capacity: 400 kPa; embedded depth of foundation: 5.00m, Force elevation: -0.500m;

 Design according to Chinese standard C35

concrete, 𝑓𝑐=16.70𝑁/𝑚𝑚2(prismatic strength), HRB335, reinforcing bar, 𝑓𝑦=



300𝑁/𝑚𝑚2

According to the American manual C35 concrete, 𝑓𝑐′=28𝑁/𝑚𝑚2(cylinder strength), reinforcing bar, 𝑓𝑦=335𝑁/𝑚𝑚2.

The various forces on the basis are shown in table 1.

Table 1 Force standard D, dead load (kN) P 𝐻𝑥 𝐻𝑌 1300 380

L, live load (kN) P 𝐻𝑥 𝐻𝑌 1500 ±220 Figure 1

E, earthquake load Y direction (kN) P 𝐻𝑥 𝐻𝑌 1500 ±1100 W, wind load Y direction (kN) P 𝐻𝑥 𝐻𝑌 ±700 ±450 Note: p is vertical load, downward to positive, 𝐻𝑥 is the horizontal load along the X-axis, 𝐻𝑌 is the horizontal load along the Y-axis.

2. Basic calculation example

2.1. Load combination

(1) China standard load combination.

As the earthquake action participates in the combination, the carrying capacity of the foundation must be adjusted according to the specifications. Therefore, this example uses the Chinese code to calculate the load combination and distinguishes them based on whether there is an earthquake or not, “Loading Codes for Building Structures” and “Codes for Seismic Design of Buildings”. The required load combinations are as follows:

Standard load combination:

𝑛

S=𝑆𝐺𝐾+𝑆𝑄1𝐾+∑Ψ𝑐𝑖𝑆𝑄𝑖𝑘

𝑖=2

Basic load combination:

𝑛

S=𝛾𝐺𝑆𝐺𝐾+∑𝛾𝑄𝑖Ψ𝑐𝑖𝑆𝑄𝑖𝑘

𝑖=1

S=𝛾𝐺𝑆𝐺𝐸+𝛾𝐸ℎ𝑆𝐸𝐻𝑘+𝛾𝐸𝑉𝑆𝐸𝑉𝑘+𝛾𝑤Ψ𝑤𝑆𝑤𝑘

According to the above combination principle of load and the standard value of force given in table 1, the standard value and design value when considering seismic action combination are respectively; 𝑃𝑘=16000𝑘𝑁, 𝐻𝑌𝑘=1700𝑘𝑁, 𝑀𝑥𝑘=7650𝑘𝑁∙𝑚 and p=1050𝑘𝑁, 𝐻𝑦=2150𝑘𝑁, 𝑀𝑥=9675𝑘𝑁∙𝑚; the standard value and design value when considering wind load combination are respectively; 𝑃𝑘=15200𝑘𝑁, 𝐻𝑌𝑘=1050𝑘𝑁, 𝑀𝑥𝑘=4725𝑘𝑁∙𝑚 and p=18288𝑘𝑁, 𝐻𝑦=1142𝑘𝑁, 𝑀𝑥=5139𝑘𝑁∙𝑚.

(2) American standard load combination.

Due to the specification relevant foundation calculation, combination condition, the earthquake is not to adjust the bearing capacity of foundation and component, so this example based calculation, only the maximum combination. According to “The minimum design load code”, the following load combination is adopted.

Standard load combination:

DL+LL, DL+0.75LL+0.75E Basic load combination:

1.2DL+1.6LL; 1.2DL+1.0LL+1.4E

According to the above combination principle of load and the standard value of force given in table 1, the standard value and design value when considering seismic action combination are respectively; 𝑃𝑘1=14500𝑘𝑁, 𝑃𝑘2=15250𝑘𝑁 𝐻𝑦𝑘1=600𝑘𝑁, 𝐻𝑦𝑘2=1370𝑘𝑁 and 𝑝1=18000𝑘𝑁, 𝑝2=19200𝑘𝑁, 𝐻𝑦1=808𝑘𝑁, 𝐻𝑦2=808𝑘𝑁. In the calculation, the larger value of the two groups of combinations is taken;𝑃𝑘=15250𝑘𝑁, 𝐻𝑦𝑘=1350𝑘𝑁, 𝑀𝑘=4.5𝐻𝑦𝑘=

6165𝑘𝑁∙𝑚 and p=19200𝑘𝑁, 𝐻𝑦=2216𝑘𝑁, M=4.5𝐻𝑦=9972𝑘𝑁∙𝑚.

2.2. The foundation calculation

In the calculation of foundation, the Chinese and American codes all adopt the standard value of the total floor slab reaction force corresponding to the standard combination of load effect. However, the Chinese code will adjust the characteristic value of foundation bearing capacity for seismic combination conditions, while the US code does not have such adjustment requirements. (1) According Chinese code.

Considering earthquake load combination

𝑝𝑘𝑚𝑎𝑥=𝑝𝑘𝑚𝑖𝑛= 𝑝𝑘=

𝑝𝑘+𝐺𝑘

𝐴𝑝𝑘+𝐺𝑘

𝐴

+−

|𝑀𝑥𝑘|𝑊𝑥|𝑀𝑥𝑘|𝑊𝑥

=357𝑘𝑃𝑎<1.2×1.3×𝑓𝑎=624𝑘𝑃𝑎, satisfied =243𝑘𝑃𝑎,

𝑝𝑘+𝐺𝑘

𝐴

=300𝑘𝑃𝑎<1.3×𝑓𝑎=400×1.3=520𝑘𝑃𝑎, satisfied

Where, A is area of base, 𝐺𝑘 is soil weigh Considering wind load combination 𝑝𝑘𝑚𝑎𝑥=𝑝𝑘𝑚𝑖𝑛=𝑝𝑘=

𝐴𝑝𝑘+𝐺𝑘

𝐴𝑝𝑘+𝐺𝑘

𝐴

+−

|𝑀𝑥𝑘|𝑊𝑥|𝑀𝑥𝑘|𝑊𝑥

=325𝑘𝑃𝑎<1.2×𝑓𝑎=480𝑘𝑃𝑎, satisfied =255𝑘𝑃𝑎

𝑝𝑘+𝐺𝑘

=290𝑘𝑃𝑎<𝑓𝑎=400𝑘𝑃𝑎, satisfied

(2) According American code.

𝑝𝑘𝑚𝑎𝑥=𝑝𝑘𝑚𝑖𝑛=𝑝𝑘=

𝐴𝑝𝑘+𝐺𝑘

𝐴𝑝𝑘+𝐺𝑘

𝐴

+−

|𝑀𝑥𝑘|𝑊𝑥|𝑀𝑥𝑘|𝑊𝑥

=337𝑘𝑃𝑎<𝑓𝑎𝐸=400𝑘𝑃𝑎, satisfied =245𝑘𝑃𝑎

𝑝𝑘+𝐺𝑘

=291𝑘𝑃𝑎

2.3. Basic calculation

A Chinese and American code, the basic combination value of net reaction force of foundation floor corresponding to the basic combination of load effect is adopted. Foundation design, the Chinese standard mainly includes the shear, scouring and bending design, and the American Standard mainly includes the shear and bending design, in which the shear calculation includes two aspects: one way and two-way directions.

2.3.1 According Chinese codes:

(1) Considering earthquake load combination

(a) Net plate reaction design value:

𝑃0=𝐴=242𝑘𝑃𝑎; 𝑃𝑚𝑎𝑥=𝐴+

𝑃

𝑃

|𝑀𝑥|𝑊𝑥

=315𝑘𝑃𝑎; 𝑃𝑚𝑖𝑛=𝐴−

𝑃

|𝑀𝑥|𝑊𝑥

=170𝑘𝑃𝑎

(b) Basic shearing resistance checking:

V=𝑃𝑚𝑎𝑥×𝐴𝑝=9236𝑘𝑁≤0.7𝛽ℎℎ𝑓𝑡𝐴𝑐=16836𝑘𝑁, satisfied

Where,ℎ0=2.41𝑚, 𝛽ℎ=0.795, 𝑓𝑡=1.57𝑀𝑃𝑎, 𝐴𝑐=19.27𝑚2, 𝐴𝑝=30.8𝑚2

(c) Basic punching check:

𝐹𝑙=𝑃𝑚𝑎𝑥𝐴𝑙=9236𝑘𝑁≤0.7𝛽ℎ𝑝ℎ𝑓𝑡𝐴𝑞=44866𝑘𝑁, satisfied Where,h=2.5𝑚,𝛽ℎ𝑝=0.9, 𝐴𝑞=45.36𝑚2, 𝐴𝑙=29.32𝑚2 (d) Base bending calculation:

Bending calculation:

2(𝑙𝑎2𝑏+𝑏′)𝑃𝑚𝑎𝑥

M==14215𝑘𝑁∙𝑚

6Reinforcement calculation:

𝑀

𝐴𝑠==2732𝑚𝑚2/𝑚

0.9×𝑓𝑦×ℎ0

Where, 𝑙𝑎 : compute area of footwall length

(2) Considering wind load combination

(a) Net plate reaction design value:

𝑃0=𝐴=229𝑘𝑃𝑎; 𝑃𝑚𝑎𝑥=𝐴+

𝑃

𝑃

|𝑀𝑥|𝑊𝑥

=267𝑘𝑃𝑎; 𝑃𝑚𝑖𝑛=𝐴−

𝑃

|𝑀𝑥|𝑊𝑥

=190𝑘𝑃𝑎

(b) Basic shearing resistance checking:

V=𝑃𝑚𝑎𝑥×𝐴𝑝=8824𝑘𝑁≤0.7𝛽ℎℎ𝑓𝑡𝐴𝑐=16836𝑘𝑁, satisfied (c) Basic punching check:

𝐹𝑙=𝑃𝑚𝑎𝑥𝐴𝑙=9236𝑘𝑁≤0.7𝛽ℎ𝑝ℎ𝑓𝑡𝐴𝑞=44866𝑘𝑁, satisfied (d) Base bending calculation:

Bending calculation:

2(𝑙𝑎2𝑏+𝑏′)𝑃𝑚𝑎𝑥

M==12052𝑘𝑁∙𝑚

6Reinforcement calculation:

𝑀

𝐴𝑠==2316𝑚𝑚2/𝑚

0.9×𝑓𝑦×ℎ0

2.3.2

Considering earthquake and wind load combination, comparing these two conditions, finally we get: bending control M=14215kN∙m, reinforcement 𝐴𝑠=2732𝑚𝑚2/𝑚.

According American codes:

(a) Net plate reaction design value:

P=

𝑃𝐴

=240𝑘𝑃𝑎; 𝑃𝑚𝑎𝑥=+

𝐴

𝑃

|𝑀𝑥|𝑊𝑥

=315𝑘𝑃𝑎; 𝑃𝑚𝑖𝑛=−

𝐴

𝑃

|𝑀𝑥|𝑊𝑥

=165𝑘𝑃

(b) Basic shearing resistance checking:

US code in computing foundation shear, need to divides one-way and two-way shear checking.

Under the one-way direction, ACI318M-05; control section of column profile, shear value is 𝑉𝑢=8813𝑘𝑁, according to ACI318M-05, 𝑉𝑐=

0.17√𝑓𝑐′𝑏𝑤𝑑=17343𝑘𝑁, ∅=0.75, then, 𝑉𝑢<∅𝑉𝑛=13007𝑘𝑁, satisfied.

Under the two-way directions, the distance around the base of the column d/2 is a control section, and its shear value is 𝑉𝑢=13𝑘𝑁, according ACI318M-05; 𝑉𝑐1=0.17(1+)√𝑓𝑐′𝑏0𝑑=106194𝑘𝑁,

𝛽

𝑉𝑐2=0.083(2+

𝑎𝑠𝑑

)√𝑓𝑐′𝑏0𝑑=144035𝑘𝑁 𝑏0

2

𝑉𝑐3=0.33√𝑓𝑐′𝑏0𝑑=79285𝑘𝑁, the minimum value is 𝑉𝑐=min(𝑉𝑐1,𝑉𝑐2,𝑉𝑐3)=79285 𝑘𝑁, so 𝑉𝑢=135𝑘𝑁<∅𝑉𝑛=594𝑘𝑁, satisfied

(c) Base bending calculation:

The selection of bending moment area is difference form Chinese code; US code selects the entire bottom side of foundation on one side of the vertical plane, and Chinese code selects to side of the bottom side of column, then the base short side of bottom as isosceles ladder.

According to ACI318M-05, the design value of bending moment at the control section of base bending is 𝑀=17535𝑘𝑁∙𝑚, then baseplate

reinforcement is 𝐴𝑠=0.81𝑓𝑑=26814𝑚𝑚2, so, reinforcement is 𝐴𝑠=

𝑦

𝑀

3352𝑚𝑚2

3. Summary

According to the above calculation process and results, we can find that:

(1) According to the Chinese and American standards, the calculated base bottom

reaction force is relatively close. However, when checking the bearing capacity of foundation, the American standard does not make seismic adjustment in the bearing capacity of foundation.

(2) US code for the foundation shear and punching shear strength is higher than

Chinese code, by the way, which may be due to the difference in the selection of the control interface; in the case of \"bidirectional action\" in the United States, in the case of the expected impact failure, the \"punching\" formulation is presented in some cases except for the form of destruction. In addition, the term \"punching\" or \"shear\" is still used, but in fact it refers to \"punching\" or \"punching resistance\". (3) The reinforcement calculation results of the American code are larger than those of

the Chinese code; the main reason is that the bending moment calculation area of the American code is significantly larger than that of the Chinese code. The area selected by the American and Chinese codes for bending moment calculation is different, which the area selected in the Chinese specification, is an isosceles

trapezoid with the bottom edge of the column as the top edge and the short edge of the foundation as the bottom edge.

(4) American standard and Chinese standard for this example, the minimum

reinforcement ratio requirements are basically the same.