Comparison of calculation methods for pile foundations
Bridge pile foundation is one of the important components of bridges. The function of the pile foundation is to transfer the load of the bridge to the soil layer with good bearing performance at a deeper underground level to meet the requirements of bearing capacity and settlement. The pile foundation has a high bearing capacity, can withstand vertical loads, can also bear horizontal loads, can resist uplift loads and can withstand vibration loads, is the most widely used form of deep foundation.
Different from the bridge superstructure design, the top of the pile foundation is directly connected with the cushion cap or pier and is in contact with the soil, and the boundary conditions are more complex. Therefore, in the process of pile foundation design, there will inevitably be many doubts, such as: how to consider the interaction between the pile foundation and the surrounding soil, how to simulate the restraint effect of the cap on the pile group and how to solve the internal force of the pile foundation?
This article is written based on the reference to various sources, mainly to introduce the current "Code for the Design of Railway Bridge and Culvert Foundation and Foundation" (TB 10093-2017) pile foundation design methods, and describe the relevant basic concepts and formula derivation.
Internal forces and displacements of monopiles under horizontal loads
1 Problem Description
Known: The following figure is a pile foundation buried in the soil, and its top is level with the ground, where there is a strong moment, transverse force, and produces transverse displacement, corner. ( The positive and negative signs stipulate that the transverse displacement is positive along the axis, and the angle of rotation is positive in the counterclockwise direction; the bending moment is positive when the left fiber is in tension, and the transverse force is positive along the axis. In the figure, sum is positive, and the corner is negative. ）
Question: How to correctly analyze the internal forces of the pile foundation and obtain its elastic curve as well as the bending moment, lateral force, lateral displacement and rotation angle at any position?
2 Calculated width b0 of pile foundation
When calculating the stress of the bottom surface of the pile, it is considered according to the actual area of the bottom surface of the pile. However, when calculating the horizontal compressive stress exerted by the pile on the side soil, due to the complexity of the stress situation, in order to simplify the calculation, the actual width or diameter of the pile of various cross-sectional shapes is converted to the width b0 of the rectangular pile with the same stress situation, and b0 is called the calculated width of the pile.
Conversion coefficient of pile foundation shape Kf: According to the test data, it is proved that the cross-sectional shape of the pile has an influence on the horizontal load bearing capacity of the pile and the horizontal pressure pattern of the pile acting on the side soil. The results of comparing the horizontal force applied to the circular piles and rectangular piles of different sizes in various soils show that the critical horizontal load values of the circular piles with a diameter of d and the rectangular piles with a side width equal to 0.9d are equal when the soil on the sides is extruded when they are subjected to horizontal forces.
Interaction coefficient between piles K: When the upper part of the pile foundation is connected with the cushion cap, and the following is composed of several piles located in the external force surface, the interaction between the piles must also be considered, and the actual width of each pile must be combined with the interaction influence coefficient.
Force conversion coefficient K0: When the pile side soil bears the horizontal load, it is actually a spatial force, but in order to simplify the calculation, the pile is considered as a rectangular pile with plane stress, therefore, the actual width of the pile must also be converted into the width of the rectangular pile equivalent to the plane force condition, that is, the actual width must be multiplied by the force conversion factor.
To sum up, after considering the three factors of pile foundation shape conversion coefficient, mutual influence coefficient and force conversion coefficient, the calculated width b0 of pile foundation is:
b0=kf*k*k0*d
3. The proportion coefficient m of the horizontal resistance coefficient of the soil around the pile foundation
(1) The soil around the pile foundation is the same kind of soil
In an article by K. Terzaghi of the United States, it is pointed out that the horizontal resistance coefficient Ch(kN/m^3) of the soil on the side of the pile is the ratio of the pressure p(kN/m^2) at any given point on the contact surface between the pile and the soil and the displacement x of the point under load, that is, Ch=p/x. Then the stress p of the pile foundation at any depth under the action of horizontal pressure and vertical pressure can be expressed by the horizontal resistance coefficient Ch.
The horizontal resistance coefficient Ch of the soil will change with the depth z, and there are four main assumptions about the variation law of the horizontal resistance coefficient in the soil, as shown in the figure below.
1) When n=0, the horizontal resistance coefficient of the foundation is a constant, which is called the "C" method, also known as the Zhang's method;
2) When n=1, the horizontal resistance coefficient of the foundation is proportional to the depth z, which is called the "m" method;
3) Above the zero point of the first deflection of the pile, it is a parabolic distribution, i.e., n=2, and the following is a constant, i.e., n=0, which is called the "K" method;
4) When n = 0.5, it is called the "c value" method.
The continental railway department and the highway department have done a lot of research work, which has confirmed that the differential equation of the elastic curve obtained by using the change law of horizontal resistance coefficient increasing in a straight line with depth ("m" method) and using the power series method to solve the obtained differential equation of the elastic curve is more consistent with the actual situation of the general soil, then the horizontal resistance coefficient Ch of the soil can be obtained by the following formula:
When there is no geological survey data, m can be taken as shown in the following table.
(2) The soil around the pile foundation is different soils
When there are several different soil layers on the pile side, the mi value of each soil layer must be converted to the m value of one soil in the whole depth. According to the test, the closer the soil is to the ground, the greater the influence on the horizontal load of the pile, and at a certain depth hm, the change of soil properties has little influence on the horizontal displacement of the pile. Here we can take the m-value from the hm depth below the ground as the m-value over the entire depth.
Depth of influence hm: According to the analysis, for rigid piles, i.e., the entire depth, i.e., adopted, for flexible piles. Wherein in meters;d is the average diameter of the pile, and for the square pile, the side width of the pile can be used in meters;is the deformation coefficient of the pile foundation.
The average value of m: The calculation principle is that the area of the horizontal resistance coefficient before conversion is equal to the area after conversion, and the calculation formula is as follows:
4. The deformation coefficient of the pile foundation is α
The characteristics of the pile foundation and the soil around the pile do not affect the stress and deformation of the pile foundation alone. According to the relative stiffness of the pile and the soil, the pile foundation is divided into rigid pile foundation and flexible pile foundation. The α of the deformation coefficient of the pile foundation is introduced, and its formula is as follows:
According to the test, when the bottom surface of the pile is placed below the ground or at a depth of h≤2.5/α below the local scour line, the pile can be considered to have infinite stiffness. The h≤2.5/α pile is calculated according to the rigid pile and the elastic pile respectively, and it is proved that the horizontal load bearing capacity of the two calculated piles and the horizontal pressure pattern of the pile on the soil are very close, but the horizontal displacement and rotation angle of the pile at the ground are different, and if the horizontal displacement and rotation of the ground obtained by the calculation method of the rigid pile are appropriately corrected, it is still possible. Therefore, for the sake of simplifying the calculation, for a pile with h≤2.5/α, it can be regarded as having infinite stiffness and as a rigid pile foundation.
On the contrary, if h>2.5/α, the actual stiffness of the pile must be considered when calculating the pile foundation, and the calculation method of the elastic pile foundation must be carried out.
Comparison case of pile foundation scheme
The six-lane mainline viaduct on the urban expressway is generally designed as a whole bridge, the width of the bridge is about 25~27m, the span diameter of the general section of the bridge is 30m, and the superstructure adopts the prestressed concrete structure, and there are cast-in-place box girders, prefabricated small box girders, segmental beams and other structural types. The lower part of the bridge is provided with piers in the central separator of the ground, and the substructure is generally a double-column pier.
Schematic diagram of cross-section of cast-in-place concrete large box girder bridge
Schematic diagram of the cross-section of a concrete small box girder bridge
Recently, in the design and consulting work of the bridge scheme, it was found that for the above-mentioned six-lane main line viaduct, the similar bridge structure type, the same rock-socketed pile scheme is adopted, and the conclusions drawn from the analysis of different engineering projects are quite different when comparing the bridge foundation scheme. To this end, I consulted relevant information and referred to the construction drawings of similar projects to further compare and select the two bridge foundation schemes.
Taking a good rock layer as an example of pile foundation bearing layer, the comparison of bridge foundation types is carried out. The pile foundation is designed as rock-socketed piles, and 4 φ1.5m pile foundations and 2 φ2.2m piles are selected for comparison. All are considered according to the center distance of the column is 4.8m.
The center of the pile foundation of the 2 φ2.2m pile foundation scheme is aligned with the center of the column, and the pile spacing of 4 .8m also meets the requirements of the adjacent pile center distance of the rock-socketed pile. Considering the overall needs, the tie beam is arranged at the top of the pile (the tie beam can also be canceled when the column is very short), and the tie beam height can meet the needs of the anchorage of the main reinforcement of the column, and 1.5m is taken here.
Layout drawing of 2 φ2.2m piles (unit: cm)
The 4 φ1.5m pile foundation scheme is still aligned according to the center of the column and the center of the two pile foundations on one side, and the distance between the pile centers in the cross-bridge direction is also 4.8m. The center distance of adjacent piles can be met along the bridge to meet the requirements of the rock-socketed pile, and the center distance of the pile is 3.5m. The thickness of the cap is suitable to take 2.5m according to experience and calculation analysis.
Layout of 4 φ1.5m piles (unit: cm)
In order to save the concrete and steel bars of the cushion cap, the 4 φ1.5m pile foundation scheme can be designed in the shape of a dumbbell on the plane. However, the distance between the left and right columns of the scheme is not far, and the proportion of work saved by making a dumbbell shape is not high, and the construction is more troublesome, so the dumbbell scheme is not considered in this comparison.
Dumbbell-shaped cushion cap plan of 4 φ1.5m pile foundation scheme (unit: cm)
It is assumed that according to the geological conditions, the pile length of 4 φ1.5m piles needs to be 35m, and the pile length of 2 φ2.2m piles needs to be 37m. In addition, it is assumed that the superstructure adopts a concrete small box girder, and all adopt ordinary plate rubber bearings, so that the stress of each bridge pier is relatively uniform. If the superstructure is an integral box girder similar to a cast-in-place box girder, the number of supports is small, there is a distinction between fixed and movable support along the bridge, and the bridge pier also has the distinction between fixed pier and movable pier, then it is necessary to compare according to the pier type.
The four φ1.5m pile foundation scheme has 112.9m3 of cushion cap concrete, 10.7t reinforcement, and the reinforcement content of each cubic concrete is 95kg/m3. The main reinforcement of the pile foundation is φ28mm, a total of 36 are arranged according to the equal spacing around the pile (spacing about 12cm), one is cut off at intervals 15m below the bearing cap, and the remaining 18 extend to the bottom of the pile. The pile foundation C30 underwater concrete is 247.6 m3, the steel bar is 22.0t, and the reinforcement content of each cubic concrete is about 89kg/m3.
The two φ2.2m pile foundation scheme has 28.9m3 of tie beam concrete, 2.3t reinforcement, and the reinforcement content of each cubic concrete is 80kg/m3. The main reinforcement of the pile foundation adopts a bundle of reinforcement φ28mm, a total of 42 pairs are arranged at equal intervals around the pile (spacing of about 17cm), one of the bundle reinforcements is cut off at 15m below the cushion cap, and the remaining 42 single ones extend to the bottom of the pile. The pile foundation C30 underwater concrete is 281.2 m3, the steel bar is 28.1t, and the reinforcement content of each cubic concrete is about 100kg/m3.
From the above comparison, it can be seen that the material consumption of the 4 φ1.5m pile foundation scheme is slightly more, and the material consumption of the two pile foundation schemes is not much different. If further economic comparisons are to be made, special calculations should be made by technical and economic professionals in conjunction with construction measures. When the diameter of the pile foundation changes greatly, it may bring about the adjustment of construction technology and equipment, thereby causing a large difference in the cost of construction measures.
It should also be noted that the structural dimensions, reinforcement schemes and material indicators mentioned in the above comparison are the structural reinforcement arrangements and comparisons under certain preconditions, the assumed superstructure type of the bridge and the assumed geological conditions, and are only individual cases.
The above comparison only focuses on the comparison of engineering quantity and economy, and there are many factors to be considered when comparing the actual bridge pile foundation scheme. First of all, for example, (1) the construction period, under some geological and construction conditions, the construction speed of the large-diameter pile scheme with a small number of pile foundation roots is fast, and under some geological and construction conditions, although the number of roots is small, the length that needs to enter the bearing layer is long, and the construction progress is slow. It is necessary to analyze and compare the specific situation. For example, (2) the water resistance rate, the water resistance rate of the foundation of some high-pile cap bridges is required, so reducing the water resistance area becomes the controlling factor for scheme selection. There is also (3) construction difficulty and risk, some small and medium-sized bridges have more karst cave distribution in the underground rock formation, in the case of the overburden and relatively thick, can also consider the smaller diameter friction pile scheme of multiple piles, the pile foundation does not enter the rock formation, and the construction risk of the pile foundation passing through the karst cave area is avoided.
How to optimize the design of pile foundations
X project is located in the central area of the city, and our company undertakes its whole process follow-up audit. The total planned land area of Phase X of the project is 17,656.36 m2, the total construction area is 80,306.12 m2, the above-ground construction area is 69,843.77 m2, and the underground construction area is 10,462.35 m2. The proposed building consists of two 40-storey (numbered 1#, 3#) and one 45-storey (numbered 2#) civil building, with a whole underground garage under it, of which the height of the 1# and 3# buildings is 112.30m, and the height of the 2# building is 126.30m, and the business formats are all super high-rise buildings, and the plot in the district is the end of the project.
(1) On-site situation
The basement floor is within 4 layers of silty clay (fak=400kPa) or 5 layers of clay (fak=420kPa). On this basis, the foundation design of the tower part of the project adopts φ900 bored pile + raft foundation, and the basement part of the garage adopts raft foundation. (2) Soil analysis
According to the geological exploration report (see the table below), the soil properties of the project site show that the groundwater in the site area is mainly composed of two types: the upper layer of the pore is deposited in the artificial fill, and the atmospheric precipitation and the surrounding domestic water are the main sources of recharge; the fracture water is deposited in the fractures of the underlying rock layer, the groundwater is deeply buried, and the groundwater and soil in the site area are slightly corrosive to the concrete and the steel bars in the concrete, and the building site category is Class II., which can not consider the impact of liquefaction.
(3) Scheme optimization assumption
When our company got the pile foundation map, we found that the pile foundation of the plot in this area was designed according to the φ900mm bored pile, and the natural foundation scheme was adopted in the early stage of the plot due to the good geological conditions, so our company proposed the scheme optimization plan to the owner from the perspective of cost.
(3) Discussion at the meeting
After a meeting and discussion between geological experts, design institutes, owners and consultants, according to the actual construction conditions, construction quality requirements, construction technology, etc., combined with the principle of economic investment, the φ900 bored pile was adjusted to the φ800 bored pile scheme, the structural raft foundation remained unchanged, and the concrete grade was adjusted from the original C35 and C40 to C35, and the rest was not adjusted.
No.3
Comparative analysis of program adjustments
(1) Scheme comparison
(2) Economic comparison
(3) Conclusions of program analysis
According to the comparison and calculation of the scheme, the difference between the two is about 874,500 yuan, accounting for 16.70% of the original cost.
No.4
Background of the adjustment of the secondary program
(1) Optimization of the secondary scheme
According to the on-site investigation, geological experts and design institutes found that the pressure-bearing capacity of the foundation of the plot in the area performed well, which may be higher than the pressure-bearing capacity of the foundation of the plot in the early stage, so the project discussed and discussed the test pile first, and then discussed whether to adjust and optimize the pile foundation scheme after the shallow slab load test of buildings 1 and 3.
(2) Plate load test
The type of local block foundation is natural foundation, the detection method is the stacking method, the loading method is the slow maintenance load method, the maximum loading value is the destructive test, the bearing area is 1m2, the number of detection points in the 1# building is 3 points, the number is S1#, S2#, S3#, and the detection points in the 3# building are 4 points, the number is S1#, S2#, S3#, S4#, see the following table for details:
1# floor shallow slab load test results table
3# floor shallow slab load test results table
(3) Optimization of secondary schemes
According to the results of the plate load test, the pressure bearing capacity of the foundation of the plot in the area is indeed better than that of the early stage, considering that the residential formats in the early stage are all high-rise buildings, and no super high-rise buildings have been done, and the local blocks are super high-rise buildings, so the residential part must adopt pile foundation engineering, but the results of the plate load test show that the pile foundation type can be adjusted, and the bored piles of the original scheme are optimized and adjusted to CFG piles, as detailed in the comparative analysis of the secondary scheme.
Comparative analysis of secondary scheme adjustments
(1) Scheme comparison
(2) Economic comparison
Conclusions of the program analysis
Through the comparison and calculation of the scheme, the difference between the two is about 1.154 million yuan, and the adjustment ratio is 15.79%, from the above, it can be seen that from the original design of the φ900 bored pile to the final φ600 CFG pile, the cost is optimized by 2.0285 million yuan