Prestressed High-strength Concrete (PHC) pipe piles are used extensively because of significant advantages in low cost, simple installation, environmental friendliness and short processing time when compared with cast-in-situ piles1,2,3,4. The axial force at certain section or level of the pile shaft, of great importance in analyzing shaft resistance and bearing capacity of PHC pipe piles, is generally calculated from the strain, which may be tested by certain methods5,6,7,8. However, as PHC pipe piles have to be heat and steam cured, gauges for strain test are generally installed when the piles are cooled down. Although certain types of gauges, which can resist high temperature, can be installed before the process of heat and steam curing, they do not find extensive engineering application due to problems such as high test cost, low survival rate and poor stability9,10,11. Moreover, at present the linear elastic function between axial force and strain is often applied to calculate axial forces of pile shaft12,13,14. However, the relationship between axial force and strain is actually not linear elastic as suggested by theory and tests of axially compressed concrete members. The linear elastic relationship is approximate and appropriate only in a range of small axial force, while in most cases the relationship is nonlinear15. As a result, errors are inevitable when the current approximate linear-elastic function relating axial force to strain is applied to calculate axial forces. No literature report has been found so far on the study of nonlinear relationship between axial force and strain of PHC pipe piles. A new and useful technology of strain test is proposed in this paper. Taking pipe pile PHC500AB-125 as a case study, a nonlinear function relating axial force to strain is proposed and an accurate approach of shaft resistance calculation is presented.

Summary of methods of axial force test of PHC pipe piles

Two steps are mainly followed to test the axial force of PHC pipe piles. Firstly, strain is tested by certain method at certain section or level of the pile shaft under the joint action of pile head load, shaft and base resistance, and secondly, the axial force is calculated based on functions relating axial force to strain16,17,18. In engineering applications, difference of axial forces at two test sections or levels of the pile shaft can be used to calculate the frictional resistance acted by the soil on the pile shaft between the two test sections.

Common methods for strain test of piles

Currently gauges are generally installed in PHC pipe piles after the heat and steam curing process to test the strain. Three methods are often used to install the strain gauges: full length groove, hollow core infill and embedded steel I-beam19,20,21,22,23, which are depicted in Figs. 1, 2 and 3. The key procedures, major disadvantages, tested strain and function of axial force calculation of the methods are summarized and compared in Table 1.

Table 1 Three common methods of strain test for PHC pipe piles.
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Fig. 1
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Diagram of full length groove.

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Fig. 2
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Diagram of hollow core infill.

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Fig. 3
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Diagram of embedded steel I-beam.

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Function between axial force and strain

The function between axial force and strain, given in Technical Code for Testing of Building Foundation Piles (JGJ 106–2014), is as follows:

$${Q_i}=\overline {{{\varepsilon _i}}} * {E_i} * {A_i}$$
(1)

where Qi is the axial force at the ith section of the shaft, \(\overline {{{\varepsilon _i}}}\) is the average strain at the ith section of the shaft, Ei is the elastic modulus of material at the ith section of the shaft, and Ai is the cross sectional area at the ith section of the shaft.

Axial force at any section is calculated by Eq. (1) when the strain is tested by methods aforementioned. The function between axial force and strain as shown in Eq. (1) is simplified as linear elastic since the cross sectional area of the same type of PHC piles is fixed with fixed diameter and wall thickness and the elastic modulus as given in Collection of Standard Drawings of Pipe Piles is fixed as well24. However, the relationship between axial force and strain is not standard linear elastic under axial compression even for members made of ordinary reinforced concrete15. For PHC pipe piles, the actual relationship between axial force and strain is more complicated and nonlinear due to the gradual relaxation of prestressed reinforcement under the action of axial compression25,26,27,28.

To conclude, the often used test methods of axial force of PHC pipe piles have disadvantages in the strain test step and insufficient accuracy in the force calculation step. In this paper, a new method is proposed for strain test and axial force calculation. Taking pipe pile PHC500AB-125 as an example, a nonlinear function is proposed.

A new method for strain test of piles

Slot-forming wood

A new method, namely the slot-forming wood method, is proposed for strain test of pipe piles. The process diagram of the method is depicted in Fig. 4. Slot-forming woods were designed and fabricated (Fig. 5). As shown in the figure, the principal part with dimensions of 22.5 cm by 3.7 cm by 4.5 cm is used to form a slot in the pile concrete for installation of strain gauges. The wooden cylinder (2), which is 0.8 cm in diameter and longer than the wall thickness of the pipe pile, is used to form a hole in the pile wall where the gauge cable can pass through. The wooden cylinder (3), 0.6 cm in diameter and 4 cm in length, is used to form a blind hole for installation of the gauge base. The slot-forming woods were installed on the reinforcement cage of the pipe pile. Four of them are installed at each test section symmetrically (Fig. 6). Concrete was then poured, and the pile was centrifugally vibrated and steam cured. The slot-forming woods were removed to form the slot for gauge installation when the piles were cured and cooled (Fig. 7). Strain gauges were installed in the slot (Fig. 8). For piles to be tested in situ, the gauge cables passed through the holes into the hollow core of the piles and came up to the pile head (Fig. 9). The slots were then filled with waterproof adhesive 703, and protective steel sheets were installed on the outside (Fig. 10).

Fig. 4
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Process diagram of the slot-forming wood method.

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Fig. 5
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The slot-forming wood (1: principal part; 2: big wooden cylinder; 3: small wooden cylinders).

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Fig. 6
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Slot-forming woods fixed on the outside of the reinforcement cage.

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Fig. 7
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The slot for installation of strain gauges after removal of the slot-forming wood.

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Fig. 8
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An installed strain gauge.

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Fig. 9
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Strain cables coming out of the hollow core at the pile head.

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Fig. 10
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External protection of the slot.

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Slots formed by this new method are small and standard due to the special slot forming process, which include embedding the slot forming woods in the PHC pipe piles and removing the woods after the process of heat and steam curing. Compared to the method of full length groove, this method minimizes the damage to pile concrete in a large area and moreover avoids the problem of stress redistribution as may be caused by grooving after curing. Strain of the pile concrete can be measured directly since the strain gauges are installed directly on the surface of the pile concrete. This is more accurate when compared to the other two methods, where strain of the infilled concrete is measured instead of the pile concrete in the method of hollow core infill and strain of the steel I-beam is measured instead of the pile concrete in the method of embedded steel I-beam.

Waterproof test

Waterproof reliability of the test points plays a key role in ensuring the survival rate and working stability of the strain gauges, most of which are placed below the groundwater level in the PHC pipe piles. Therefore laboratory test was conducted to verify the waterproof reliability of the slot-forming wood method. A test pile specimen was fabricated for the waterproof test. Four slots were formed in the specimen and strain gauges were installed in the slots and waterproofed as aforementioned. The specimen was soaked in water for 45 consecutive days, during which the working resistance of the gauges was measured to determine whether they were affected by water. The total resistance of the gauge circuit is about 170 ohms with a deviation less than 5 ohms. If affected by water, the gauge will be short-circuited, resulting in a significant decrease of the working resistance to less than 20 ohms. The total resistance of the gauge circuit was around 170 ohms in the 45 consecutive days of soaking and resistance monitoring, indicating that the waterproof measures of the gauges installed by the slot-forming wood method were reliable and could be used in conditions with ground water.

Test of relationship between axial force and strain

A laboratory test was performed on pipe pile PHC500AB-125 to reveal the relationship between axial force and strain and to establish an accurate function for axial force calculation based on tested strains.

Test process

The loading apparatus and specimens

Axial compression tests were conducted for the pipe pile specimens. A loading apparatus YE-5000 F was used to apply incremental load. The slot-forming wood method was applied to form 4 test slots, which were evenly and symmetrically distributed along the circumferential surface at each test section of the PHC500AB-125 pipe pile. The pile was cut after heat and steam curing to make 6 specimens (Fig. 11), the parameters of which are shown in Table 2. Intelligent vibrating wire strain gauges JMZX-212HAT were installed at the test slots located at the middle of the specimens. Perpendicularity and flatness were strictly controlled to meet the test requirements when the specimens were cut. Four satisfactory specimens were lifted to the load test table one by one with a hoist to test the relationship between axial force and strain (Fig. 12).

Fig. 11
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Specimens for laboratory test.

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Fig. 12
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Installation of a specimen in laboratory test.

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Table 2 Parameters of specimens of PHC pipe piles for laboratory test.
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Loading scheme

An incremental loading scheme, with an increment of 100kN, was used in the laboratory test. Each load increment was maintained for at least 15 min before the next increment was applied, during which the strain was recorded many times. The maximum load was 1.2 times of the designed allowable bearing capacity that could be applied axially on the pile.

Data collection

Data from the intelligent vibrating wire strain gauges JMZX-212HAT were collected by a data collector JMBVC-1140 (Fig. 13) and recorded by a corresponding software (Fig. 14). The strains were recorded at an interval of 1 min when each load increment was stably maintained.

Fig. 13
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Data collector JMBVC-1140.

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Fig. 14
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Interface of software for data collection.

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Analysis of the test results

Test curves

The strains of four test points at each section were averaged to draw the curves between axial force and strain for the specimens in laboratory test as shown in Fig. 15, and the strains of all specimens were averaged to draw the curve for a typical pipe pile PHC500AB-125 as shown in Fig. 16. As the specimens were axially compressed, the relationship curve between load and strain is equivalent to the relationship curve between axial force and strain.

Fig. 15
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Relationship curves between axial load and strain for the specimens.

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Fig. 16
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Relationship curve between load and strain for the test pile.

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Establishment of the function between axial force and strain

The relationship between the axial force and strain of PHC pipe piles is not linear elastic as indicated by the laboratory test. The vertical and horizontal axes as shown in Fig. 16 were interchanged to establish a function between axial force and strain for convenient application. Quadratic polynomial fitting was used to establish the function for pile PHC500AB-125. Both the test curve and fitted curve of relationship between axial force and strain for pipe pile PHC500AB-125 are plotted in Fig. 17.

Fig. 17
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Fitted curve of relationship between axial force and strain for the test pile.

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The fitted nonlinear function between axial force and strain for pipe pile PHC500AB-125 is shown in Eq. (2):

$$y={\text{98}}{\text{0.129}}+{\text{7}}{\text{0.273}}x{\text{-0}}{\text{0.00273}}{x^2}$$
(2)

where y is the axial force at the test section of the pile shaft in kN, and x is the average axial strain at the test section of the pile shaft in µε.

Engineering application test

Engineering application test was performed on basis of the strain test method of slot-forming wood and new function between axial force and strain. Objectives of the test include: testing the shaft resistance and ultimate bearing capacity of a single PHC pipe pile, verifying the engineering applicability of the new strain test method, comparing the calculation results between the fitted nonlinear function and the approximate linear equation, analyzing the change of shaft and base resistance of pipe piles before and after grouting, and exploring the characteristics of bearing capacities of pipe piles.

Test conditions

The test site was investigated in detail with a borehole drilled at each pile ___location to accurately design the length of the test pile and to control the depth of pile installation. The ground conditions of the test site are shown in Table 3.

Soil layers from top down are listed as follows: the first layer is mixed backfill, loose, with an average thickness of 1.5 m; the second layer is silty clay, mainly hard plastic, with an average thickness of 3.9 m; the third layer is silt, mainly medium dense, with an average thickness of 3.3 m; the fourth layer is fine sand, loose, with an average thickness of 2.8 m; and the fifth layer is gravel, medium dense, with an average thickness more than 25 m. The standard values of ultimate shaft and base resistance as shown in Table 3 are parameters determined by geological investigation and tests, which are reference values for selection of pile type and preliminary design of piles.

Table 3 Ground parameters of the test site.
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Seven PHC500AB-125 test piles, the length of which are presented in Table 4, were designed and fabricated based on the above mentioned ground conditions of the test site. Except length, these piles have the same properties as the pile specimens used in laboratory test, which are shown in Table 2. The upper section of strain test is located at 1.5 m to the pile head of each test pile, and the lower section is located at 1.5 m to the pile base. Four test points were placed evenly along the circumference of the pile at each section where the intelligent JMZX-212HAT vibrating wire strain gauges were installed by the slot-forming wood method. Fabrication of piles for field test and pile installation are shown in Figs. 18 and 19 respectively.

Fig. 18
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Installation of gauges on piles for field test.

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Fig. 19
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Jacking of the field test pile.

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Field test

The test piles were installed with a grip type hydraulic pile jacking machine while the jacking force, load maintaining time and jacking cycles were in accordance with JGJ/T406-2017, Technical Standard for Prestressed Concrete Pipe Pile. The test piles were jacked into the gravel layer for a depth between 1 and 3 times of the pile diameter29. Length of the test piles, actual depth of the piles jacked into the gravel layer and the test scenarios are shown in Table 4. Compressive static load tests were conducted for test piles WZ01 to WZ03, which were not grouted. Test piles WZ04 to WZ07 were grouted with cement grout at the pile base after pile jacking. Compressive static load tests were conducted after a curing time of 15 days.

The slow method of compressive static load test was applied for all test piles. The maximum load of test was estimated based on the geological exploration data and the current technical standards in China30,31. The maximum test load for piles without grouting was estimated to be 5280kN, which was divided into 11 equal load increments. As grouting was expected to increase the ultimate bearing capacity of the test piles, the maximum test load for piles with grouting was estimated to be 6240kN, which was divided into 13 equal load increments. During the test, settlements at the pile head as well as strains at the upper and lower test points were read and recorded many times in accordance with the technical standards when each load increment was maintained.

Table 4 Parameters of the field test piles and the test scenarios.
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Test results

All of the 56 strain gauges installed by the slot-forming wood method worked normally in field test with a survival rate of 100%. The strains at 4 test points of each section of the test pile were averaged to calculate the axial force at each section based on the nonlinear function established in laboratory test aforementioned. The difference of axial force between the upper and lower section was then calculated, which would be the shaft resistance between the upper and lower section.

The relationship curves between the load and axial force for test piles WZ01 to WZ03 are shown in Fig. 20a,c respectively, and the relationship curves for test piles WZ04 to WZ07 are shown in Fig. 20d,g respectively. The same pattern could be found among the curves for all test piles. The axial forces at both the upper and lower test section increase with the load. The difference of axial forces between the upper and lower test section increases with the increase of load at a large rate for the first several load increments. With the subsequent increase of load, however, the change in difference of axial forces slows down. The difference in axial forces decreases after the peak difference which appears at a certain load increment in the middle. The peak difference of axial forces is the ultimate shaft resistance between the test sections of the pile.

Fig. 20
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Relationship curves between axial load and axial force.

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The shaft resistance and ultimate bearing capacity of the field test piles are shown in Table 5.

Table 5 Test and analysis result of the field test piles.
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The results in Table 5 indicate that the base resistance of pipe piles, with or without grouting, is the major part of bearing capacity, although the shaft resistance can not be ignored. Grouting is an effective measure to improve the bearing capacity of pipe piles.

Comparison of calculation result of the nonlinear function and the traditional linear function

Both the fitted nonlinear function proposed by this paper and the traditional linear equation were applied to calculate the ultimate shaft resistance based on the strains where the differences of axial force between the upper and lower test sections are maximum. The result is compared in Table 6 and the difference is shown for each pile. The ultimate shaft resistances of all test piles calculated by the nonlinear function are less than that calculated by the traditional linear equation. The average difference is 130.2kN or 8.37% in percentage.

Table 6 Comparison of the calculation results.
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Conclusion

A new method is proposed for strain test and axial force calculation of PHC pipe piles which must be cured in heat and steam. Laboratory and engineering application tests were performed by taking pipe piles PHC500AB-125 as an example. The major findings are as follows:

  1. (1)

    A new method, the slot-forming wood method, was proposed for installation of strain gauges. The method minimizes the impact of stress redistribution and possible damage to the pile concrete as may be caused by the full length groove method. It also minimizes the impact to the stiffness of the pile shaft when compared with methods such as hollow core infill and embedded steel I-beam. As a result, the accuracy of strain test is improved.

  2. (2)

    Corresponding to the slot-forming wood method, a nonlinear function between axial force and strain was established based on laboratory test. The accuracy of axial force calculation is improved by this function since the impact of relaxation of prestressed reinforcements due to the compression of pile shaft is accounted for.

  3. (3)

    The new methods are applicable and useful as indicated by the engineering application test. The survival rate was 100% for the strain gauges installed at 56 test points of the field test piles. The ultimate shaft resistances of all test piles calculated by the fitted function are less than that calculated by the conventional linear equation with an average difference of 8.37%.

  4. (4)

    Quadratic polynomial functions can be used to present the relationships between axial force and strain for all types of heat and steam cured PHC pipe piles since they have fixed size of cross sections. The coefficients of the functions can be determined by specific tests of the pile type in practical applications.