Design method, design device, and program

Abstract

To provide a design method for an expanded bottom portion that can prevent destruction of an unreinforced protruding part due to tensile stress.SOLUTION: A design method according to the present invention is for designing an enlarged bottom portion of a reinforced concrete pile to be installed in the ground. The enlarged bottom portion has a flared inclined portion and a rising portion continuing downward from a lower end of the inclined portion. An unreinforced protruding portion outside a reinforced cage of the enlarged bottom portion is unreinforced. In this design method, after setting an external force of the pile, an enlarged diameter of the enlarged bottom portion or an inclination angle of the inclined portion, a height of the rising portion, and a design standard strength of concrete are determined so that tensile stress of the unreinforced protruding portion obtained as a result of stress analysis of the enlarged bottom portion against the external force is equal to or smaller than an allowable tensile stress of the concrete.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a pile design method and the like. [Background technology]

[0002] The cast-in-place concrete flared pile method involves pouring concrete into a borehole formed in the ground to form a pile with a flared bottom.

[0003] FIG. 8 is a diagram showing the expanded bottom portion 12 of a pile 100 (hereinafter referred to as the expanded bottom portion). The conventional approach to designing the expanded bottom portion 12 is to assume that the vertical force (ground bearing capacity) acting from the ground on the protruding portion 22 of the expanded bottom portion 12 is borne by the shear force of the cylindrical surface of the shaft portion 21 of the expanded bottom portion 12, and to determine the shape of the expanded bottom portion 12 so that the shear stress intensity generated on the cylindrical surface falls within the allowable shear stress intensity of concrete (Non-Patent Document 1, etc.). The shaft portion 21 of the expanded bottom portion 12 is a portion with the same diameter as the shaft portion 11 of the pile 100, and the protruding portion 22 of the expanded bottom portion 12 is a portion that protrudes laterally from the shaft portion 21. The shaft portion 11 of the pile 100 is a portion of approximately the same diameter above the expanded bottom portion 12.

[0004] It is also known that when the above-mentioned vertical force acts, circumferential and radial tensile stresses are generated at the bottom surface of the expanded portion 12, and that these tensile stresses cause the bottom surface to undergo tensile failure under a load smaller than the ultimate bearing capacity of the ground (Non-patent documents 2, 3, etc.). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Fumio Kuwahara: Recent trends and issues of cast-in-place concrete enlarged piles, Foundation Works, Vol.37, No.8, pp.2-7, August 2009 [Non-Patent Document 2] Masahiro Yamazaki et al.: Analysis of the effect of the tip construction shape on the strength of enlarged cast-in-place concrete piles, Journal of Structural Engineering, Architectural Institute of Japan, No. 470, pp. 95-103, April 1995. [Non-Patent Document 3] Haruyuki Yamamoto et al.: Model Experiments on the Effects of Overburden Pressure and Tip Shape on the Tip Bearing Capacity of Pile, Journal of Structural Engineering, Architectural Institute of Japan, Vol. 49B, pp. 157-162, March 2003 Summary of the Invention [Problem to be solved by the invention]

[0006] Non-Patent Documents 2 and 3 disclose that in order to prevent the above-mentioned destruction due to tensile stress, the entire bottom surface of the expanded bottom portion 12 is designed to have a convex shape such as a pyramid shape. However, with conventional construction machines, it is difficult to form the expanded bottom portion 12 with the entire bottom surface having a convex shape, and there was a problem in terms of feasibility.

[0007] The present invention has been made in consideration of the above problems, and aims to provide a design method for an expanded bottom portion that can prevent destruction due to tensile stress. [Means for solving the problem]

[0008] The first invention for solving the above-mentioned problems is a design method for designing an expansion portion of a reinforced concrete pile to be installed in the ground, the expansion portion having a flared inclined portion and a rising portion that continues downward from the lower end of the inclined portion, and the unreinforced protruding portion outside the reinforced cage of the expansion portion is unreinforced, the design method comprising: a step (a) of setting an external force on the pile; and a step (b) of determining the maximum diameter of the expansion portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of stress analysis of the expansion portion against the external force is equal to or less than the allowable tensile stress of the concrete.

[0009] In the design method of the present invention, the maximum diameter of the expanded base, the inclination angle of the inclined portion, and the height of the rising portion are determined so that the tensile stress of the unreinforced protruding portion outside the reinforced cage does not exceed the allowable tensile stress of concrete for a given external force. This makes it possible to design an expanded base that can prevent the destruction of the unreinforced protruding portion due to tensile stress without making the bottom surface of the expanded base a special shape, contributing to ensuring the quality and safety of the pile. In particular, the height of the rising portion is an aspect that was not emphasized in conventional design methods, but in the present invention, by appropriately determining the height of the rising portion, it is possible to effectively prevent the destruction of the unreinforced protruding portion due to tensile stress.

[0010] In step (b), it is desirable to determine the maximum diameter of the expanded portion or the inclination angle of the inclined portion, the height of the raised portion, and the design standard strength of the concrete to determine whether the tensile stress is below the allowable tensile stress of the concrete, and to repeat the determination by changing the height of the raised portion until the tensile stress is below the allowable tensile stress of the concrete. In the present invention, by repeatedly determining the tensile stress intensity while changing the height of the rising portion as described above, an appropriate height of the rising portion can be obtained.

[0011] It is also desirable to use a chart showing the relationship between the maximum diameter of the expanded bottom portion or the inclination angle of the inclined portion, and the height of the raised portion, and the tensile stress intensity, as the stress analysis results. By using the above chart as the stress analysis result, the feasibility of the bottom expansion can be easily determined without performing a separate stress analysis.

[0012] The second invention is a design device for designing the expansion of a reinforced concrete pile to be installed in the ground, the expansion having a flared inclined portion and a rising portion that continues downward from the lower end of the inclined portion, and the unreinforced protruding portion outside the reinforced cage of the expansion is unreinforced, the design device being characterized by executing a step (a) of accepting the setting of an external force on the pile, and a step (b) of determining the maximum diameter of the expansion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of stress analysis of the expansion against the external force is equal to or less than the allowable tensile stress of the concrete. A second invention is a design apparatus for executing the design method of the first invention.

[0013] The third invention is a program for causing a computer to function as a design device for designing an expanded portion of a reinforced concrete pile to be installed in the ground, the expanded portion having a flared inclined portion and a rising portion that continues downward from the lower end of the inclined portion, and the unreinforced protruding portion outside the reinforced cage of the expanded portion is unreinforced, the program for causing a computer to function as a design device that executes the steps of (a) accepting the setting of an external force on the pile, and (b) determining the maximum diameter of the expanded portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of stress analysis of the expanded portion against the external force is equal to or less than the allowable tensile stress of the concrete. A third invention is a program for causing a computer to function as the design device of the second invention. Effect of the Invention

[0014] The present invention makes it possible to provide a design method for an expanded bottom portion that can prevent destruction of the unreinforced protruding portion due to tensile stress. [Brief description of the drawings]

[0015] [Figure 1] A diagram showing the expanded base portion 12 of the pile 1. [Diagram 2] FIG. 2 is a block diagram showing the configuration of a design apparatus 3. [Diagram 3] 4 is a flowchart showing a method for designing the expanded bottom portion 12. [Figure 4] A diagram showing the relationship between the enlarged base diameter R or inclination angle α, the height of the rising portion 122, and the tensile stress of the unreinforced protruding portion 23. [Diagram 5] An example of an analytical model used in stress analysis. [Figure 6] A diagram showing a chart. [Figure 7] 4 is a flowchart showing a method for designing the expanded bottom portion 12. [Figure 8] A diagram showing the expanded portion 12 of the pile 100. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the drawings.

[0017] [First embodiment] (1.Pile 1) 1 is a diagram showing an expanded base portion 12 of a pile 1 that is the design target of a design method according to an embodiment of the present invention. The pile 1 is made of reinforced concrete and is formed by pouring concrete into an excavated hole in the ground using a cast-in-place concrete expanded base pile construction method.

[0018] The expanded bottom portion 12 is a portion that is wider in diameter laterally than the shaft portion 11 of the pile 1, and is provided at the bottom of the pile 1. The expanded bottom portion 12 has a flared inclined portion 121 and a rising portion 122 that continues downward from the lower end of the inclined portion 121. The shaft portion 11 of the pile 1 is a portion of approximately the same diameter above the expanded bottom portion 12.

[0019] While the shaft portion 11 and the expanded base portion 12 are classifications of the height-wise range of the pile 1, in the explanation of this embodiment, the terms shaft portion 21 and unreinforced protruding portion 23 are used to classify the radial range of the pile 1 (particularly the expanded base portion 12). The shaft portion 21 has the same diameter as the shaft portion 11, and the reinforcing cage 2 is embedded in it. The unreinforced protruding portion 23 is a portion that protrudes outward beyond the reinforcing cage 2, and is the above-mentioned protruding portion 22 (see Figure 8) plus the portion of the shaft portion 21 outside the reinforcing cage 2. The unreinforced protruding portion 23 is an unreinforced portion where the concrete is not restrained by the reinforcing cage 2.

[0020] In this embodiment, the shape, etc. of the expanded base portion 12 are designed so that the tensile stress generated in the unreinforced protruding portion 23 of the expanded base portion 12 in response to the vertical force (ground bearing force) A applied from the ground to the bottom surface of the expanded base portion 12 does not exceed the allowable tensile stress of the concrete of the pile 1.

[0021] (2.Design device 3) Fig. 2 is a block diagram showing the configuration of a design device 3 that executes the design method of this embodiment. As shown in Fig. 2, the design device 3 can be realized by a computer configured by connecting a control unit 31, a storage unit 32, an input unit 33, a communication unit 34, a display unit 35, etc. via a bus or the like. However, the design device 3 is not limited to this and can have various appropriate configurations.

[0022] The control unit 31 is composed of a CPU, a ROM, a RAM, etc. The CPU loads programs related to the processing of the design device 3 stored in storage media such as the storage unit 32 and the ROM into a work area on the RAM and executes them. The ROM is a non-volatile memory, and permanently stores programs such as the boot program and BIOS, data, etc. The RAM is a volatile memory, and temporarily stores programs and data loaded from the storage unit 32, the ROM, etc., and also has a work area that the control unit 31 uses to perform various processes.

[0023] The storage unit 32 is a hard disk drive, a solid state drive, a flash memory, or the like, and stores programs executed by the design device 3 during processing described below, data necessary for executing the programs, an OS, etc. These programs and data are read and executed by the control unit 31 as necessary.

[0024] The input unit 33 inputs various settings to the design device 3 . The communication unit 34 is a communication interface that mediates wireless communication and performs communication with various devices. The display unit 35 includes a liquid crystal display or the like, and displays various screens related to the processing of the design device 3.

[0025] (3. Design method of the expanded bottom portion 12) 3 is a flowchart showing the process (the design method of the expanded bottom portion 12) executed by the design device 3. Steps S1 to S6 in FIG.

[0026] In this embodiment, a designer operates the design device 3 and first sets the limit value (ultimate bearing capacity) of the vertical force A applied from the ground to the expanded base portion 12 as the external force of the pile 1. The design device 3 accepts the setting of the external force (S1).

[0027] Next, the designer operates the design device 3 to set the expanded-bottom diameter R (see FIG. 1) of the expanded-bottom portion 12 or the inclination angle α (see FIG. 1) of the inclined portion 121. The design device 3 accepts the setting of the expanded-bottom diameter R or the inclination angle α (S2). The expanded-bottom diameter R is the maximum diameter of the expanded-bottom portion 12, and corresponds to the diameter of the expanded-bottom portion 12 at the lower end of the inclined portion 121.

[0028] The expanded bottom portion 12 in this embodiment is formed by excavating the ground laterally using a bottom expanding bucket (not shown), and the specifications of the bottom expanding bucket dictate that the larger the inclination angle α, the larger the expanded bottom diameter R. Therefore, the shape of the inclined portion 121 of the bottom expanding portion 12 can be specified by either the expanded bottom diameter R or the inclination angle α. However, if the above-mentioned relationship does not exist for the bottom expanding portion 12, the expanded bottom diameter R and the inclination angle α can also be set individually.

[0029] The designer also operates the design device 3 to set the standard design strength of the concrete of the pile 1. The design device 3 receives the setting of the standard design strength (S3).

[0030] Next, the designer operates the design device 3 to provisionally set (provisionally set) the height of the rising portion 122 of the expanded bottom portion 12. The design device 3 accepts the provisional setting of the height of the rising portion 122 (S4).

[0031] The design device 3 then uses the external force of the pile 1, the expanded base diameter R or the inclination angle α, and the height of the rising portion 122 set in S1, S2, and S4 to perform a stress analysis of the expanded base portion 12 when an external force acts on the bottom surface of the expanded base portion 12 (S5). This calculates the tensile stress at each point on the expanded base portion 12. The stress analysis can use the finite element method described later in Fig. 5, etc., but is not limited to this.

[0032] Fig. 4 is a graph showing the tensile stress (maximum value of tensile stress) generated in unreinforced protruding portion 23 of expanded bottom portion 12 when a predetermined external force (vertical force A) is applied to the bottom surface of expanded bottom portion 12. As shown in Fig. 4, the tensile stress generated in unreinforced protruding portion 23 varies not only with expanded bottom diameter R or inclination angle α but also with heights h1 to h3 (h1>h2>h3) of rising portion 122, and it can be seen that appropriately determining rising portion 122 is important in suppressing the tensile stress in unreinforced protruding portion 23.

[0033] The design device 3 compares the allowable tensile stress obtained from the design standard strength of the concrete set in S3 (see, for example, Construction Ministry Notification No. 1450 of 2000) with the stress analysis results of S5, and determines whether or not a tensile stress that exceeds the allowable tensile stress of the concrete is occurring in the unreinforced protruding portion 23 of the enlarged base portion 12 (S6).

[0034] If the design device 3 finds that there is no point in the unreinforced protruding portion 23 of the expanded portion 12 where tensile stress exceeding the allowable tensile stress is occurring (S6; No), it approves the specifications of the expanded portion 12 and determines the specifications of the expanded portion 12 (the expanded portion diameter R or inclination angle α set in S2, the height of the rising portion 122 set in S4, and the design standard strength of the concrete set in S3) (S7), and ends the processing by displaying this fact on the display unit 35, etc.

[0035] On the other hand, if the design device 3 finds that there is a location in the unreinforced protruding portion 23 of the expanded bottom portion 12 where tensile stress exceeding the allowable tensile stress is occurring (S6; Yes), it rejects the specifications of the expanded bottom portion 12 and returns to S4 to accept the resetting of the height of the raised portion 122.

[0036] The designer repeats steps S4 to S6 by changing the height of the rising portion 122 until there are no more locations in the unreinforced protruding portion 23 of the expanded bottom portion 12 where tensile stress exceeding the allowable tensile stress occurs. This allows the height of the rising portion 122 of the expanded bottom portion 12 to be set to an appropriate value.

[0037] As explained above, in the design method of this embodiment, the expansion radius R, the inclination angle α of the inclined portion 121, and the height of the rising portion 122 are determined so that the tensile stress of the unreinforced protruding portion 23 does not exceed the allowable tensile stress of concrete against a specified external force. This makes it possible to design the expansion portion 12 that can prevent the destruction of the unreinforced protruding portion 23 due to tensile stress without giving the bottom surface of the expansion portion 12 a special shape, contributing to ensuring the quality and safety of the pile 1.

[0038] In addition, in this embodiment, by repeatedly changing the height of the rising portion 122 and determining the tensile stress level as described above, it is possible to obtain an appropriate height for the rising portion 122. The height of the rising portion 122 is an aspect that has not been emphasized in conventional design methods, but in this embodiment, by appropriately determining the height of the rising portion 122, it is possible to suitably prevent destruction of the unreinforced protruding portion 23 due to tensile stress.

[0039] However, the present invention is not limited to the above embodiment. For example, in this embodiment, the height of the rising portion 122 is provisionally set, and the height of the rising portion 122 is changed according to the judgment result in S6, but the above-mentioned expanded diameter R or inclination angle α may be provisionally set, and the expanded diameter R or inclination angle α may be changed according to the judgment result in S6. Furthermore, the design standard strength of the concrete may be provisionally set, and the design standard strength of the concrete may be changed according to the judgment result in S6.

[0040] In this way, in this embodiment, one of the design elements, the expansion diameter R or inclination angle α, the height of the rising portion 122, and the design standard strength of the concrete, is provisionally set (the other design elements are set to one value), and the provisionally set value is changed depending on the judgment result in S6, and the value can be set so that the tensile stress of the unreinforced protruding portion 23 falls within the allowable tensile stress of the concrete.

[0041] In this embodiment, the external force on the pile is set to a vertical force A applied from the ground to the expanded bottom portion 12, but it is also possible to simulate the ground below the expanded bottom portion 12 using a spring or the like and set a force applied to the head of the pile as the external force on the pile.

[0042] In the above embodiment, stress analysis of the pile 1 was performed using a computer (design device 3) to calculate the tensile stress of the unreinforced protruding portion 23, and this was compared with the allowable tensile stress of the concrete. However, stress analysis may be performed in advance for external forces of various magnitudes while changing the values ​​of the expansion diameter R or inclination angle α, and the height of the rising portion 122, and the results of the stress analysis may be compiled in a chart and used to determine the tensile stress.

[0043] A design method using a chart will be described below as a second embodiment. The second embodiment will be described mainly in terms of differences from the first embodiment, and a description of similarities will be omitted.

[0044] [Second embodiment] (1. Preliminary stress analysis) Fig. 5 shows an example of an analytical model used in the above-mentioned preliminary stress analysis. In this analytical model, the shaft 11 and the enlarged base 12 of the pile 1 are modeled using finite elements 10.

[0045] The diameter of the shaft portion 21 of the analysis model is determined in advance, and the number and division method of the finite elements 10 are set appropriately depending on the shape of the pile 1 and the analysis environment. As boundary conditions, the contact point 101 at the center of the pile head is a pin, and the other contact points 102 are horizontal rollers, and as an external force, a vertical force A equivalent to the ultimate bearing capacity is applied vertically upward to all nodes on the bottom surface of the expanded base portion 12. As physical properties of concrete, the Young's modulus and Poisson's ratio of concrete are determined, and under these analysis conditions, multiple values ​​for the expanded base diameter R or inclination angle α, and the height of the rising portion 122 are determined, and the tensile stress generated in the expanded base portion 12 is obtained by finite element analysis.

[0046] However, the boundary conditions and physical properties of the analysis model are not limited to the above, and are set in various ways depending on the pile 1 to be constructed. In addition, the enlarged base diameter R or the inclination angle α, and the height of the rising portion 122 can be set in multiple values, for example, at 300 mm intervals for the enlarged base diameter R and at 500 mm intervals for the height of the rising portion 122, but are not limited to this.

[0047] The results of stress analysis using the finite element method are organized as a chart as shown in Figure 6. The chart in Figure 6 plots analysis results 103 of the tensile stress (maximum tensile stress) generated in the unreinforced protruding portion 23 for each value of the enlarged base diameter R or inclination angle α, and for each height of the rising portion 122, and further obtains an approximation curve 104 for multiple analysis results 103 with the same value for the height of the rising portion 122. The chart is created for multiple external forces (vertical force A).

[0048] (2. Design method of the expanded bottom portion 12) Fig. 7 is a flow chart showing a method for designing the expanded bottom portion 12 using the above chart. In this embodiment, the designer first sets the ultimate value (ultimate bearing capacity) of the vertical force A applied from the ground to the expanded bottom portion 12 as an external force (S11). The designer also sets the design standard strength of the concrete in the expanded bottom portion 12 (S12).

[0049] Next, the designer provisionally sets the aforementioned expanded base diameter R or inclination angle α, and the height of the rising portion 122 (S13).

[0050] Then, as a result of the stress analysis of the expanded portion 12 based on the provisionally set expanded diameter R or inclination angle α, and the height of the rising portion 122, the designer calculates the tensile stress generated in the unreinforced protruding portion 23 using a chart corresponding to the external force set in S11 (S14).

[0051] For example, symbol B in Figure 6 is a case in which the base diameter R is set as shown by symbol R1 and the height of the rising portion 122 is set to h3, and the value of the tensile stress in this case can be obtained from the chart as shown by symbol P1.

[0052] Then, the designer compares the tensile stress determined in S14 with the allowable tensile stress of the concrete determined from the design standard strength set in S12, and determines (judges) whether or not a tensile stress exceeding the allowable tensile stress has occurred in the unreinforced protruding portion 23 of the expanded portion 12 (S15).

[0053] If there is no tensile stress exceeding the allowable tensile stress in the unreinforced protruding portion 23 of the expanded portion 12 (S15; No), the designer determines that the specifications of the expanded portion 12 are acceptable, and determines the specifications of the expanded portion 12 (the expanded diameter R or slope angle α and the height of the rising portion 122 set in S13, and the design standard strength of the concrete set in S12) (S16), and completes the design.

[0054] On the other hand, if tensile stress exceeding the allowable tensile stress is occurring in the unreinforced protruding portion 23 of the expanded bottom portion 12 (S15; Yes), the designer rejects the specification of the expanded bottom portion 12 and returns to S13 to reset the values ​​of the expanded bottom diameter R or inclination angle α and the height of the raised portion 122.

[0055] For example, when the allowable tensile stress of concrete obtained from the design standard strength set in S12 is P2 in Fig. 6, the tensile stress P1 generated in the unreinforced protruding portion 23 in Case B exceeds the allowable tensile stress P2 of the concrete. Therefore, the designer increases the height of the rising portion 122 from h3 to h2 (h2>h3) so that the tensile stress P1' generated in the unreinforced protruding portion 23 in Case B' is equal to or less than the allowable tensile stress P2 of the concrete. Instead of changing the height of the rising portion 122, the value of the expanded base diameter R or the inclination angle α may be changed.

[0056] In the second embodiment described above, the same effect as in the first embodiment can be obtained by determining the base expansion diameter R, the inclination angle α of the inclined portion 121, and the height of the rising portion 122 so that the tensile stress of the unreinforced protruding portion 23 does not exceed the allowable tensile stress of concrete against a specified external force. Furthermore, in this embodiment, by using the above chart as the stress analysis result, the suitability of the base expansion portion 12 can be easily determined without carrying out a separate stress analysis.

[0057] In this embodiment, the expanded diameter R or the inclination angle α and the height of the rising portion 122 are provisionally set, and the values ​​of these design elements are changed depending on the judgment result in S15, but the expanded diameter R or the inclination angle α and the standard design strength of the concrete may be provisionally set (the height of the rising portion 122 is set to one value), and the expanded diameter R or the inclination angle α and the standard design strength of the concrete may be changed depending on the judgment result in S15. Furthermore, the height of the rising portion 122 and the standard design strength of the concrete may be provisionally set (the expanded diameter R or the inclination angle α is set to one value), and the height of the rising portion 122 and the standard design strength of the concrete may be changed depending on the judgment result in S15.

[0058] In this way, in this embodiment, two design elements of the expanded base diameter R or inclination angle α, the height of the raised portion 122, and the design standard strength of the concrete are provisionally set (the remaining design elements are set to one value), and the value of the provisionally set design element can be changed depending on the judgment result in S6, while the value of the design element can be determined so that the tensile stress of the unreinforced protruding portion 23 falls within the allowable tensile stress of the concrete.

[0059] In this embodiment, the procedure in FIG. 7 is executed by a designer, but it is also possible for the design device 3 to execute the procedure in FIG. 7 by accepting the settings of necessary values.

[0060] Although the preferred embodiment of the present invention has been described above with reference to the accompanying drawings, the present invention is not limited to the above examples. It is clear that a person skilled in the art can come up with various modified or altered examples within the scope of the technical ideas disclosed in this application, and it is understood that these also naturally belong to the technical scope of the present invention. [Explanation of symbols]

[0061] 1, 100: Pile 2: Reinforced concrete cage 3:Design equipment 11: Shaft 12: Enlarged base 21: Shaft part 22: Overhanging part 23: Unreinforced overhanging part 121: Inclined part 122: Rising part

Claims

1. A design method for designing an enlarged base portion of a reinforced concrete pile to be installed in the ground, comprising: The expanded bottom portion has a flared inclined portion and a rising portion continuing downward from the lower end of the inclined portion, and the unreinforced protruding portion on the outer side of the reinforced cage of the expanded bottom portion is unreinforced, Step (a) of setting an external force of the pile; Step (b) of determining the maximum diameter of the enlarged bottom portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of the stress analysis of the enlarged bottom portion against the external force is equal to or less than the allowable tensile stress of the concrete; A design method comprising the steps of:

2. In the step (b), Determine the maximum diameter of the enlarged bottom portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete to determine whether the tensile stress is equal to or less than the allowable tensile stress of the concrete; 2. The design method according to claim 1, wherein the height of the rising portion is changed and the judgment is repeated until the tensile stress becomes equal to or less than the allowable tensile stress of the concrete.

3. The design method according to claim 1, characterized in that a chart showing the relationship between the maximum diameter of the expanded portion or the inclination angle of the inclined portion, and the height of the raised portion, and the tensile stress intensity is used as the stress analysis result.

4. A design device for designing an enlarged base portion of a reinforced concrete pile to be installed in the ground, The expanded bottom portion has a flared inclined portion and a rising portion continuing downward from the lower end of the inclined portion, and the unreinforced protruding portion on the outer side of the reinforced cage of the expanded bottom portion is unreinforced, A step (a) of receiving a setting of an external force of the pile; Step (b) of determining the maximum diameter of the enlarged bottom portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of the stress analysis of the enlarged bottom portion against the external force is equal to or less than the allowable tensile stress of the concrete; A design apparatus comprising:

5. Computer, A program for functioning as a design device for designing an enlarged bottom portion of a reinforced concrete pile to be installed in the ground, The expanded bottom portion has a flared inclined portion and a rising portion continuing downward from the lower end of the inclined portion, and the unreinforced protruding portion on the outer side of the reinforced cage of the expanded bottom portion is unreinforced, A step (a) of receiving a setting of an external force of the pile; Step (b) of determining the maximum diameter of the enlarged bottom portion or the inclination angle of the inclined portion, the height of the rising portion, and the design standard strength of the concrete so that the tensile stress of the unreinforced protruding portion obtained as a result of the stress analysis of the enlarged bottom portion against the external force is equal to or less than the allowable tensile stress of the concrete; A program that functions as a design device to execute the above.

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