JP7447654B2 - Calculation method for pull-out resistance at the joints of knotted piles - Google Patents

Description

The present invention relates to a method for calculating the pull-out resistance at the joints of a cast-in-place concrete knotted pile.

BACKGROUND ART Conventionally, knotted piles have often been used as foundation piles to accommodate larger and higher-rise buildings, as they can ensure high vertical bearing capacity while suppressing increases in pile length. The knotted pile has an expanded bottom portion at the lower end of the shaft portion and one or more knot portions at the middle portion of the shaft portion in order to increase the vertical supporting force.

The knots provided in the knotted pile can bear not only the vertical support force but also the pull-out resistance force, but the pull-out resistance force that can be borne differs depending on the embedment length. Specifically, when a predetermined pulling force is applied to a knotted pile, if the knots are shallowly embedded, the knots resist the pulling force in the ground, but the knots do not penetrate into the ground. A fracture surface that reaches the ground surface is generated and the pull-out resistance is lost.

On the other hand, if the knot has sufficient penetration length, or if the entire knot is buried in a hard intermediate layer or support layer, the knot will continue to resist the pull-out force in the ground. , bear the pull-out resistance force over a long period of time.

For example, Patent Document 1 discloses a method for calculating the pull-out resistance of a multi-stage diameter-expanding pile formed by forming an enlarged-diameter portion on the shaft, assuming that the enlarged-diameter portion has a sufficiently deep penetration length. There is. Here, the pull-out resistance force is calculated by adding together the peripheral surface friction force of the enlarged diameter portion and the shaft portion and the pile's own weight.

When calculating the circumferential friction force of the enlarged diameter part, first, the diameter of the enlarged diameter part is taken as the diameter, and the effective height (range where the bearing pressure effect of the enlarged diameter part extends) is set to twice the diameter of the enlarged diameter part. Define the set vertical cylindrical slip surface. Next, the shear resistance force exerted on this sliding surface is calculated as the peripheral surface friction force, and the area of the vertical cylindrical sliding surface is multiplied by the ultimate peripheral surface friction force determined from the ground.

Japanese Patent Application Publication No. 2002-21070

As described above, Patent Document 1 is a method that can be applied when the enlarged diameter portion is sufficiently deeply embedded to the extent that the effective height of the vertical cylindrical sliding surface is contained in the ground. However, if the enlarged diameter part is not sufficiently embedded and the effective height does not fit within the ground, the pullout resistance of the enlarged diameter part cannot be calculated.

The present invention has been made in view of the above problem, and its main purpose is to prevent the joints from being shallowly embedded when a pull-out force is applied to a cast-in-place concrete knotted pile. To provide a method for calculating the pull-out resistance force at the joints of a knotted pile, which is capable of calculating the pull-out resistance force at the joints even when a cylindrical fracture surface occurs in the ground.

In order to achieve such an object, the method for calculating the pull-out resistance at the joint of a knotted pile of the present invention is to calculate the pull-out resistance of the joint in a knotted pile that includes a shaft and a joint provided on the shaft. The joint portion of a knotted pile in which the force is calculated based on the shear resistance force of a cylindrical fracture surface that reaches the ground surface from the joint portion generated in the ground, and the weight of the clod between the fracture surface and the shaft portion. A method for calculating a pull-out resistance force, wherein the target range for calculating the shear resistance force on the fracture surface is divided into a joint section adjacent to the joint section and a shaft section adjacent to the shaft section, It is characterized in that the earth pressure coefficient used when calculating the shear resistance force of the joint section is increased from the earth pressure coefficient used when calculating the shear resistance force of the shaft section.

According to the method of calculating the pull-out resistance force at the joints of a knotted pile of the present invention, when pulling out a knotted pile, the penetration length is such that a cylindrical fracture surface reaching the ground surface from the joints occurs in the ground. The pull-out resistance of shallow joints can be calculated with high accuracy. Therefore, it becomes possible to reflect the pull-out resistance force of a joint with a shallow penetration length, which has not been considered in the design in the past, in the same way as the vertical support force of the joint.

Further, when the knot is provided for the purpose of resisting the pull-out force acting on the knotted pile, it is also possible to estimate the penetration length according to the magnitude of the required pull-out resistance force. This makes it possible to set the penetration length of the knot to an appropriate depth, and to design a rational knotted pile that is both safe and economical.

According to the present invention, when a pullout force is applied to a knotted pile, even if the penetration length of the knot is shallow and a cylindrical fracture surface is generated in the ground from the knot to the ground surface, the knot It is possible to calculate the pull-out resistance force with high accuracy, making it possible to perform a rational design.

It is a figure showing an outline of a knotted pile in an embodiment of the present invention. It is a figure showing the detail of the joint part in embodiment of the present invention. FIG. 3 is a diagram showing the penetration length of a joint and the influence range of underground stress in an embodiment of the present invention. It is a figure which shows the state of the pull-out experiment using the model pile in embodiment of this invention. It is a graph which shows the relationship between the displacement of the pile head obtained from the pull-out experiment of the model pile in embodiment of this invention, and the earth pressure which acts on the upward truncated cone part of a node. It is a figure which shows the fracture surface which occurs when pulling out the knotted pile in embodiment of this invention. It is a figure which shows the division at the time of calculating a shearing resistance force in calculating the pull-out resistance force in embodiment of this invention. It is a graph showing the relationship between the displacement of the pile head and the difference in axial force above and below the joint (resistance of the joint) obtained from a pull-out experiment of a model pile in an embodiment of the present invention.

The present invention relates to knotted piles made of cast-in-place concrete, and calculates the pull-out resistance of the knots by the shear resistance of a cylindrical fracture surface that reaches the ground surface from the knots generated in the ground, and the shear resistance of the fracture surface and the shaft. This is a calculation method based on the weight of the soil between the two parts. The details will be explained below with reference to FIGS. 1 to 8.

As shown in FIG. 1, a knotted pile 1 that supports a building has a pile length that reaches a support layer G3, and includes a shaft portion 2, an enlarged bottom portion 3 provided at the lower end of the shaft portion 2, and a shaft portion 2. and a joint portion 4 provided at the intermediate portion of the.

As shown in FIG. 2, the joint portion 4 includes a cylindrical portion 41 having a larger diameter than the shaft portion 2, an upward truncated conical portion 42 located above the cylindrical portion 41, and a downward conical portion located below the cylindrical portion 41. It has a shape that combines the base portion 43.

In the joint portion 4 having such a shape, the downward truncated conical portion 43 is provided in an intermediate layer G2 such as a gravel layer as shown in FIG. 1, and when a pushing force is applied to the joint pile 1, This can be resisted by the enlarged bottom portion 3 and the knot portion 4. On the other hand, when a pull-out force is applied to the knotted pile 1, the mode differs depending on how the upward truncated conical portion 42 of the knotted portion 4 is buried in the ground.

For example, as shown in FIG. 1, when the upward truncated conical portion 42 of the knot 4 is provided on the surface layer G1, if the penetration length H of the knot 4 is sufficiently secured, the ground near the knot 4 At all times, the joints 4 resist pull-out forces in the ground without breaking.

When the penetration length H of the joint 4 is sufficiently secured, as shown in FIG. , refers to the case where the influence range A of underground stress falls within the ground. Note that the range A of influence of underground stress refers to the range in which the bearing effect is exerted when the upward truncated conical portion 42 presses the ground.

On the other hand, if the penetration length H of the knot 4 is not sufficient, that is, if the influence range A of the underground stress does not fit within the ground as shown in Fig. 3(b), the knot 4 will be pulled out in the ground. Although it resists the force, the ground eventually experiences destruction that reaches the surface, and the power to resist is lost. In other words, even if the joint portion 4 does not have a sufficient penetration length H, it bears the pulling resistance force until the ground breaks.

In calculating the pull-out resistance force borne by the joint 4 where the penetration length H is not sufficient, it is necessary to clarify what kind of fracture surface will occur in the ground around the joint 4, and to calculate the We decided to calculate the pull-out resistance using the following method.

≪Extraction experiment using model pile≫
As shown in FIGS. 4(a) to 4(c), a centrifugal force model experiment was carried out using a half-split model pile 1' to confirm the resistance mechanism of the joint 4' during pull-out. Dry Toyoura sand was used as the ground material, and a model ground G' with a predetermined relative density was created in a container.

On the other hand, with reference to FIG. 2, the dimensions of the model pile 1' were as follows: shaft diameter D0 = 48 mm, node diameter D = 68 mm, node protrusion width Dn = 10 mm, and upper inclination angle θn = 20°. In addition, on the model pile 1', an earth pressure gauge EG is installed at the joint 4', a strain gauge SG is installed at the shaft 2' located above and below the joint 4', and a displacement gauge DG is installed at the pile head. is installed.

The above model pile 1' penetrated into the model ground G' at three penetration lengths H (Case 1 to Case 3) as shown in FIGS. 4(a) to 4(c). Case 1 corresponds to a case where the penetration length H is set to 20Dn, and the penetration length H of the joint portion 4 is sufficient (comparative example). On the other hand, Case 2 and Case 3 correspond to the case where the penetration length H of the joint portion 4 is shallow; in Case 2, the penetration length H is set to 12Dn, and in Case 3, the penetration length H is set to 6Dn.

When a pulling force was applied to the model pile 1' having such a configuration, the displacement of the pile head and the upward truncated cone of the node 4' were determined from the measurement results of the displacement gauge DG and the soil pressure gauge EG, as shown in Fig. 5. The relationship between the earth pressure acting on 42 was obtained. Furthermore, FIGS. 6(a) to 6(c) are contours representing displacements in the surrounding ground of the model pile 1' for these Cases 1 to 3 through image analysis.

Looking at Case 1 in FIG. 6(a), in which the node 4' is fully rooted, it can be seen that no fracture surface reaching the ground surface has been generated. Looking at Figure 5, in Case 1, as the pile head displacement increases, the earth pressure also increases, and it appears that the model ground G' near the joint 4 is being pressed against the joint 4 without breaking. Recognize.

Looking at Case 2 in which the penetration of the node 4' is shallower than that of Case 1 in Fig. 6(b), a fracture surface Fs is created in the model ground G' near the node 4, where a cylindrical fractured soil mass is formed. I can see how it is. Also, looking at FIG. 5, in Case 2, when the pile head displacement exceeds about 3 mm, the joint 4' is pressed against the cylindrical fracture surface Fs in a range of about 0.1 Mpa, and when the pile head displacement exceeds about 3 mm, It can be assumed that the state of sliding along the surface is repeated.

Looking at Case 3 in Figure 6(c), where the penetration is the shallowest, it can be seen that a fracture surface Fs, in which a cone-shaped fractured soil mass is formed, has occurred in the model ground G' near the node 4'. . Moreover, looking at FIG. 5, similarly to Case 2, the joint portion 4' repeats a state in which it is pressed against the fracture surface Fs and a state in which it slides along the fracture surface Fs. However, the earth pressure is in the range of approximately 0 to 0.05 MPa, which shows that it is extremely small.

As can be seen from the above-mentioned pull-out experiment using the model pile 1', when the joint 4 provided on the jointed pile 1 has a shallow penetration length H, the fracture surface Fs generated in the ground forms a cone shape. It can be seen that there are cases where the surface has a cylindrical surface shape. Cone fracture, in which the fracture surface Fs has a cone shape, as shown in FIG. 6(c), is generally widely known, and various methods for calculating the pull-out resistance force have already been studied.

Therefore, in the case where the fracture surface Fs has a cylindrical shape when a pullout force is applied to the knotted pile 1, a method for calculating the pullout resistance force of the knotted portion 4 will be described below with reference to FIG. 7.

≪How to calculate the pull-out resistance force≫
As shown in FIG. 7, when a cylindrical fracture surface Fs occurs in the ground around the joint 4 (hereinafter referred to as cylindrical surface Fs) when the knotted pile 1 is pulled out, the joint resistance force Fr is as follows: It can be calculated using formula (1).

Fr=Wg+Rf・・・・・・・・・(1)
Wg: Weight of cylindrical soil just above the joint (kN)
Rf: Shear resistance force of cylindrical surface Fs (kN)

Here, the weight Wg of the cylindrical soil mass directly above the joint is the weight of the soil mass Vn surrounded by the cylindrical surface Fs and the shaft portion 2, and can be calculated using the following equation (2).

Wg=Vn×ρ・・・・・・・・・(2)
Vn: Volume obtained by rotating area ABCD by 360 degrees (m ³ )
ρ: Unit volume weight of soil (kN/m ³ )

Further, the shear resistance force Rf of the cylindrical surface Fs can be calculated using the following equation (3) based on the area of the cylindrical surface Fs and the shear strength of the soil. At this time, the shear resistance force Rf may be calculated using the total height (embedment length H) of the cylindrical surface Fs reaching the ground surface from the joint 4. However, in the present embodiment, the target range HA in which the shear resistance force Rf is considered in the cylindrical fracture surface Fr is set to the height defined based on the joint protrusion width Dn from the lower end of the cylindrical part 41 at the joint 4. The first feature lies in the settings.

The target range HA in which the above-mentioned shear resistance force Rf is considered is set to a size corresponding to a multiple of the joint protrusion width Dn, depending on the properties of the ground based on the results of experiments. For example, if the ground is sandy soil, the target range HA may be set to six times the joint protrusion width Dn.

In addition, this target range HA is divided into a joint section H ₂ adjacent to the joint 4 and a shaft section H ₁ adjacent to the shaft section 2 above the joint 4, and the shearing is performed for each section. The second feature is that the resistance forces are calculated and the sum thereof is used as the shear resistance force Rf of the joint portion 4.

Rf=(F1×Af1)+(F2×Af2)・・・・・・・・・(3)
Af1: Area of shaft section H ₁ on cylindrical surface Fs (m ² )
Af2: Area of node section H ₂ on cylindrical surface Fs (m ² )
F1: Shear strength of the ground in shaft section _H1 (kN/ ^m2 )
F2: Shear strength of the ground at node section _H2 (kN/ ^m2 )

The shear strength F1 of the ground in the shaft section _H1 and the shear strength F2 of the ground in the joint section _H2 can be calculated using the following equations (4) and (5). At this time, the third feature is that the shear strength F2 of the ground in the joint section _H2 uses an additional coefficient αf.

The extra coefficient αf takes into consideration that the ground in the joint section H ₂ adjacent to the joint 4 is pressed against the upward truncated conical part 42 when the jointed pile 1 is pulled out. Specifically, the earth pressure coefficient of the joint section H ₂ is obtained by multiplying the earth pressure coefficient of _the shaft section H ₁ (static earth pressure coefficient K ₀ ) by the additional coefficient αf. By increasing the load, the bearing pressure effect of the joints 4 is reflected in the shear strength F2 of the ground.

F1=C+K ₀ ×σv1'×tanφ (4)
F2=C+K ₀ ×αf×σv2'×tanφ (5)
C: Adhesive force of soil (kN/ ^m2 )
K ₀ : Static earth pressure coefficient
σv1': Average effective overload pressure of shaft section _H1 (kN/ ^m2 )
φ: Soil shear resistance angle (internal friction angle) (°)
σv2': Average effective overload pressure in the joint section _H2 (kN/ ^m2 )
αf: Additional coefficient

In setting the additional coefficient αf, K ₀ A value between the two coefficients should be taken, and preferably the average value of both coefficients should be used. For example, if the ground is sandy soil and the shear resistance angle (internal friction angle) φ' is 40°, the static earth pressure coefficient K ₀ is 0.35 and the passive earth pressure coefficient K _p =4.6. Therefore, from the average of these, an additional coefficient αf=7.1, which is K ₀ ×αf, is adopted.

The static earth pressure coefficient K ₀ is calculated using the well-known Yerkey equation (K ₀ =1-sinφ'), and the passive earth pressure coefficient K _p is calculated using the known Rankine earth pressure equation (K _p =tan2(45°+φ) Calculated using '/2)). Further, the additional coefficient αf differs depending on the ground conditions. Therefore, by adopting the shear resistance angle (internal friction angle) φ' corresponding to the ground, calculating the static earth pressure coefficient K ₀ and the passive earth pressure coefficient K _p , and setting the optimal additional coefficient αf from these results. good.

Further, the average effective overload pressure σv1' of the shaft section _H1 and the average effective overload pressure σv2' of the joint section _H2 can be calculated using the following equations (6) and (7).
σv1'=ρ×(H0+H ₁ /2)・・・・・・・・・・・・・・・(6)
σv2'=ρ×(H0+H ₁ +H ₁ /2)・・・・・・・・・・・・(7)
H0: Difference between penetration length H and target area HA (m)

≪Verification of calculation formula for pull-out resistance force≫
Regarding the calculation formula for the pull-out resistance force Fr of the joint portion 4 described above, the validity of the additional coefficient αf was verified using the model pile 1' and the model ground G' used in the model experiment described above.

First, the verification is based on Case 2 of FIG. 4(b) in which a cylindrical fracture surface Fr occurs in FIG. Calculated according to formula 1). In calculating the pull-out resistance Fr, the shear strength F2 of the ground in the joint section _H2 was calculated using the following two patterns.

In the first pattern, a coefficient obtained by multiplying the earth pressure coefficient (stationary earth pressure system K ₀ ) of the shaft section H ₁ by an additional coefficient αf is used as the earth pressure coefficient of the joint section H ₂ . At this time, the additional coefficient αf was set to 7.4. In the second pattern, a coefficient similar to the earth pressure coefficient of the shaft section H ₁ is adopted as the earth pressure coefficient of the joint section H ₂ .

As a result, the pull-out resistance force Fr was calculated to be 0.72 kN when the extra coefficient αf was adopted, and 0.27 kN when the extra coefficient αf was not adopted. The ground constants are as follows: soil shear strength (adhesive force) C = 9.14 (kN/m ² ), soil shear resistance angle φ = 40.9 (°), and soil unit volume weight ρ = 15. 8 (kN/m ³ ).

On the other hand, from the measurement results of the strain gauge SG obtained when the model experiment in which a pulling force is applied to the model pile 1' was carried out for Cases 1 to 3 in Figs. 4(a) to (c), it was found that The relationship between the displacement of the pile head and the difference in axial force between the upper and lower portions of the joint portion 4 (resistance force of the joint portion 4) was obtained as shown. Looking at FIG. 8, in Case 2 where a cylindrical fracture surface Fr occurs, the knot resistance force changes around 0.7 kN, and in Case 3 where a cone-shaped fracture surface Fr occurs, the knot resistance force changes approximately. It can be seen that the force changes around 0.3kN.

Therefore, by applying the result of calculating the pull-out resistance force Fr according to the above equation (1) to Fig. 8, the pull-out resistance force Fr = 0.27 kN calculated without using the additional coefficient αf is the same as the experimental result of Case 3. It cannot be said that the pull-out resistance force Fr of the joint portion 3 where the cylindrical fracture surface Fr occurs can be evaluated. On the other hand, the pull-out resistance force Fr=0.72 kN calculated by employing the additional coefficient αf almost agrees with the experimental result of Case 2, and the pull-out resistance force Fr of the joint portion 3 is evaluated with high accuracy.

In order to convert the above model pile 1' to the actual size, its dimensions are as follows: shaft diameter D0 = 2.4 m, joint diameter D = 3.4 m, joint protrusion width Dn = 0.5 m, upper inclination angle θn = 20°, and the penetration length H was 6 m. When the pull-out resistance force Fr is calculated under these conditions, it is 3609 kN when the extra coefficient αf is adopted, and 1327 kN when not adopted, and it can be seen that when the extra coefficient αf is not adopted, the result is an underestimation with an error of about 2300 kN.

As mentioned above, the pull-out resistance force Fr of the knot 4 is set at a height that defines the range HA in which the shear resistance force Rf is considered on the cylindrical fracture surface Fr from the knot 4 based on the knot protrusion width Dn. At the same time, the set target range HA is divided into a joint section H2 adjacent to the joint section ₄ and a shaft section _H1 adjacent to the shaft section 2. Furthermore, in calculating the shear resistance force Rf for each section, for the joint section _H2 adjacent to the joint section 4, the earth pressure coefficient of the shaft section _H1 is multiplied by a surcharge coefficient αf as the earth pressure coefficient. Adopt new products.

This makes it possible to calculate with high precision the pull-out resistance force of the knot 4 in which a cylindrical fracture surface Fr reaching the ground surface from the knot 4 is generated in the ground when the knotted pile 1 is pulled out. Therefore, it becomes possible to reflect the pull-out resistance force Fr of the joint 4 with a shallow penetration length H, which has not been considered in the design in the past, in the same way as the vertical support force of the joint 4. .

In addition, when providing the knot 4 for the purpose of resisting the pull-out force acting on the knotted pile 1, the penetration length H corresponding to the required pull-out resistance Fr can be determined using the above equation (1). It can be estimated by Thereby, the penetration length H of the knot portion 4 can be set to an appropriate depth, and it becomes possible to design a rational knotted pile that is both safe and economical.

Note that the method for calculating the pull-out resistance force at the joints of the knotted pile of the present invention is not limited to the above-described embodiments, and various changes can be made without departing from the spirit of the present invention. Needless to say.

In this embodiment, the knot portion 4 has a shape that is a combination of a cylindrical portion 41, an upwardly facing truncated conical portion 42, and a downwardly facing truncated conical portion 43. However, the present invention is not limited to this, and any shape of the joint can be used.

1 Knotted pile 2 Shaft part 3 Expanded bottom part 4 Knot part 41 Cylindrical part 42 Upward truncated conical part 43 Downward truncated conical part G1 Surface layer G2 Middle layer G3 Support layer HA Target range H ₁ Shaft section H ₂ Knot section 1' Model Pile 2' Shaft 4' Joint G' Model ground

Claims (1)

In a knotted pile comprising a shaft and a joint provided on the shaft, the pull-out resistance of the joint is defined as the shear resistance of a cylindrical fracture surface reaching the ground surface from the joint generated in the ground, and A method for calculating pullout resistance at a joint of a knotted pile, the method comprising: calculating based on the weight of the soil mass between the fracture surface and the shaft,
The target range for calculating the shear resistance force on the fracture surface is divided into a joint section adjacent to the joint section and a shaft section adjacent to the shaft section,
A joint of a knotted pile, characterized in that the earth pressure coefficient used when calculating the shear resistance of the joint section is higher than the earth pressure coefficient used when calculating the shear resistance of the shaft section. Calculation method of pull-out resistance force.

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