# Uplift Behavior of Belled Short Piles in Weathered Sandstone

Authors: Bai Yang; Jianlin Ma; Wenlong Chen; Yanxin Yang
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

Field pull out test results of 500 kV double-circuit line of Luping-Fule are presented in this paper to investigate the uplift bearing behavior of rock-socketed belled short piles. A calculation model of rock-socketed belled short pile has been proposed. During the initial stage of loading test, uplift load is shared by even section and bell of the pile, and the bell continues to bear uplift load after the lateral resistance of even section pile reaches the limit. A different performance has been found on the case of long belled pile. At the ultimate state, the uplift resistance provided by bell accounts for about 54.9% and 34.7% of the total uplift capacity for the 6.0 m long and 7.0 m long piles, respectively. Increasing pile length has been found to noticeably increase the ultimate uplift bearing capacity, while it has less effect on the displacement of pile top. The uplift capacity of even section pile is associated with the shear strength of rock mass around the pile, and the test results demonstrate that the ultimate resistance can be equal to the shear strength. The calculation method proposed in this paper is proven to be able to accurately predict the ultimate uplift bearing capacity of the rock-socketed belled short piles.


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## Body

## 1. Introduction

With the development of society and economy, uplift piles are widely used in high-rise buildings, underground space, transmission lines, offshore wind power, and other engineering practices. Compared with even section piles, belled piles can significantly increase the uplift bearing capacity with extra materials, which is favored in the project.In the past decades, achievements have been made in the study of uplift piles with different methods. The study of uplift piles mainly focuses on the bearing behavior (influencing factors of bearing capacity) and the ultimate bearing capacity.The key influence of pile length (Slenderness ratio, Embedment ratio) on ultimate bearing capacity has been verified in model tests and field tests [1–4]. The influence of rock or soil properties on the ultimate uplift capacity of piles is that the bearing capacity of piles in dense sand is much higher than in loose sand [2, 3, 5–7]. The uplift capacity of rock-socketed piles is controlled by the relative strength between piles and rocks when the material strength of piles is sufficient [8]; estimating the pulling capacity of piles in cohesive soils is based on an empirical relationship between soil adhesion and the undrained shear strength [1]. The effect of the loading method on the uplift capacity of piles is that the compressive loading can reduce the ultimate uplift capacity of piles [9, 10]; the oblique loading can increase the ultimate uplift capacity of piles [11]; the combined loading can increase the uplift or lateral capacity of piles [12, 13]. The increase of pile diameter can effectively increase the ultimate uplift capacity of piles (Lai Ying, 2010). Pile installation method is also affecting the uplift behavior. The bored piles yield higher shaft resistance than the driven piles [14], and the driven piles yield higher shaft resistance than the jacked piles [6]. The bearing capacity of rough piles is much higher than that of smooth piles [6, 15].The failure mechanisms for piles subject to uplift loads mainly include vertical slip surface model, inverted truncated cone model, and curved slip surface model.Several calculation models for ultimate bearing capacity have been proposed based on Figure1 [15–20]. The abovementioned calculation models for the bearing capacity of uplift piles are mainly applied to the even section piles, while for the rock-socketed belled short piles, they are uncertain to apply. In this study, field tests were conducted to study the uplift behavior of rock-socketed belled short piles. According to the side resistance distribution of the piles, a method for calculating the ultimate bearing capacity of belled short piles was proposed.Figure 1
Assumed failure mechanisms for piles subject to uplift loads.


## 2. Previous Studies on Belled Piles

In recent years, achievements have been made in research of the belled pile. Dickin and Leung [3, 21] observed that the uplift capacity of belled piles is strongly dependent upon embedment ratio and sand density by centrifugal model tests. The influence of the shaft/bell diameter ratio and bell angle was suggested to be considered in the design of the uplift pile. Nazir [7] observed that the ultimate uplift capacity of belled piles was influenced by the embedment ratio, the shaft diameter, the base diameter, the base angle, and the soil density. According to the large-scale modelling experimental tests, Chae [22] conducted field tests and numerical analysis for belled piles in weathered sandstones and the geometric shape of the bell has more influence on the pile displacement than the bearing capacity. Niroumand [23] observed that the ultimate uplift capacity is dependent on the relative undrained or drained shear strength of cohesionless soil, the depth ratio of embedment, and soil thickness ratio. Moayedi [24] found that the bell can effectively reduce the ground surface deformation based on small scale tests and FEM studies.The failure mechanisms for belled piles subject to uplift loads are great different from even section piles. Many scholars have proposed the idea that failure modes are shown in Figure2 based on experimental results [25–27] and proposed the corresponding calculation method for the uplift capacity.Figure 2
Assumed failure mechanisms for belled piles subject to uplift loads.


## 3. Field Test

### 3.1. Geological Conditions

The test site is located at the Hongxing Village, in Sichuan Province of China, and on the slope of the right bank of the Qingjiang River. The main strata are as follows: silty clay, about 0.3~3m thick; strong weathered sandstone is about 0.5~3m thick, a soft rock; medium weathered sandstone that is relatively complete. The joints and fractures are developed. The properties of soil, sandstone, and piles are summarized in Table1.Table 1
Summary of properties of soil/sandstone and piles.
Names γ/kN/m3 c/kPa φ/° E/MPa ν f r/MPa Silty clay 19.5 30 25 - 0.33 - Strong weathered sandstone 24 400 32.8 80 0.25 5.0 Medium Weathered sandstone 25 1000 40.6 300 0.22 22.4 Piles 25 - - 37000 0.2 - γ is the unit weight, c is the cohesion, φ is the internal friction angle,E is the elastic modulus, ν is the Poisson ratio, and fr is the uniaxial compressive strength.


### 3.2. Test Pile Design

The even section pile was mechanically drilled to form hole, and the bell was manually digged. The normalized height of the bell was one time pile diameter, bell diameterD=d+2 · 0.2m (d is the shaft diameter). The overview of test piles is shown in Figure 3, and the dimensions of test piles are shown in Table 2. The concrete of test piles is C30, the longitudinal reinforcement of the steel cage is HRB500 grade rebar, the arrangement is 21Φ36+4Φ18, the stirrups are HPB300, and the arrangement is Φ8@150. During the test, the displacement of the pile top was measured with displacement meters, and the axial force of the pile was measured with vibrating wire type steel bar gauges. A strain gauge is placed every 0.5m down from the top of the pile up to the end of the pile. The elevation of each pile is set to 0.0m.Table 2
Parameters of piles.
Pile No. d/m D/m L/m H B/m TP1 0.8 1.2 6.0 0.8 TP2 0.8 1.2 7.0 0.8 d is the shaft diameter, D is the bell diameter, L is the pile length, and HB is the bell height.Figure 3
Profile of piles.In order to reduce the influence of the eccentric load during loading, a 1.5 × 1.5 × 1.5m pile cap is set on the pile top. The main tendons of the uplift pile extend into the reinforced concrete pile caps set on the top of the pile and are pulled up through the pile cap.


### 3.3. Test Programme

The test device consists of counterforce beams, hydraulic jacks, reaction piles (even section piles, the diameter is 0.8m, pile length is 6.6m for TP1 and 7.6m for TP2), and measuring devices. The maximum designed uplift ultimate load of the test pile is 12000 kN. Therefore, a 6000 kN hydraulic jack is placed on each bearing and two hydraulic jacks are used in parallel to apply the vertical uplift force in parallel. The sum of the two loads is the uplift load of the test pile. The field test device is shown in Figure4.Figure 4
Site image of field test device.The test adopts the slow maintenance load method. During the test, when one of the following conditions is reached, the loading can be terminated.(a) The top uplift load of the pile reaches 0.9 times of the total ultimate bearing capacity of the steel bar, or a certain steel bar is broken;(b) Under a certain load, the pile top displacement is 5 times more than that under the previous stage of load;(c) Cumulative displacement exceeds 100 mm.


## 3.1. Geological Conditions

The test site is located at the Hongxing Village, in Sichuan Province of China, and on the slope of the right bank of the Qingjiang River. The main strata are as follows: silty clay, about 0.3~3m thick; strong weathered sandstone is about 0.5~3m thick, a soft rock; medium weathered sandstone that is relatively complete. The joints and fractures are developed. The properties of soil, sandstone, and piles are summarized in Table1.Table 1
Summary of properties of soil/sandstone and piles.
Names γ/kN/m3 c/kPa φ/° E/MPa ν f r/MPa Silty clay 19.5 30 25 - 0.33 - Strong weathered sandstone 24 400 32.8 80 0.25 5.0 Medium Weathered sandstone 25 1000 40.6 300 0.22 22.4 Piles 25 - - 37000 0.2 - γ is the unit weight, c is the cohesion, φ is the internal friction angle,E is the elastic modulus, ν is the Poisson ratio, and fr is the uniaxial compressive strength.


## 3.2. Test Pile Design

The even section pile was mechanically drilled to form hole, and the bell was manually digged. The normalized height of the bell was one time pile diameter, bell diameterD=d+2 · 0.2m (d is the shaft diameter). The overview of test piles is shown in Figure 3, and the dimensions of test piles are shown in Table 2. The concrete of test piles is C30, the longitudinal reinforcement of the steel cage is HRB500 grade rebar, the arrangement is 21Φ36+4Φ18, the stirrups are HPB300, and the arrangement is Φ8@150. During the test, the displacement of the pile top was measured with displacement meters, and the axial force of the pile was measured with vibrating wire type steel bar gauges. A strain gauge is placed every 0.5m down from the top of the pile up to the end of the pile. The elevation of each pile is set to 0.0m.Table 2
Parameters of piles.
Pile No. d/m D/m L/m H B/m TP1 0.8 1.2 6.0 0.8 TP2 0.8 1.2 7.0 0.8 d is the shaft diameter, D is the bell diameter, L is the pile length, and HB is the bell height.Figure 3
Profile of piles.In order to reduce the influence of the eccentric load during loading, a 1.5 × 1.5 × 1.5m pile cap is set on the pile top. The main tendons of the uplift pile extend into the reinforced concrete pile caps set on the top of the pile and are pulled up through the pile cap.


## 3.3. Test Programme

The test device consists of counterforce beams, hydraulic jacks, reaction piles (even section piles, the diameter is 0.8m, pile length is 6.6m for TP1 and 7.6m for TP2), and measuring devices. The maximum designed uplift ultimate load of the test pile is 12000 kN. Therefore, a 6000 kN hydraulic jack is placed on each bearing and two hydraulic jacks are used in parallel to apply the vertical uplift force in parallel. The sum of the two loads is the uplift load of the test pile. The field test device is shown in Figure4.Figure 4
Site image of field test device.The test adopts the slow maintenance load method. During the test, when one of the following conditions is reached, the loading can be terminated.(a) The top uplift load of the pile reaches 0.9 times of the total ultimate bearing capacity of the steel bar, or a certain steel bar is broken;(b) Under a certain load, the pile top displacement is 5 times more than that under the previous stage of load;(c) Cumulative displacement exceeds 100 mm.


## 4. Test Results

### 4.1. Load-Displacement Curve

The curve of the uplift load and pile top displacement of test piles are shown in Figure5, and the test results are shown in Table 3.Table 3
Results of pile tests.
Pile No P m a x/kN S m a x/mm P U/kN S U/mm TP1 6704 >38.3 6328 20.6 TP2 9626 >70.7 8396 22.4 P m a x is the maximum uplift load, Smax is the maximum displacement of pile top, PU is the ultimate uplift load, and SU is the displacement of pile top under the ultimateuplift load.Figure 5
Load-displacement curve of pile top.Taking TP1 as an example, the test piles were lifted by 17.70 mm under the finial-stage load, which is 5 times more (3.37 × 5=16.85mm) than that under the load of the previous stage. The test piles reached the state of failure. Figure6 shows that the top load-displacement curve at the top of two rock-socketed piles with deep-buried piles is steep, which is consistent with the pile top load in the soft soil area obtained by Wang [28].Figure 6
Axial forces distribution along the pile.
(a)
TP1 (b)
TP2Uplift load of TP2 is 32.7% higher than TP1, indicating that increasing the pile length can increase the bearing capacity effectively, while the displacement of the pile top increases by 8.7%, indicating that the effect of increasing pile length on the displacement of the pile top is limited.


### 4.2. Axial Forces Distribution and Side Resistance Distribution of Piles

The axial force of pile is obtained according to formula (1) by the reinforcing steel gauge stress at each section, and the side resistance of pile is obtained according to formula (2). The axial force distribution curve of 2 belled short piles under different loads is shown in Figure 6, and the side resistance distribution curve is shown in Figure 7.(1)Nij=σijAsi+σijEsEcAciwhereNij is the measured axial force of the pile under the stage load of the measured section,σij is the measured stress of the steel bar stress meter under the stage load of the measured section,Asi is the total area of the steel bar in the measured section,Ec is the elastic modulus of the concrete,Es is the elastic modulus of the steel bar, andAci is the concrete area of the measured section.(2)fij=Nij-Ni-1jAiwherefij is the side resistance of the i~i+1 section pile body under the stage load j,Ai is the pile side area within the i~i+1 measured sections, andN(i-1)j is the axial force of the i-1 measured section under the stage load j.Figure 7
Side resistance distribution of piles.
(a)
TP1 (b)
TP2Figure6 shows that the axial force along the pile under the load at each stage gradually decreases along the depth, and the reduction rate varies among different rock and soil layers. As the load increases, the slope of the axial force curve in the overlying soil layer tends to be stable and the slope of the axial force curve in the rock layer continuously increases. The test pile shows different bearing behavior compared to the long belled pile (19m long pile, 30 m long pile) [28]. Figure 7 shows that, at the first stage of loading, side resistance of bell is ranging from 49.3 to 82.8 kPa for TP1 and ranging from 148.6 to 274.5 kPa for TP2, which is greater than the even section pile. It is observed that at, the initial stage of loading, the even section part of the pile and the bell part are bearing the uplift load at the same time. With the increase of the load, the lateral resistance of the even section pile continue to be mobilized until the limit is reached, and the bell continues to bear the uplift load.According to the principle of force balance, the axial force curve of the pile provided by the rock and soil along the pile to a certain extent can respond to the pullout force. Taking the TP1 pile as an example, after the pile top acts more than 2239 kN, the rock resistance force provided by the rock exceeds 80% of the uplift force provided by the rock and soil layer and the ratio increases slightly with the increase of the pile top load. Under this effect, the ratio reached 85%, indicating that the rock layer dominated the pullout resistance when the pile top load exceeds a certain value for overlying rock-socketed belled short uplift piles.Because reinforcing bar gauges were not installed at the boundary between the bell and even sections, for the convenience of analysis, the slope of the axial force curve of the last measurement interval is extended to the interface between the even section and the bell section. The bell is obtained by measuring the axial force curve of the interval. Bearing capacities of the bell under ultimate uplift load of piles is shown in Table4.Table 4
Bearing capacities of the bell.
Pile No P’/kN P U/kN P’/PU TP1 3472 6328 54.9% TP2 2918 8396 34.7% P’ is the load provided by the bell and PU is the ultimate uplift load.Table4 shows that, for rock-socketed belled short piles, with the increases of pile length, the proportion of the load provided by the bell will decreases. Therefore, for the long-inlaid rock piles, the base-enlarging foundation should be used with caution.


## 4.1. Load-Displacement Curve

The curve of the uplift load and pile top displacement of test piles are shown in Figure5, and the test results are shown in Table 3.Table 3
Results of pile tests.
Pile No P m a x/kN S m a x/mm P U/kN S U/mm TP1 6704 >38.3 6328 20.6 TP2 9626 >70.7 8396 22.4 P m a x is the maximum uplift load, Smax is the maximum displacement of pile top, PU is the ultimate uplift load, and SU is the displacement of pile top under the ultimateuplift load.Figure 5
Load-displacement curve of pile top.Taking TP1 as an example, the test piles were lifted by 17.70 mm under the finial-stage load, which is 5 times more (3.37 × 5=16.85mm) than that under the load of the previous stage. The test piles reached the state of failure. Figure6 shows that the top load-displacement curve at the top of two rock-socketed piles with deep-buried piles is steep, which is consistent with the pile top load in the soft soil area obtained by Wang [28].Figure 6
Axial forces distribution along the pile.
(a)
TP1 (b)
TP2Uplift load of TP2 is 32.7% higher than TP1, indicating that increasing the pile length can increase the bearing capacity effectively, while the displacement of the pile top increases by 8.7%, indicating that the effect of increasing pile length on the displacement of the pile top is limited.


## 4.2. Axial Forces Distribution and Side Resistance Distribution of Piles

The axial force of pile is obtained according to formula (1) by the reinforcing steel gauge stress at each section, and the side resistance of pile is obtained according to formula (2). The axial force distribution curve of 2 belled short piles under different loads is shown in Figure 6, and the side resistance distribution curve is shown in Figure 7.(1)Nij=σijAsi+σijEsEcAciwhereNij is the measured axial force of the pile under the stage load of the measured section,σij is the measured stress of the steel bar stress meter under the stage load of the measured section,Asi is the total area of the steel bar in the measured section,Ec is the elastic modulus of the concrete,Es is the elastic modulus of the steel bar, andAci is the concrete area of the measured section.(2)fij=Nij-Ni-1jAiwherefij is the side resistance of the i~i+1 section pile body under the stage load j,Ai is the pile side area within the i~i+1 measured sections, andN(i-1)j is the axial force of the i-1 measured section under the stage load j.Figure 7
Side resistance distribution of piles.
(a)
TP1 (b)
TP2Figure6 shows that the axial force along the pile under the load at each stage gradually decreases along the depth, and the reduction rate varies among different rock and soil layers. As the load increases, the slope of the axial force curve in the overlying soil layer tends to be stable and the slope of the axial force curve in the rock layer continuously increases. The test pile shows different bearing behavior compared to the long belled pile (19m long pile, 30 m long pile) [28]. Figure 7 shows that, at the first stage of loading, side resistance of bell is ranging from 49.3 to 82.8 kPa for TP1 and ranging from 148.6 to 274.5 kPa for TP2, which is greater than the even section pile. It is observed that at, the initial stage of loading, the even section part of the pile and the bell part are bearing the uplift load at the same time. With the increase of the load, the lateral resistance of the even section pile continue to be mobilized until the limit is reached, and the bell continues to bear the uplift load.According to the principle of force balance, the axial force curve of the pile provided by the rock and soil along the pile to a certain extent can respond to the pullout force. Taking the TP1 pile as an example, after the pile top acts more than 2239 kN, the rock resistance force provided by the rock exceeds 80% of the uplift force provided by the rock and soil layer and the ratio increases slightly with the increase of the pile top load. Under this effect, the ratio reached 85%, indicating that the rock layer dominated the pullout resistance when the pile top load exceeds a certain value for overlying rock-socketed belled short uplift piles.Because reinforcing bar gauges were not installed at the boundary between the bell and even sections, for the convenience of analysis, the slope of the axial force curve of the last measurement interval is extended to the interface between the even section and the bell section. The bell is obtained by measuring the axial force curve of the interval. Bearing capacities of the bell under ultimate uplift load of piles is shown in Table4.Table 4
Bearing capacities of the bell.
Pile No P’/kN P U/kN P’/PU TP1 3472 6328 54.9% TP2 2918 8396 34.7% P’ is the load provided by the bell and PU is the ultimate uplift load.Table4 shows that, for rock-socketed belled short piles, with the increases of pile length, the proportion of the load provided by the bell will decreases. Therefore, for the long-inlaid rock piles, the base-enlarging foundation should be used with caution.


## 5. Calculation of Ultimate Uplift Capacity of Rock-Socketed Belled Short Piles

The above analysis shows that the ultimate uplift bearing capacity of rock-socketed belled short piles consists of the side resistance and the pile weight. The side resistance includes the side resistance provided by the even section pile and the expansion of the head-cone. Force diagram of the pile is shown in Figure8.Figure 8
Force diagram of the pile.Therefore, the formula for predicting ultimate uplift capacity of rock-socketed belled short piles can be expressed as follows:(3)PU=PS+PB+WC=∑πdiLifsi+SEfB+γCVwherePS is the uplift bearing capacity provided by the even section pile,PB is the uplift bearing capacity by the expansion of the head-cone,WC is the weight of the pile body,di is the pile diameter for the even section,Li is the thickness of rock or soil layer,fsi is the ultimate side resistance of the pile the rock and soil layer with even section,SE is the area of the side of the cone-shaped conical table,fB is the ultimate side resistance value of the cone-shaped conical table,γC is unit weight of pile, andV is the pile volume.The geometric parameters in formula (3) can be calculated based on the test pile, but the values of fsi and fB need to be considered separately.The value of the ultimate side resistance of the pile is mainly based on the code or the field test. The code values are generally conservative. Field test is high cost and takes a long time, which does not apply in small projects. Many scholars have concluded some relationships between the ultimate side resistance and the uniaxial compressive strength of rock. Exponential relationship [29–32] and linear relationship [33, 34] that facilitates the design work greatly.


### 5.1. Value offsi

During the loading test, pile and the surrounding rock mass generate slip surface that is governed by the strength of pile. If piles and rocks have the same strength, failure mode in such cases is expected to be the pull out of piles along with surrounding rocks attached. With the rock strength decreasing, the uplift bearing capacity of the pile gradually depends on rock strength. The pile and the surrounding rock mass are congealed. When the strength of the pile is higher, the slip surface is within the rock mass. The slip surface will be a cylindrical surface of which the diameter is similar to the pile diameter, and the surrounding rock mass is subjected only to the shear stress by the pile. During the early casting of rock-socketed piles, normal stress acts on the wall of the pile hole, while due to the structural planes in the rock mass, the normal stress gradually dissipates as the concrete solidifies. The pile body and the surrounding rock mass condensed. So the normal stress on the rock shear section was supposed to be nonexistent. The uplift bearing capacity of the pile is provided by the shear strength of the rock mass. The ultimate side resistance of the pile is equivalent to the shear strength of the rock mass. The soil has a continuous normal stress on the pile side. Within a certain depth range, with the increase of soil depth, the ultimate side resistance of the pile also increases [14]. The ultimate side resistance of the clay layer can be based on the value of the clay undrained shear strength. The soil thickness of the test site in this paper is 3.0 m, and the shear resistance of the soil at a depth of 1.5 m is selected.By the Mohr-Coulomb strength criterion(4)τ=c+σtan⁡φ.(5)σ=γ·zwhereτ is the shear stress of silty clay,σ is the normal stress, andz=1.5m.By formulas (4)-(5), the ultimate side resistance of the clay is obtained as 43.6 kPa.For strong and medium weathered sandstone, whereσ=0, the shear strength of the strong and medium weathered sandstone is equal to the cohesion of the soil, which is 400 kPa and 1000 kPa, respectively, and it is equal to the ultimate side resistance of the rock mass surrounding the pile.


### 5.2. Value offB

When the uplift load is applied, the external force on the conical side is shown in Figure9.Figure 9
Force diagram of the conical side.By the Mohr-Coulomb strength criterion(6)T=c+Ntan⁡φwhereN is the normal stress provided by the rock mass andTis the side resistance along the bell.By the balance condition of force(7)Ncos⁡α=Tsin⁡αwhereα is the inclination angle of bell.(8)fB=N2+T2by formulas (6)–(8), fB=1476kPa.The value of each parameter is brought into formula (3) to determine the ultimate bearing capacity of the uplift piles.The friction cylinder method [35] is used to apply in calculating the uplift capacity of rock-socketed belled piles and the formula is as follows:(9)PU=πD∑λiqsikli+πD∑hjfrsi+WC+Wrwhereλi is the uplift coefficient,qsik is ultimate compressive side friction value for soil of i layer of pile’s surface,li is the thickness of soil of i layer,hj is the thickness of rock of j layer,frsi is the rock shear strength of each layer,WC is the weight of the pile body, andWr is the weight of rock and soil above pile’s bottom.The field test results, calculation results of this paper, and method of friction cylinder are compared, as shown in Table5.Table 5
Comparison of results.
Pile No. Field test This approach Method of friction cylinder TP1 6328 (100%) 6968 (110.1%) 7981 (126.1%) TP2 8396 (100%) 7985 (95.1%) 9516 (113.3%)As it can be seen from Table5 that the calculation model proposed in this study can accurately calculate the ultimate uplift bearing capacity of the rock-socketed belled short pile and can be applied to similar projects.


## 5.1. Value offsi

During the loading test, pile and the surrounding rock mass generate slip surface that is governed by the strength of pile. If piles and rocks have the same strength, failure mode in such cases is expected to be the pull out of piles along with surrounding rocks attached. With the rock strength decreasing, the uplift bearing capacity of the pile gradually depends on rock strength. The pile and the surrounding rock mass are congealed. When the strength of the pile is higher, the slip surface is within the rock mass. The slip surface will be a cylindrical surface of which the diameter is similar to the pile diameter, and the surrounding rock mass is subjected only to the shear stress by the pile. During the early casting of rock-socketed piles, normal stress acts on the wall of the pile hole, while due to the structural planes in the rock mass, the normal stress gradually dissipates as the concrete solidifies. The pile body and the surrounding rock mass condensed. So the normal stress on the rock shear section was supposed to be nonexistent. The uplift bearing capacity of the pile is provided by the shear strength of the rock mass. The ultimate side resistance of the pile is equivalent to the shear strength of the rock mass. The soil has a continuous normal stress on the pile side. Within a certain depth range, with the increase of soil depth, the ultimate side resistance of the pile also increases [14]. The ultimate side resistance of the clay layer can be based on the value of the clay undrained shear strength. The soil thickness of the test site in this paper is 3.0 m, and the shear resistance of the soil at a depth of 1.5 m is selected.By the Mohr-Coulomb strength criterion(4)τ=c+σtan⁡φ.(5)σ=γ·zwhereτ is the shear stress of silty clay,σ is the normal stress, andz=1.5m.By formulas (4)-(5), the ultimate side resistance of the clay is obtained as 43.6 kPa.For strong and medium weathered sandstone, whereσ=0, the shear strength of the strong and medium weathered sandstone is equal to the cohesion of the soil, which is 400 kPa and 1000 kPa, respectively, and it is equal to the ultimate side resistance of the rock mass surrounding the pile.


## 5.2. Value offB

When the uplift load is applied, the external force on the conical side is shown in Figure9.Figure 9
Force diagram of the conical side.By the Mohr-Coulomb strength criterion(6)T=c+Ntan⁡φwhereN is the normal stress provided by the rock mass andTis the side resistance along the bell.By the balance condition of force(7)Ncos⁡α=Tsin⁡αwhereα is the inclination angle of bell.(8)fB=N2+T2by formulas (6)–(8), fB=1476kPa.The value of each parameter is brought into formula (3) to determine the ultimate bearing capacity of the uplift piles.The friction cylinder method [35] is used to apply in calculating the uplift capacity of rock-socketed belled piles and the formula is as follows:(9)PU=πD∑λiqsikli+πD∑hjfrsi+WC+Wrwhereλi is the uplift coefficient,qsik is ultimate compressive side friction value for soil of i layer of pile’s surface,li is the thickness of soil of i layer,hj is the thickness of rock of j layer,frsi is the rock shear strength of each layer,WC is the weight of the pile body, andWr is the weight of rock and soil above pile’s bottom.The field test results, calculation results of this paper, and method of friction cylinder are compared, as shown in Table5.Table 5
Comparison of results.
Pile No. Field test This approach Method of friction cylinder TP1 6328 (100%) 6968 (110.1%) 7981 (126.1%) TP2 8396 (100%) 7985 (95.1%) 9516 (113.3%)As it can be seen from Table5 that the calculation model proposed in this study can accurately calculate the ultimate uplift bearing capacity of the rock-socketed belled short pile and can be applied to similar projects.


## 6. Conclusions

In this paper, the uplift behavior of rock-socketed belled short piles is studied based on field test results. A semiempirical method for calculating the ultimate uplift capacity of rock-socketed belled short piles has been proposed. The following main conclusions are drawn.The rock-socketed belled short pile showed different bearing behavior compared to the long belled pile during the field tests. At the initial stage of loading, the even section pile and the bell take up the uplift load synchronously. With the increase of the load, the lateral resistance of the even section pile continue worked until the limit is reached and the bell continues to bear the uplift load. At the ultimate state, the uplift resistance provided by the bell accounts for about 54.9% and 34.7% of the total uplift capacity for the 6.0 m long and 7.0 m long piles, respectively. The increase of the pile length can effectively increase the ultimate uplift bearing capacity, while it has less effect on the displacement of the pile top. The influence of the bell has weakened with the increase of the pile length. When the strength of the pile exceeds that of the rock mass around pile, the uplift capacity of the even sections is provided by the shear strength of the rock mass and the ultimate side resistance becomes equal to the shear strength of the rock mass around the pile. The calculation method proposed in this paper can accurately calculate the ultimate uplift bearing capacity of the rock-socketed belled short piles.



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*Source: 8614172-2018-09-16.xml*