A numerical study of the pullout behavior of grout anchors underreamed by pulse discharge technology

Computers and Geotechnics 47 (2013) 78–90

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A numerical study of the pullout behavior of grout anchors underreamed by pulse discharge technology Hyunku Park a, Seung Rae Lee a,⇑, Nak Kyung Kim b, Tae Hoon Kim c a

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea Department of Civil, Architectural and Environmental System Engineering, Sungkyunkwan University, Suwon, 440-746, South Korea c Daewoo Institute of Construction Technology, Daewoo Engineering and Construction Co., Ltd., Seoul 100-741, South Korea b

a r t i c l e

i n f o

Article history: Received 12 December 2011 Received in revised form 3 July 2012 Accepted 4 July 2012 Available online 13 August 2012 Keywords: Ground anchor Underreaming Uplift capacity Pulse discharge technology Underwater explosion

a b s t r a c t Pulse discharge technology (PDT) is an innovative construction method used to enhance the bearing capacity of piles and the resisting capacity of anchors by underreaming using a high-pressure shockwave induced by an underwater electric discharge. This study numerically analyzes the pullout behavior of a grout anchor underreamed by PDT. A series of finite element analyses were performed to examine the pullout behavior of the anchor based on successive simulations from underreaming to subsequent pullout tests. The electric blasting and shockwave generation by PDT was equivalently modeled using the underwater explosion (UNDEX) model, and the appropriate UNDEX parameters were determined by benchmarking the laboratory PDT tests. Full-scale PDT underreaming and the subsequent pullout tests in dry sand deposits reported in the literature were then simulated on the basis of fluid–structure interaction (FSI) analyses and static uplift analyses. The predicted expansion of the borehole and the pullout behaviors were compared with field test results to validate the numerical model. Moreover, the results from a parametric study conducted to investigate the influence of soil and anchor characteristics on the uplift behavior of the PDT underreamed anchor are discussed. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Over the last two decades, pulse discharge technology (PDT) has been applied to enhance the resisting capacity of small-sized castin-place grout piles and anchors [10]. PDT is an electric technique used to induce a high-powered electric discharge over a very short duration [41]. When the pulse discharge is conducted in water, which is called an underwater electric discharge (UED), a strong shockwave develops in the fluid medium based on the electrochemical-hydrodynamic environment surrounding the electrodes. The UED occurs in the following sequence: formation of a plasma channel by an arc discharge, expansion of the channel, development of inertial resistance in the surrounding water, and generation of the shockwave in the water [3,13,38]. The application of PDT creates an expanded bulb in the body of the grout piles or anchors by imposing a shockwave induced by pulse discharge on the predrilled ground borehole, which is filled with weak cement paste or mortar. The general procedures for PDT underreaming in practice, described in Fig. 1, include (1) drilling a ground borehole and install a steel-tube casing, (2) filling the casing with a weak cement paste or mortar with a water to cement ratio higher than 0.5, (3) immersing an electrode to the desired depth and apply several ⇑ Corresponding author. Tel.: +82 42 350 3617; fax: +82 42 350 3610. E-mail address: [email protected] (S.R. Lee). 0266-352X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2012.07.005

tens of pulse discharges, and (4) inserting a steel cage (pile) or tendon (anchor) and curing the cement for 28 days. Several previously reported field experiments have revealed that PDT significantly increases the resisting capacity of the pile or anchor compared to unremediated cases based on an increase in the section area of the grout body by deforming the borehole and an improvement of the frictional resistance along the shaft by recompacting the disturbed soil around the borehole [4,10,18,20,22]. In general, the PDT method is more effective in sandy soils than in clayey soils for underreaming and improving the resisting capacity of pile and anchor. Dzhantimirov et al. [10] reported that PDT treatment increased the bearing capacity of piles by factors of 2–2.2, and 1.2–1.4 times in sands and clayey soils, respectively. For anchors, Bakholdin and Dzhantimirov [4] stated that the uplift capacity of a PDT-treated anchor was 1.5–2 times higher than that of a conventional shaft anchor in sandy soil. The PDT technique involves several distinctive physical phenomena at each phase: underwater electric discharge and shockwave development (electrodynamics, plasma mechanics, and hydrodynamics), soil deformation by the shockwave developed in the fluid (fluid–structure interaction, FSI), and the bearing or uplift behavior of the underreamed anchor or piles (static geomechanics). Several experimental studies have been conducted in the following areas: (1) characterizing the electric system of currently used PDT device [37], (2) applying the theory of underwater explosion

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can be predicted using the theory of UNDEX, based on the equivalency between the electric discharge energy during PDT and the combustion energy of the explosive charge during UNDEX. This equivalency was experimentally confirmed by Wakeland et al. [42]. The theory, a similitude relation, provides a far-field pressure vs. time history of the shockwave induced by UNDEX, as described by Eqs. (1)–(4) [8].

  1þA  Pðr; tÞ ¼ K m1=3  f ½rc =rB  t=T c c =r

ð1Þ

 1þA Pmax ðrÞ ¼ K m1=3 c =r

ð2Þ

 B  r c =m1=3 c

ð3Þ

f ðsÞ ¼ f ðt=T c Þ ¼ et=T c ;

ð4Þ

1=3

T c ¼ kmc

Fig. 1. General procedure for PDT application.

(UNDEX) for an analytical representation of the PDT-induced shockwave by an equation of similitude relation with appropriate experimental calibrations [42], (3) establishing empirical relationships between the number of pulse discharges and the amount of borehole expansion in sandy and clayey soils [23], and (4) examining the effects of the number of pulse discharges, the extent of the expanded area, and the number of bulbs formed in the grout body on the resisting capacity of PDT-treated anchors [18,20,22]. Park et al. [30] performed numerical simulations of borehole expansion by PDT application. In their study, the shockwaves induced by PDT observed from the lab-scale tests were numerically benchmarked using an equivalent UNDEX shockwave model, i.e., similitude relation. The model was applied to coupled fluid-structural medium analysis of borehole expansion in sandy and clay soils. The design of PDT-applied piles continues to be conducted on a case-by-case basis or using empirical methods [22,33] because no comprehensive experimental or numerical study has been performed to analyze the bearing or uplift behaviors of PDT-applied piles or anchors. Thus, for a reliable estimation of the resisting behavior of a PDT-applied pile or anchor, the above-described physical problems must be represented using a reasonable and simple numerical model. In addition, the appropriate coupled analysis schemes should be applied to model dynamic and static behaviors in the overall PDT application procedures. In the present study, a numerical study was carried out to analyze the pullout behavior of a small-diameter grout anchor in dry sand underreamed by PDT. Emphasis was placed on practical modeling of the uplift behavior of a compression grout anchor in combination with the borehole expansion analysis, in which the shockwave induced by PDT and subsequent borehole expansion was modeled based on equivalent UNDEX model and the FSI analysis scheme proposed by Park et al. [30]. The proposed modeling scheme was applied to simulate the full-scale underreaming and pullout tests in dry weathered granite soil deposit conducted by Kim et al. [20]. The predicted expansions of the borehole and the uplift force–displacement behaviors were compared with the field test results. Lastly, the results from a parametric study to investigate the resisting mechanism of PDT-treated anchors and the influence of soil and anchor characteristics on the uplift behavior are discussed. 2. Models and methods 2.1. Modeling of a shockwave based on the UNDEX model Although the explosion mechanism of UED is different from that of UNDEX, the waveform of the resultant UED shockwave

where r is the distance from the blasting source, t is the time, rc is the radius of the spherically shaped charge, and mc is the mass of the charge. K, k, A, and B are the material constants of the charge related to the peak pressure, detonation speed, and attenuation, respectively. Based on the energy equivalency mentioned above, mc in Eq. (1) can be calculated using Eq. (5), where ED is the electric discharge energy and Wc is the specific combustion energy of the explosive (J/kg). Using mc obtained from Eq. (5), the peak pressure of the shockwave Pmax can be estimated by Eq. (2).

mc ¼ ED =W c

ð5Þ

The energy equivalency depicted in Eq. (5) was found to be valid for PDT conducted in water [42], while Eq. (5) overestimated the peak pressure of PDT consistently in cement paste, i.e., a mixture of cement and water that underwent the hydration process [30]. In addition, for a reasonable calibration of the terms related to the peak pressure and impulse of the shockwave (i.e., K, k, A, and B), trial-and-error benchmarking of the waveform observed from the actual PDT tests is indispensible [30,42]. Hence, laboratory pulse discharge tests were conducted in this study, and the resultant actual shockwaves were numerically benchmarked to optimize the UNDEX parameters. 2.2. Coupled acoustic-structural medium analysis of borehole expansion A number of numerical methods have been proposed to analyze the response of a structure under an UNDEX shockwave as summarized in Refs. [19,26,43]. The methods can be divided into two broad categories depending on whether the explosion behavior of the explosive charge is simulated [34]. In cases where the main focus is on the behavior of the structure, many researchers adopt a doubly asymptotic approximation (DAA) to model UNDEX and the subsequent FSI [16]. The DAA model is used because it is simple, can provide a reasonable prediction of the shockwave and reduces the calculation time compared to the analysis methods using direct modeling of the explosion. In our analyses of borehole expansion, the modeling methods of Park et al. [30] were adopted, in which the UNDEX model and a coupled acoustic-structural medium analysis based on the DAA scheme implemented in ABAQUS/explicit [2] were applied. The far-field pressure profile of a spherical shockwave induced by an underwater explosion is estimated by the bubble acceleration model [11], which is an extended form of the similitude relation and demonstrates the dilatational bubble pressure wave that occurs after the primary shockwave. The propagation of the pressure wave developed in the fluid is modeled by an acoustic element, which can demonstrate the elastic pressure–volumetric behavior

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of the fluid as small deformations and the cavitations of the fluid when the pressure in the fluid drops to a cavitation limit. A Lagrangian (for fluid) – Lagrangian (for structure) process implemented in ABAQUS/Explicit was used to simulate the FSI during an UNDEX event by means of a surface-based acoustic-structural coupling at the interface. The acoustic element involves small deformations and a single degree of freedom for the isotropic pressure p. Therefore, the numerical problems induced by large deformations in the fluid, such as mesh tangling or overflow of the fluid, do not need to be considered. The equations of motion for calculating the coupled behavior of the acoustic and structural elements are shown in Eqs. (6) and (7), respectively.

€ þ K s u ¼ ½Sfs T p Ms u

ð6Þ

€ þ K f p ¼ ½Sfs T T Mf p

ð7Þ

p ¼ pS þ pI ;

ð8Þ

Strand Grout

Sheath tube

Steel tube

(a) Composition of the compression grout anchor Spring element for strand Not attached to grout elements

Solid elements for grout

Node set for rigid steel tube Connected to spring element

where the subscripts s and f represent structure and fluid, respectively. M is the mass matrix, K is the stiffness matrix, Sfs is the coupled matrix, T is the traction imposed on the fluid, and p is the total fluid pressure, which is the summation of the incident shockwave pressure pS and the scattered wave pressure pI, i.e., the wave reflected from the structure. The coupling is based on the continuity conditions of acoustic pressure and the acceleration of solid elements under tied displacement restriction at the interface. In particular, the coupling matrix Sfs depends on the acoustic boundary conditions that can be designated at the interface to assign the boundary pressure value or to model rigid, free-radiating, and specified impedance conditions by means of a combination of a spring and a dashpot. At the first encounter of a shockwave at the surrounding structure, the intensive pressure wave propagating in acoustic elements only imposes isotropic pressure p on all of the solid elements. The resultant acceleration ü in the solid elements defines the displacements of the tied nodes at the interface (Eq. (6)). The normal traction of the solid elements is then imposed on the acoustic elements at the interface, which is defined as T in Eq. (7), and is used to calculate pressure field in the fluid domain based on Eq. (7). The above-described coupling procedures repeat until the end of the underreaming analysis for a single pulse discharge.

(b) Simple modeling of the compression grout anchor Fig. 2. Modeling of the compression grout anchor. (a) Composition of the compression grout anchor. (b) Simple modeling of the compression grout anchor.

[5,9,12,29,32,40], the expanded and compacted condition of the soil induced by PDT may cause numerical difficulties when adopting sophisticated contact formulations because of the curved contact surface and the irregular distribution of stresses in the ground. Hence, we adopted a simple approach to model the contact behavior at the shaft interface by assuming a fully bonded condition, i.e., tied surface interaction, while a surface behavior with softened attachment and separation was considered for the interface at the bottom of the borehole. Conventional PDT anchors usually adopt a compressive loading mechanism. Fig. 2a shows the composition of the compression anchor, in which the steel bars for the strand are directly connected to the bonded-steel pipe at the end-tip because the sheath tubes prevent contact between the strand and the grout. In this study, the strand was modeled using a spring element, and it was connected to the nodes at the bottom of the anchor (Fig. 2b), where a kinematic constraint was assigned to those nodes to give an identical vertical displacement during the uplift loading, which represents the rigid steel pipe at the end-tip. 3. Numerical simulation of the full-scale field tests

2.3. Modeling the uplift behavior of a PDT-underreamed grout anchor

3.1. Description of the field and laboratory pulse discharge tests

The uplift analysis in this study was based of the static simulation of the pullout behavior of an anchor using the implicit static analysis of ABAQUS/standard [2]. Before the pullout simulation, the results of the previous expansion analysis performed in ABAQUS/explicit were imported into the static analysis using the IMPORT command provided in the ABAQUS program. Using the IMPORT command, the expanded state of the soil and the deformed nodal coordinates of the cement paste constrained within the soil elements during the expansion analysis were given as the initial conditions of the pullout analysis. In addition, the inertia force remaining from the underreaming analysis was eliminated in the importing process. After importing, the uplift simulation was conducted based on a simple modeling of the compression ground anchor and the soil-grout contact behavior. The anchor elements were newly defined using the imported coordinates of the cement paste. Modeling of the soil-grout interface requires information on the normal pressure–displacement relationship, such as contact or separation, and the tangential friction behavior, including stick or slippage [21]. Although numerous finite element analysis techniques have been proposed to handle the interface behavior

3.1.1. Field underreaming and pullout tests In this study, the field tests performed by Kim et al. [20] were considered to be references to validate the suitability of the numerical model. Kim et al. conducted full-scale PDT tests to investigate the borehole expansion characteristics and the effect of PDT treatment on the pullout behavior of an anchor. The expansion tests were conducted in dry weathered soil deposits, in which the blow count numbers of the Standard Penetration Test (SPT) ranged from 11 to 20. After filling the borehole with a weak cement paste (water-to-cement ratio of 0.5), a series of 5, 10, 20, and 40 electric discharges were applied 0.25 m apart from the bottom of the borehole with an initial charging voltage of 4 kV. Additional cement paste was then injected into the borehole to form an anchor body with a bond length of 2 m. After the cement was cured, the pullout tests were carried out in accordance with the test procedures provided by the AASHTO [1]. Fig. 3 shows a schematic diagram of the tests, in which the uplift force and displacement at the anchor head were measured by a load cell and LVDT, respectively. The vertical displacement of the anchor head is a summation of the elastic elongation of the strand and the residual movement of the anchor-ground combination. Kim et al.

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H. Park et al. / Computers and Geotechnics 47 (2013) 78–90

Optical measurement target

Reference beam

LVDT

Fixing Wedge Load cell

A tripod

Hydraulic jack Loading frame Steel strand

Fig. 3. Schematic diagram of the full-scale field tests of Kim et al. [20].

Co-axial cable

Electro impact cell

Electro Power Impactor (D/C converter, capacitor)

Current & voltage

pressure

Oscilloscope (DPO4034)

Instrumented chamber

and 7 kV. The current and voltage at the electrode and the pressure waveforms of the shockwaves imposed on the inner surface of the chamber were monitored using sensors and oscilloscope whose specifications and locations are described in Fig. 5. Fig. 5a and b depict the measured voltage V(t), current I(t), electric power P(t), and cumulative electric energy E(t), where the latter two were calculated using Eqs. (9) and (10). Immediately after the electric discharge, most of the initial charging voltage suddenly dropped within 1 ms, and intensive current impulses were generated. Accordingly, an extremely high power was produced soon after the discharge, with peak values ranging from 65 to 170 MW. The curves of the electric energy dissipated at the electrode commonly indicated a gradual linear increase at the early stage and nearly constant values after the end of the voltage drop.

Sensors

PðtÞ ¼ VðtÞ  IðtÞ

Current : Rogowskicoil (CWT1500R) Voltage : High voltage probe (P6015) Pressure : Dynamic blast pressure sensor (M109C12)

EðtÞ ¼

Z 0

Fig. 4. The experimental setup for the lab-scale pulse discharge tests.

[20] estimated the limit load of an anchor from the load-residual movement curve based on the method suggested by Briaud et al. [7], which determines the ultimate pullout capacity of the load when the residual displacement reaches 10% of the anchor diameter. The residual uplift displacement was obtained by subtracting the elastic elongation of the strand from the total vertical displacement at the anchor head, which indicates the vertical movement of the steel tube at the end-tip. 3.1.2. Laboratory pulse discharge tests To obtain the electric characteristics and actual waveforms of the shockwaves induced by PDT, lab-scale pulse discharge tests were conducted using the same electric device as Kim et al. [20], which is different from the device used in the study of Park et al. [30]. Fig. 4 shows the equipment for the tests, which includes the electric devices for generating the pulse discharge and an instrumented chamber for measuring the shockwave. The electroimpact cell was immersed in a 250-mm diameter chamber, which contained fresh weak cement paste with a water-to-cement ratio of 0.5 and a unit density of 24 kN/m3. After charging a capacitor bank using direct current generated by an electric power impactor (EPI), the circuit was then shorted to induce the electric discharge. The tests were performed at three levels of charging voltage: 4, 5,

t

PðsÞds ¼

ð9Þ Z

t

VðsÞ  IðsÞds

ð10Þ

0

Fig. 6 presents the observed pressure waveforms during the tests. Strong pressure waves on a megaPascal scale were induced by the PDT, in which a larger initial charging voltage caused a larger value of peak pressure. However, the results of the monitoring after 1 ms showed considerable noise in the tests with charging voltages of 4 and 5 kV, which were caused by malfunctioning pressure sensors. 3.2. Numerical benchmarking of the PDT-induced shockwave based on the UNDEX model On the basis of the above-mentioned concept of energy equivalence between UED and UNDEX proposed by Wakeland et al. [42], the peak values of the shock pressure wave were predicted using Eqs. (2) and (5) and compared with the test results summarized in Table 1. Although the measured peaks were much smaller than the predictions, consistent ratios between them can be found, ranging from 4% to 5%. Although the observed ratio is smaller than that in Park et al. [30], the result indicates a consistent relationship between the electric energy induced by the PDT tests and the peak pressure of the resultant shockwave. As mentioned above, the UNDEX parameters, such as k, A, and B, should be calibrated for a reasonable demonstration of the spatial and temporal variations in the shockwave.

H. Park et al. / Computers and Geotechnics 47 (2013) 78–90

40

40 Current (charging voltage = 7 kV)

30

160

160 140

Current (charging voltage = 4 kV)

20

20 Initial charging voltages

10

7 kV 5 kV 4 kV

Power (kW)

Power (charging voltage = 7 kV), Max = 170 MW

Current (charging voltage = 5 kV)

10

180

140

Voltage (kV)

Current (kA)

30

180

120 100

0

100

Power (charging voltage = 4 kV), Max = 65 MW

80

80 Electric Energy (charging voltage = 7 kV), Max = 56 kJ

60 40

0

120

Power (charging voltage = 5 kV), Max = 91 MW

Electric Energy (charging voltage = 5 kV), Max = 25 kJ

20

Electric Energy (charging voltage = 4 kV), Max = 20 kJ

1

2

0

3

40 20 0

0 0

60

Electric Energy (kJ)

82

1

Time (ms)

2

3

Time (ms)

(a) Voltage and current

(b) Power and electric discharge energy

Fig. 5. The electric characteristics during the PDT tests.

C L 5

4

Pressure (MPa)

25 mm 125 mm

Charging voltage = 7 kV, Pmax = 5 MPa

75 mm

Sacoustic-structrual

Charging voltage = 5 kV, Pmax = 4 MPa

3 Charging voltage = 4 kV, Pmax = 3 MPa

2

1

Sincident wave 0 0

1

2

cement paste

3

Time (ms)

(ACAX4R)

Fig. 6. Monitored shock pressure during the PDT tests.

500 mm

Blasting Point

Table 1 A comparison of the observed peak pressure of shockwave and UNDEX predictions for TNT [31]. Charging voltage (kV)

Electric energy (kJ)

Max. pressure (MPa) observed [A]

Max. pressure (MPa) prediction [B]

[A]/ [B] (%)

4 5 7

20 25 56

3 4 5

71 77 107

4.2 5.1 4.7

chamber (CAX4R)

AVG. 4.6%

Rigid Surface

Fig. 7 shows the finite element model used in the simulation of the lab PDT tests, which was established based on the actual size of the testing equipment. Four-node axisymmetric acoustic and solid elements with reduced integration scheme (ACAX4R and CAX4R, respectively) were applied to model the cement paste and chamber, respectively. We assumed that the underwater explosion occurs at the blasting point shown in Fig. 7, while the actual electric discharge occurs on the periphery of the impact cell, at a distance of 25 mm from the blasting point. Hence, the acoustic load induced by UNDEX was imposed on the surface Sincident wave, which represents the exterior boundary of the impact cell. The FSI was modeled on the acoustic-structural analysis scheme, in which a fully tied displacement constraint was maintained at Sacoustic-structural, the interface between the cement paste and the chamber. To prevent repeated reflection of the shockwave inside the chamber, a free radiation acoustic boundary condition

Fig. 7. The finite element model used in the simulation of the lab PDT tests.

was assigned for the acoustic elements facing the solid elements. A cavitation limit of zero was assumed for the acoustic elements to represent the absence of tensile fluid pressure on the inner surface of the chamber, which can be induced by the expansion of the fluid. Table 2 presents the material properties used in the analyses. The material properties of the cement paste at an early age were estimated on the assumption that the speed of sound in the cement paste at its initial stage is equal to that of water, following the experimental study of Boumiz et al. [6]. Hence, the bulk modulus of the cement paste Kpaste can be calculated using Eq. (11).

K paste ¼ qpaste  t2 ;

ð11Þ

83

H. Park et al. / Computers and Geotechnics 47 (2013) 78–90 Table 2 The material properties used in simulation of the lab PDT tests. Material

Density (kg/m3)

Bulk modulus (GPa)

Young’s modulus (GPa)

Speed of sound (m/s)

Cement paste Nylon chamber

2400 1300

4.9 2.2

2.0

1425 980

Test (4 kV) Test (5 kV) Test (7 kV) Prediction - best fitted (4 kV) Prediction - best fitted (5 kV) Prediction - best fitted (7 kV)

6

Pressure (MPa)

5 4 3 2 1 0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Time (ms) Fig. 8. The best-fitted predictions of shockwave.

where qpaste is the unit density of the cement paste and tc is the speed of sound in the initial cement paste, assumed to be 1425 m/s. A number of simulations were conducted to determine the UN-

borehole, which was 125 mm in diameter and 2 m in height (Fig. 9). The elements close to the pulse discharge point were finely discretized to have a size of 12.5  20 mm, and a time increment of 6.32  106 was chosen based on the automatic time increment scheme in ABAQUS/explicit [1]. The selected element size and time increment were used to provide a reasonable solution with favorable computational efficiency for the results of the mesh convergence tests and the number of total increments. At the exterior boundaries of the finite elements, infinite elements were applied to prevent any reflections of the stress waves from the boundaries. Kalinin et al. [17] experimentally found that soil particles near the pulse discharge point generally underwent a single or oneand-a-half cycles of movement by a longitudinal wave induced by the PDT. This movement indicates minor reflection or refraction of the shockwave within the borehole. Hence, in this study, a nonreflecting acoustic boundary condition was assigned at the interface between the cement paste and the ground so that the first reflected wave into the cement paste was assumed to have no influence on the subsequent interaction calculations. The material properties of the weak cement paste shown in Table 2 and the UNDEX parameters for a charging voltage of 4 kV obtained from the benchmarking of the laboratory pulse discharge tests were used in the simulation. The ground was assumed to have a linear elastic–plastic behavior, where a Drucker–Prager yield criterion with a non-associative flow rule was applied to model the plastic behavior. Table 4 shows the material parameters of the soil, which were previously examined and used for the uplift analysis of a grout anchor in this test site by Kim et al. [21]. The expansion simulation was conducted according to sequences presented in Table 5.

2m Table 3 The optimized UNDEX parameters for the PDT tests. Charging voltage (kV)

K

k

A

B

mc (kg)

TD (s)

4 5 7

2.2  106 2.5  106 2.6  106

5.5  105 5.5  105 5.5  105

0.18 0.18 0.18

0.185 0.185 0.185

4.4  103 5.9  103 1.1  102

5.5  104 5.5  104 5.5  104

DEX parameter k in Eq. (3) and the bubble simulation time TD that provides the closest prediction of the actual shockwave. The values of K in Eq. (2) were reduced to 4% or 5% of K of TNT [31] to conform to the experimentally observed peak pressure of the shockwave. Fig. 8 shows the best-fitted waveforms of the shockwave. Table 3 presents the optimized k and TD, where the value of k is smaller than that of TNT [31] and TD is almost identical to the arrival time of the peak pressure on the inner surface of the chamber and equals to 0.55 ms. Because the parameters k and TD are related to the detonation speed of the explosion and the lifetime of the bubble, the estimated values indicate faster blasting characteristics and negligible bubble duration in the PDT tests. The estimated UNDEX parameters for the PDT tests with charging voltages of 4 kV presented in Table 3 were applied in the underreaming analyses.

Solid Elements

8m

Acoustic Elements

Infinite Elements 1.75 m

0.25 m

Pulse discharge point

3.3. Simulation of the field underreaming tests 3.3.1. Finite element modeling For the simulation of the borehole expansion tests of Kim et al. [20], an axisymmetric finite element model was developed, in which 4-node axisymmetric solid elements and acoustic elements were used to model the ground and the cement paste that fills the

Fig. 9. The finite element model for the simulation of the expansion tests of Kim et al. [20].

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H. Park et al. / Computers and Geotechnics 47 (2013) 78–90

Parameter

Value

Unit bulk density, c Poisson’s ratio, v0 Young’s modulus, E0 Friction angle, u0 Coefficient of at rest earth pressure, K0 Dilatancy angle, w Cohesion intercept, c0

1960 kg/m3 0.3 45 MPa 38° 0.4 6° 20 kPa

1.6

1.4

1.2 Numerical prediction Field tests (Kim et al., 2009)

1.0

Table 5 The simulation sequences of borehole expansion.

0

Step

Details

1 2 3

Impose gravity load of soil to establish initial K0-stress state of ground Impose hydrostatic load of cement paste to borehole surface of soil Conduct FSI simulation of borehole expansion by imposing shockwave on the borehole for 100 ms Repeat step 3 for 39 times

4

Coefficient of Expansion EC

Table 4 The material parameters of weathered soil [21].

3.3.2. Comparison with the field test results Fig. 10a shows the predicted shape of the borehole after imposing 40 pulse discharges. The prediction for the deformed shape of the acoustic elements as an anchor body agrees with the field observation shown in Fig. 10b. For a quantitative estimation of the amount of borehole expansion, Kim and Cha [23] proposed a coefficient of expansion EC as represented by Eq. (12), where r0 is the original radius of the borehole and re is the radius of the expanded borehole.

EC ¼ r e =r 0

10

20

30

40

Number of Discharges ND Fig. 11. A comparison of the coefficients of expansion EC.

ND = 5

ND = 10

ND = 20

ND = 40

ð12Þ

The EC values obtained from the numerical analysis and the field tests are plotted in Fig. 11 against the number of discharges ND, and they showed good agreement. Both results indicate a gradual increase of EC with ND in a logarithmic relationship, consistent with the results obtained by Kim and Cha [23]. Fig. 12 shows the predicted contours for the variation of the mean effective stress p0 of the soil after 5, 10, 20, and 40 pulse discharges obtained from the simulation. The elements around the discharge point denote a substantial increase of p0 , and p0 increases

Fig. 12. Variation in the mean effective stress induced by the PDT.

with an increase in the number of discharges, which is consistent with previous experimental and numerical studies [22,24,30]. 3.4. Simulation of uplift behavior

Acoustic elements

(a) Prediction

(b) Field observation [20]

Fig. 10. The shape of the expanded borehole.

3.4.1. FE modeling of pullout test Based on the state of the stresses and deformation in the soil obtained from the underreaming analysis, uplift simulations were conducted. Fig. 13 shows the finite elements for the grout anchor, strand, and deformed soil used in the simulation. The axial behavior of the strand was assumed to be linear elastic, and a linear elastic/perfectly plastic stress–strain behavior obeying the von-Mises yield criterion was applied to the grout considering (1) the compression-dominant behavior in the grout domain, (2) the relatively high unconfined compressive strength of the grout up to 20 MPa, and (3) a slight dependency for the expected stress level in the pullout analysis. The material properties are presented in Table 6. The loading procedure was simulated by imposing a linearly

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H. Park et al. / Computers and Geotechnics 47 (2013) 78–90

(spring element)

Grout Anchor

Deformed soil

Residual Uplift Displacement (m)

Uplift displacement of 10 % of anchor diameter

Strand

0.0125

0.0100

ND = 0

ND = 10

ND = 5

ND = 20

0.0075

ND = 40

0.0050

0.0025

0.0000 0

100

200

300

400

500

Uplift Force (kN)

Underreamed Region

Fig. 14. The predicted uplift force-residual displacement curve.

4. Parametric studies 4.1. The resisting mechanism of a PDT-treated anchor

Steel tube Constrained nodes

Fig. 13. The finite element model for the uplift simulation.

Table 6 The material properties of strand and grout.

a

Material

Axial stiffness (kN/m)

Strand Grouta

1.2  104

Young’s modulus (GPa)

Poisson’s ratio, v

Yield strength (MPa)

21

0.2

20 (comp.) / 2 (tens.)

Obtained from Neville [28].

increasing uplift force up to 1000 kN at the top node of the strand. The uplift capacity in the numerical analysis was determined as suggested by Kim et al. [20]. The curve of the uplift force at the top node of the spring element and the residual displacement of the node at the bottom of the anchor were evaluated in advance. The uplift capacity was then estimated when the load at a residual displacement of the anchor reached 10% of the anchor diameter, i.e., 12.5 mm. 3.4.2. The simulation results and the comparison with the field test results The predicted uplift force-residual displacement curves are depicted in Fig. 14. The PDT significantly enhances the pullout performance, and stiffer pullout behavior is observed as the number of discharges increases. From the curves shown in Fig. 14, the uplift capacities qPDT were estimated. The estimations were plotted in association with ND and EC and compared with the experimental results (Fig. 15a and b). Although there is considerable difference in the estimation of the uplift capacity for ND = 5, the numerical predictions and experimental results agree. Both indicate that the application of PDT improved the uplift resistance of the grout anchor. qPDT increased to 1.6 times the uplift capacity of the shaft anchor after 40 discharges. Thus, the numerical model in this study seems reasonable for evaluating grout anchor underreamed by PDT.

Although the enhancement of the uplift capacity by the PDT was confirmed, how the PDT method increases the uplift capacity was compared to a conventional shaft anchor. Hence, with different bonded anchor lengths of 2.0, 2.5, and 3.0 m, additional borehole expansion and anchor pullout analyses were conducted in the weathered soil as described in [20] using the finite element model shown in Fig. 13. Fig. 16a presents the estimated uplift capacities, where nearly constant gaps are found among the predictions for each length of anchors. Fig. 16b shows that the differences between qPDT and qshaft seem to be almost identical regardless of the anchor length. Those results indicate that the gaps in Fig. 16a represent an increase in the uplift capacity due to the extended length of the anchors. Hence, the uplift capacity of a PDT-underreamed anchor may be composed of two independent factors: shaft-resistance and PDT effects, such as the formation of the bulb and the increase of the confining pressure in the surrounding soils. Fig. 17 compares the predicted yielding areas in the soil at the moment of mobilizing uplift capacity predicted by the pullout simulations of anchors with 0 and 15 pulse discharges, respectively. In the untreated case, yielding mainly develops along the circumferential area of anchor body, which implies that the frictional resistant behavior of soil around the anchor is dominant. The PDT-treated anchor shows a broad yielding zone above the expanded bulb. The yielding zone of soil around the bulb was significantly reduced compared to the unremediated case. This difference may be caused by existence of the expanded bulb and the changed stress state of the soil around the bulb. The yielding area over the expanded bulb seems to be similar to that usually predicted in the analysis of plate anchor behavior in sand [27]. Hence, the bulb induces earth resistance in the soil above the bulb. When considering the increase in the mean effective stress around the underreamed region shown in Fig. 13, the smaller amount of yielding predicted in Fig. 17 suggests that the PDT-induced shockwave prohibits yielding of the soil by enhancing the soil’s strength. 4.2. Effect of soil properties As previously mentioned, the SPT procedure is usually accompanied by boring for the PDT application to obtain the local properties of the soil surrounding the borehole [23]. In this study, a set of soil parameters were determined on the basis of their empirical correlations with the SPT N values, conforming to the elastoplastic

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450

Uplift Capacity qPDT (kN)

Uplift Capacity qPDT (kN)

450

400

350

300

Numerical prediction Field tests (Kim et al., 2009)

250

400

350

300 Numerical prediction Field tests (Kim et al., 2009)

250 0

10

20

30

40

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Number of Discharges ND

Coefficient of Expansion EC

(a) qPDT – ND

(b) qPDT – EC

1.7

Fig. 15. A comparison of the uplift capacity q with the field test results [20].

160

500

450

120

qPDT - qshaft (kN)

Uplift Capacity qPDT (kN)

140

400

350

100

Anchor bond length = 2.0 m Anchor bond length = 2.5 m Anchor bond length = 3.0 m

300

80 60 Anchor bond length = 2m Anchor bond length = 2.5m Anchor bond length = 3m

40 20 0

250 0

5

10

15

0

20

5

Number of Discharges ND

10

15

20

Number of Discharges ND

(b) The differences between qPDT and qshaft

(a) Variation of the uplift capacity with bond length

Fig. 16. Variation in the anchor uplift capacity with variations in the anchor bond length.

modeling of the stress–strain behavior of the soil described in the previous section, i.e., linear elastic–plastic behavior obeying the Drucker–Prager yield criterion. Considering the pressure–volume relationship of dry sand [25], i.e., the equation of state, a pressure–volume relationship defined by the above-described elastoplastic model and the constant density of the soil can be assumed during the underreaming analysis because of the relatively low peak pressure amplitude of the PDT-induced shockwave at 3 MPa. For sandy soil having a maximum void ratio emax of 0.7 and a minimum void ratio emin of 0.3, the bulk density was estimated using the relative density Dr estimated by Eq. (13), which was proposed by Skempton [39].

pffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dr ¼ N1 =a ¼ 2NSPT =að1 þ r0v Þ;

ð13Þ

where NSPT is the field-measured SPT N value, rm is the overburden effective stress (tonf/m2), N1 is the SPT N value corrected with respect to the overburden effective stress, and a is a soil constant that generally ranges from 40 to 60 [39]. Using Dr, the void ratio e and bulk density c are calculated by Eqs. (14) and (15), where Gs is the specific gravity of the soil grain (assumed to be 2.7) and cw is the bulk weight of water (=10 kN/ m3). 0

e ¼ emin þ Dr ðemax  emin Þ

ð14Þ

c ¼ Gs cw =ð1 þ eÞ

ð15Þ

For a simple representation of the elastic soil behavior during the complicated stress path for underreaming and pullout, the shear stiffness of the soil G was evaluated by Eq. (16) as half of the initial shear modulus G0 as suggested by Seed and Idriss [35]. K Ge is the modulus coefficient that is equal to 434N1 [36]. pa is the atmospheric pressure taken as 101.3 kPa. p00 is the mean effective stress of the skeleton at the initial state, and m is the stressdependency parameter with a typical value of 0.5. G

G ¼ 1=2  G0 ¼ 1=2  ke pa ðp00 =pa Þm

ð16Þ

Then, the bulk modulus can be determined by Eq. (17).

B¼

2ð1 þ m0 Þ G 3ð1  2m0 Þ

ð17Þ

The friction angle of the soil u0 can be obtained from NSPT by Ohsaki’s empirical correlation [14] as represented by Eq. (18).

u0 ¼

pffiffiffiffiffiffiffiffiffiffiffiffi 20N1 þ 15; in degrees

ð18Þ

Using the above u0 , the coefficient of the at-rest earth pressure K0, i.e., the ratio of the horizontal to vertical effective stress of the

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Coefficient of Expansion EC

2.2 NSPT = 1 NSPT = 10 NSPT = 20 NSPT = 30 NSPT = 40

2.0 1.8 1.6 1.4 1.2 1.0 0

5

10

15

20

Number of Discharges ND Fig. 18. The predicted coefficients of expansion EC.

(a) Anchor with straight shaft

(b) PDT-underreamed anchor

Fig. 17. The predicted yielding zone by the anchor pullout simulations.

soil, was estimated using Jaky’s equation [15] as represented by Eq. (19).

K 0 ¼ 1  sin u0

ð19Þ

Table 7 presents the SPT N values and the corresponding soil properties used in the analyses, where the dilation angle of the soil was assumed to be one-sixth of the friction angle. The same finite elements and UNDEX inputs for the PDT used in the previous section were applied in the expansion simulations, except for the elements representing the cement paste and grout anchor, for which the length was changed to 2.5 m. The pullout analyses were then conducted for the grout anchors, underreamed by 0, 1, 5, 10, 15, and 20 pulse discharges. Fig. 18 presents the predicted coefficients of expansion EC. Gradual increases of EC were found with the increasing number of discharges ND. Depending on the magnitude of NSPT, different expansion behaviors are shown. Larger NSPT values leads to smaller Ec values. In particular, for ND of 20, EC dramatically decreased from 2.2 to 1.24 as NSPT increased from 1 to 40. These results are consistent with the previous testing results of Kim et al. [24] for loose sandy soil with EC greater than 2.0 and Kim et al. [20] for the medium to dense sandy soil that was considered in the previous field test simulation.

Table 7 The SPT N values and the corresponding soil properties used in analyses. SPT N value NSPT

a

E  (MPa)

v

u0 (°)

c (kPa)

c (kg/m3)

w (°)

1 10 20 30 40

50

47.4 103 123 140 160

0.25

19.5 29.1 35.0 39.5 43.3

10

1641 1764 1857 1926 1968

3.3 4.9 5.8 6.6 7.2

Estimated for soil at the depth where pulse discharge imposed, , values were used.

 

 

,

900

Mean Effective Stress (kPa)

Yielded Zone

Yielded Zone

The variations in the mean effective stress p0 of the soil element adjacent to the discharge point are depicted in Fig. 19. With a larger value of NSPT, a bigger increase in p0 was predicted, and this tendency seems to be opposite to that shown in Fig. 18. Thus, as the soil becomes stiffer, the PDT induces less expansion of the borehole but involves a larger increase in the confining pressure of the neighboring soil. Fig. 20 shows the uplift capacities qPDT of the PDT-underreamed anchors obtained from the numerical simulations. Compared to the cases where PDT was not applied, enhanced pullout capacities were predicted with increasing EC and ND. After a significant increase in the uplift capacity due to the first pulse discharge, the growth trend of qPDT weakened as EC and ND increased. Slight discrepancies were observed in the increasing patterns of qPDT depending on the SPT N values. For loose soil (NSPT = 1), a nearly linear relationship was found between qPDT and EC and between qPDT and ND. The increasing trends slowed as NSPT became larger. Fig. 21 shows the relative magnitude of qPDT for an anchor with PDT normalized to qshaft of the anchor without PDT. The application of PDT is favorable for the enhancement of the uplift capacity of anchors in sandy soils in which NSPT is smaller than 20. Greater than 40% growth was estimated compared to the unremediated case, while slight increases in the uplift capacity are shown for soils with NSPT values larger than 30. An enhancement that was lower than 25% was predicted. This result infers that PDT is effective for increasing the uplift capacity of anchors in loose to medium sandy soil deposits when constructing a single expanded bulb.

800 700 NSPT = 1 NSPT = 10 NSPT = 20 NSPT = 30 NSPT = 40

600 500 400 300 200 100 0 0

5

10

15

20

Number of Discharges ND

: common Fig. 19. The predicted variation in the mean effective stress of the surrounding soil.

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H. Park et al. / Computers and Geotechnics 47 (2013) 78–90

600

600

NSPT = 40

N SPT = 1 N SPT = 10 N SPT = 20 N SPT = 30 N SPT = 40

Uplift Capacity qPDT (kN)

Uplift Capacity qPDT (kN)

NSPT = 30 NSPT = 20

500

NSPT = 10

400

NSPT = 1

300

500

400 ND = 20

300 ND = 10 ND = 1

200

200 0

5

10

15

20

ND = 15

ND = 5

ND = 0

1.0

1.2

1.4

1.6

1.8

2.0

Number of Discharges ND

Coefficient of Expansion EC

(a) qPDT – ND

(b) qPDT – EC

2.2

Fig. 20. The predicted uplift capacities for sandy soils with NSPT values ranging from 1 to 40.

1.6

NSPT = 1 NSPT = 10 NSPT = 20 NSPT = 30 NSPT = 40

2.5

1 bulb , 1 bulb , 1 bulb , 1 bulb ,

2 bulbs , 2 bulbs , 2 bulbs , 2 bulbs ,

3 bulbs 3 bulbs 3 bulbs 3 bulbs

1.4

qPDT / qshaft

qPDT / qshaft

1.5

[ NSPT = 1, qshaft = 205 kN ] [ NSPT = 10, qshaft = 318 kN ] [ NSPT = 20, qshaft = 379 kN ] [ NSPT = 30, qshaft = 436 kN ]

1.3 1.2

2.0

1.5

1.1 1.0 1.0

0

5

10

15

20

Number of Discharges ND Fig. 21. The predicted relative magnitude of qPDT normalized to qshaft.

4.3. The effect of configuration of the bulbs in the anchor body PDT is also applied to make an anchor with multi-bulbs. In the field, two or three bulbs are usually created, and a previous study reported that the use of multi-bulbs increased the resistance capacity compared to a single bulb [18]. To obtain an optimized resistance performance of the multi-underreamed anchor, PDT should account for the effects of the characteristics of bulbs, including the number of bulbs, the number of pulse discharges in each bulb, and the distance between the bulbs. Here, a parametric study was carried out to examine the aforementioned properties of the bulbs in an anchor body that was 2.5 m in length. The analyzed cases are presented in Table 8. Fig. 22 shows the predicted values of qPDT/qshaft from analyses 2A and 3-A, where qPDT and qshaft represent the uplift capacities of

Table 8 The analysis cases for the estimation of the pullout capacity of anchors with multibulbs. Group

Number of bulbs

Number of discharges, ND

SPT N values, NSPT

Distance between bulbs (m)

2-A 2-B 3-A 3-B

2 2 3 3

1, 1, 1, 1,

1, 1, 1, 1,

1.0 0.5 0.75 0.5

5, 5, 5, 5,

10, 10, 10, 10,

15, 15, 15, 15,

20 20 20 20

10, 20, 30 10, 20, 30 10, 20, 30 10, 20, 30

0

5

10

15

20

Number of Discharges ND Fig. 22. The predicted qPDT/qshaft from analyses 2-A and 3-A.

anchors with and without bulbs, respectively. With a higher number of bulbs, larger uplift capacities are denoted; however, slightly different growth tendencies are found, depending on NSPT. For soils with NSPT smaller than 10, the increase in qPDT/qshaft between the prediction for two bulbs and that for three bulbs is smaller than between that for one and two bulbs. The opposite behaviors are observed for soils with NSPT larger than 10. Soils with smaller NSPT values have a higher efficiency in terms of pullout capacity enhancement. As NSPT increases from 1 to 30, the values of qPDT/ qshaft vary from 1.97 to 1.40 (2 bulbs) and 2.28 to 1.63 (3 bulbs). The predicted overall trends in the uplift capacities with the number of bulbs agrees with the field test results of [18], although differences exist in the absolute values of qPDT/qshaft. The effect of the distance between the bulbs on the pullout capacity of the anchors was investigated in analyses 2-B and 3-B, and the results were compared with those obtained from 2-A and 3-A (Fig. 23). For anchors with two bulbs, slightly lower uplift capacities were predicted as the distance between the bulbs became smaller. However, depending on NSPT, the effect of the distance between the bulbs appeared to be substantial in the estimation of the pullout capacity of anchors with three bulbs. For soils with NSPT less than 10, the effect seems to be insignificant. The predictions for soils having larger NSPT denote a considerable decrease in the pullout capacity as the distance between the bulbs became smaller when the number of discharges was larger than 10.

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NSPT = 1, distance = 1 m NSPT = 10, distance = 1 m NSPT = 20, distance = 1 m NSPT = 30, distance = 1 m

600 500 400 300

NSPT = 1, distance = 0.5 m NSPT = 10, distance = 0.5 m NSPT = 20, distance = 0.5 m NSPT = 30, distance = 0.5 m

NSPT = 1, distance = 0.75 m NSPT = 10, distance = 0.75 m NSPT = 20, distance = 0.75 m NSPT = 30, distance = 0.75 m

800

Uplift Capacity qPDT (kN)

Uplift Capacity qPDT (kN)

700

NSPT = 1, distance = 0.5 m NSPT = 10, distance = 0.5 m NSPT = 20, distance = 0.5 m NSPT = 30, distance = 0.5 m

700 600 500 400 300

Anchors with 2 bulbs

200

Anchors with 3 bulbs

200 0

5

10

15

20

Number of Discharges ND

(a) 2 bulbs

0

5

10

15

20

Number of Discharges ND

(b) 3 bulbs

Fig. 23. The effect of distance between the bulbs on the estimation of the uplift capacity.

Fig. 24 shows the yielding areas in the soil at the moment of mobilizing uplift capacity, predicted from the analysis in cases 3-A and 3-B. The result from 3-A indicates similar yielding behavior compared to the anchor with a single bulb as shown in Fig. 16, which presents a broad and a slight yielding zone of soil above and around the expanded bulb, respectively. The prediction in 3-B denotes a significant reduction in the yielding zones among the bulbs, except for soil regions above the top bulb. The shapes of anchors in the figure appear to be slight different. In Fig. 24a, the parabolic shape of the anchor shaft is shown between two bulbs, whereas a nearly straight shape is shown in Fig. 24b. This difference implies that when the distance between two bulbs decreases, the deformations by each PDT-induced shockwave are superim-

posed. Hence, PDT underreaming forms a cylindrical shaft-anchor with an increased diameter in soil conditions where a small amount of underreaming is induced by PDT. In such a case, the earth resistance above the bulb may not be sufficiently mobilized, which can reduce the uplift capacity (Fig. 22). The yielding zone in Fig. 23b may refer to the decrease in the yield area among the bulbs due to the strengthening of the soil during shock loading. This result means that for an anchor embedded in medium to dense sandy soil, the neighboring bulbs need to be sufficiently apart from each other to ensure a larger uplift capacity of the anchor. 5. Summary and conclusions To analyze the uplift behavior of a grout anchor underreamed by pulse discharge technology (PDT), a series of numerical simulations were performed for the entire PDT procedure and the pullout tests. The electric blasting and shockwave generation by PDT were alternatively modeled by the underwater explosion (UNDEX) model. The equivalent UNDEX parameters were determined by benchmarking the laboratory PDT tests. Full-scale PDT-underreaming and the subsequent pullout tests in dry sand deposits conducted by Kim et al. [20] were then simulated on the basis of FSI analyses and uplift analyses based on simple modeling of the compression anchor behavior. The predicted expansion of the borehole and uplift force–displacement behaviors were compared with the field observations to validate the numerical model. Lastly, a parametric study was conducted to examine the effects of soil and anchor characteristics on the uplift behavior of the PDT-underreamed anchors. Based on the results obtained in this study, the following conclusions were reached.

Yielded Zone (a) Case 3-A

Yielded Zone (b) Case 3-B

Fig. 24. The predicted yielding zone from the anchor pullout simulations in dry sand with NSPT = 30.

1. Based on a comparison with the field tests conducted by Kim et al. [20], the FSI analysis of borehole expansion and the simple modeling of the uplift behavior of the grout anchor applied in the study were found to be suitable to simulate the actual performances of soils and anchors treated by PDT. Conforming to previous experimental studies, a logarithmic relationship was predicted between the coefficient of expansion and the number of discharges. In addition, agreement was found between the estimation of the uplift capacity of the anchor and the test results, although the interface behavior between the soil and shaft of the grout was simply modeled as being roughly tied. 2. From the limited cases of analyses that were performed to investigate the effects of anchor length on the uplift capacity, the predicted increased amount of uplift capacity by PDT under-

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reaming appeared to be independent of the anchor length. In turn, the overall uplift capacity is the sum of the frictional resistance along the shaft and the underreaming effect, which can be presumed as an earth pressure resistance above the expanded bulb and enhanced frictional resistance of soil around the bulb. Hence, by supplementing various cases of analytical and experimental studies, estimating the pullout capacity of a PDT-underreamed anchor may be possible using a simple linear equation. 3. The results of the parametric study indicated a more than 40% increase in the uplift capacity compared to the unremediated when the PDT was conducted in loose to medium sand, in which the blow count number of standard penetration tests, NSPT, was less than 20. The predicted increase in the uplift capacity was insignificant in dense soils with NSPT over 30, where the enhancement of uplift capacity was found to be lower than 25% of that of the shaft anchor. This finding implies that PDT is more effective for increasing the uplift capacity of anchors in loose to medium sand than in dense sandy soil. 4. The analysis results with multi-underreaming showed sufficient increases in the uplift capacities: up to twice the shaft anchor’s capacity in loose sand and over 50% growths in very dense sand by forming three bulbs in the anchor. Particularly for an anchor embedded in medium to dense sand with three bulbs, it was predicted that narrower spacing between the neighboring bulbs results in smaller increase in the uplift capacity due to the reduction of the earth resistance among the bulbs due to the straightened shape of the underreamed anchor.

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