Drilling Mechanism of Autonomous Burrowing Robotfor Lunar Subsurface Exploration

Kenji NAGAOKA ∗1, Takashi KUBOTA∗2, Ichiro NAKATANI ∗2, Satoshi TANAKA∗2∗1The Graduate University for Advanced Studies,∗2JAXA/ISAS

E-mail:nagaoka@nnl.isas.jaxa.jp

Abstract

　 Lunar and planetary subsurface exploration is ofconsiderable significance. The authors have studiedthe strategies for subsurface excavation and propul-sion for the development of a lunar subsurface ex-plorer. The authors have proposed an autonomousrobotic explorer which can burrow into the soils.Based on the strategies the authors have already con-sidered, this paper especially focuses on the excava-tion mechanism of a robotic system for near-future lu-nar subsurface exploration. The main objective of theproposed robot is to bury a scientific observation in-strument like a long-term seismometer under the lunarsurface, which is covered with very compacted lunarregolith. Therefore, an efficient excavation mechanismis required. In this paper, the authors propose a newscrew drilling system with double rotation, which iscalled N-RDM (Non-Reaction Drilling Mechanism).Through some experiments and analyses, this paperdiscusses the feasibility and effectiveness for the pro-posal of a burrowing robot system.

1 Introduction

　 Since the creation of time, the Moon is one of mostattractive celestial bodies for human beings. The out-comes of the Apollo missions by the U.S. is partic-ularly recognized as significant achievement in spacedevelopment [1]. Many countries have tried to im-prove upon it. From various sample returns and mea-surements, a lot of important knowledge has beengained in lunar and space science. However, theMoon still has a lot of unanswered questions such asits origin, chemical components, and internal struc-ture. To answer these questions, it is required to ob-tain global information about the Moon in future lu-nar exploration missions. Therefore, the authors pro-pose a robotic system for burying a scientific obser-vation equipment like a long-term seismometer un-der the surface to investigate the internal of the Moon(Fig.1). In general, the lunar surface is covered withvery fine soils, called lunar regolith, and the lunar re-golith has high adiabatic property. Given this, the in-struments buried in the lunar regolith can be kept at a

constant temperature, even at night. To accomplishthis, some scientists say that the instrument shouldbe placed about 1 meter below the surface. Conse-quently, this enables it to function for a long timewithout any heaters. Also, the buried seismometercan realize better contact with the surrounding lunarregolith, so it would be able to capture very small lu-nar seism. This paper first describes the strategies forsubsurface propulsion of a burrowing robotic systemand its required mechanisms. Then, this paper espe-cially discusses the excavation mechanism, which isvery important for such a system. Finally the authorspropose a novel excavating mechanism that is suitablefor a burrowing robot, and present the results of someexperiments.

2 Burrowing Robot

2.1 Subsurface mobile robots

　 So far, there have been numerous researches ofrobots with a locomotion mechanism. But, most ofthem have paid attention to just only mobility. Thereare several environments for movement, such as onthe ground, inside of tubes, and under water. Mean-while, some have developed biomimetic robots thatcan move like underground creatures, for instancean earthworm or a snake, and their locomotion ismostly restricted to the above. However, studies onautonomous robots that can move underground are es-pecially rare. That is because soils are too complexand unsteady as a locomotion environment. Also, anysuch study would need to consider both the locomo-tion and how to generate the space for locomotion.

Fig.1: Lunar subsurface exploration mission

Table 1:Planetary excavation systemsmechanism size weight robustness purpose

Bucket Wheel simple large heavy × sampling

Penetrator simple middle, long middle × investigation

Drill simple narrow, long light sampling

Burrowing Robot complex compact light investigation

Fig.2: Overview of planetary excavating robots

2.2 Conventional robots for planetarysubsurface exploration

　 Planetary exploration with excavation of soils hasreceived a lot of attention in the world. Table 1 showsa comparison of planetary excavation systems. Here,the robustness refer to the capability to have differentexcavating opportunities. So far, there have been pro-posal for digging robots for planetary subsurface ex-ploration [2]-[6]. However, it would be hard for theserobots to bury a large instrument such as a seismome-ter. An overview of some proposed ideas which areclassified by length and diameter is shown in Fig.2.The ICEBREAKER of CMU and the Lunar-A pene-trators of JAXA are not actually autonomous burrow-ing robots, but robotic systems for subsurface investi-gation or a similar objective. Hence, these two differ-ent methods are included in Fig.2 for comparison.

2.3 Strategies for subsurface propulsion

　 Based on the past researches, the authors set thefollowing assumptions:

• The burrowing robot is carried by the rover

• Power is supplied by a cable from the ground sta-tion

• Target depth is several meters from the surface

• Target soil-layer is lunar regolith

• The robot diameter is about 0.1 m(The seismometer’s diameter: about 0.05 m)

Next, the authors define two phases for subsurfacepropulsion by a burrowing robot, and consider differ-ent strategies for each phase as follows.

1. Make space

• Compress regolith

• Remove and back transport regolith

2. Advance forward

• Utilize contact with surrounding regolith

• Utilize excavated regolith

• Self advancing without utilizing regolith

Now there are different ways to achieve the abovestrategies [7], and the proposed robots shown in Fig.2can be classified by these strategies.　 By applying Apollo’s data regarding compressionindex [1], the authors have previously concluded thatit would be unlikely that the regolith can be com-pressed for making space. Also the authors concludedquantitatively by applying the rankine’s soil pressuretheory that a burrowing robot needs to generate apropulsive force [7]. Therefore, from the next sectionthis paper describes a concrete excavating mechanismand uses it as a baseline.

3 Screw Drilling Mechanism

　The earth-auger method is a screw mechanism usedin excavation systems on Earth. According to the ref-erense [8], the screw drilling state can be in one of thefollowing 3 states.

〈1〉 Auger moves forward one pitch forward after onerotation, soils are not excavated, and there is noshear on the edges of the screw.

〈2〉 Auger moves forward less than one pitch forwardafter one rotation, and soils are excavated andtransported backward.

〈3〉 Auger cannot move forward at all despite rota-tion.

In general, the state of an earth-auger is in the state〈2〉. This paper also assumes this state. This exca-vating mechanism using a helical screw is one of themajor methods in the field of construction and civil

engineering. The shapes of these helical screws is de-termined by past empirical knowledge. The actionperformance is the almost completely controlled byoperation, and there have been very few theoreticalstudies. The method involves human beings and largescale systems in order to treat the behavior of compli-cated soils. Some researchers focus on the estimationof discharging soils and the description of the dynam-ics [9]. The results indicate a very good estimation,but the objective is limited to such discharging estima-tion and some theoretical considerations are lacking.　 Another use of screw mechanism is in screw piles.The application is for improving soft ground, as acountermeasure against liquefaction almost all of theresearches are focused on the bearing capacity. Ad-ditionally, like the earth-auger its mechanism is notclearly understood.　 A third use of the screw mechanism is found insystems for conveying materials. These researchesare principally focused on the screw conveyors, whichtransport materials obliquely upward, so it is hard toapply the concept to a burrowing robot system.　 From these, the authors have decided to do somebasic experiments for the analysis and clarification ofthe behavior of the screw excavating mechanism.

4 Non-Reaction Mechanism

4.1 Proposal of Double Rotation System

　 With the above considerations, the required prop-erties for a robotic excavation mechanism are the fol-lowing:

• Fore-soil removal and transportation backward

• Generation of propulsive force

• Dust prevention mechanism

Therefore, a screw drill, which has a series of spiralwings, is one of candidates. However, a serious prob-lem is that a single spinning drill results in a reactionforce to the body. This reaction can generate the fric-tion between the body and the supporting soil reduc-ing the drilling efficiency. It can also lead to the wob-bling of the propulsion axis. This paper proposes anew type of spiral screw drill unit as a novel excava-tion mechanism to improve this problem.　 A mechanism using double rotations already ex-ists as the doughnut-auger method. It has two rotat-ing parts, an inner-screw and an outer-casing. Themechanisms of the reaction reduction have not beenstudied so well. Thus, it cannot effectively reduce thereaction. An outer-casing for reducing the reactionis very useful for drilling a hole, but it increases thenumber of driven parts, which means an increase inpower consumption. It is also structural redundant fora burrowing robot. Due to these factors the authors d-

(a) Contra-rotor　　 (b) Twin-rotor　　 (c) Dual-spin　Fig.3: Double rotation screws

evelop a new screw mechanism with N-RDM (Non-Reaction Drilling Mechanism) by separating thescrew parts, and applied it to a burrowing robot. Here,the double rotation methods are classified into threetypes as shown in Fig.3. The contra-rotor type (a) hasone drilling unit which has the contra-rotation axis atcoincident with the rotation axis. The twin-rotor type(b) consists of two drilling units whose rotation axesare fixed and parallel to each other. The dual-spintype (c) has one drilling unit whose rotation axis isspinning around another spin axis. Each type has tworotation axes, so it is possible to cancel the reaction.However, there are some notable differences. Firstly,the contra-rotor type (a) is compact in size, and it canbe estimated that it would have an equivalent excavat-ing performance with the single screw drilling mech-anism. Secondly, the twin-rotor type (b) has an unex-cavated space between the two drilling units, resultingin an anomalous shape. It is impossible to make onecircular hole, and a constraint on the body shape mustbe considered. Thus, it can be estimated that it wouldhave lower efficiency. Thirdly, the dual-spin type (c)has a driven part not used for drilling, so the efficiencywould be ever lower. According to these considera-tions, the authors adopt the contra-rotor type and willdo some experiments in the near future.

4.2 SSD

　 The schematic of the basic model, which is calledSSD (Single Screw Drilling) unit, is represented inFig.4(a). Also Fig.4(b) shows the prototype. The de-veloped SSD is a conceptual model of the contra-rotortype screw, and it serves as a basic dynamics modelfor theoretical analysis.　 The SSD unit consists of a body part and an exca-vation part. Furthermore, the excavation part has aninner cone, called CONE, and a helical screw wingwhich winds around the CONE, called SCREW. Asshown in Fig.4,αSC[rad] denotes the angle of inclina-tion of the SCREW’s center position andp[m] denotesthe SCREW’s variable pitch. The screw length isL[mm], and the maximum screw diameter isD[mm].In general, the SCREW model can be mathematicallyexpressed as a function of a logarithmic spiral.

　　 (a) Simplified model　　　　　 (b) Prototype　Fig.4: SSD unit

4.3 Contra-rotor

　 Figure 5(b) shows the prototype of a new contra-rotor screw, which the authors developed. This pro-totype consists of the body, the front screw and therear screw. The two screws can be driven indepen-dently by separated motors to analyze the behavior.Also Fig.5(a) represents the schematic. From this thelength of the front and the rear screw is bothL/2, thefront’s diameter isD/2, the rear’s diameter isD, andthe ratio between the moment of inertia between thefront and the rear is approximately 1:31.

4.4 Basic experiments

4.4.1 Experimental set-up

　 Some experiments with the SSD and the contra-rotor screw have been carried out as shown in Fig.6.Also in the experiment, the soil is silica sand and thespecifications are shown in Table 2. The front screwand the rear screw of the contra-rotor are indepen-dently controlled. The starting situation is that thescrew is completely buried and the body stands outon the surface, and the propulsive force comes fromjust its weight. Through the experiments, the encodervalue which indicates motor rotation speeds, the ac-tive time and the average sinkage are measured, andthe average penetration speed is calculated.

　　 (a) Simplified model　　　　　 (b) Prototype　　Fig.5: Contra-rotor screw unit

Fig.6: Experimental environment

4.4.2 Drilling performance: SE

　 The Specific Energy, which is calledSE, is a ma-jor index of drilling performance [10]. In this paper,the authors evaluate the excavating properties by ap-plying this index. The required energy per minute,E[MJ/min], is calculated as follows.

E = W× πD × f × 10−9 (1)

W = w1 × g+ w2 (2)

where,D[mm] is the diameter of hole,f[rpm] is therotation speed,W[N] is propulsive force,w1[kg] isthe robot mass,g[m/s2] is the gravity accelerationand w2[N] is all external forces without the weight.Here, the volume of the soil removed per minute,V[m3/min], is calculated by using the penetrationspeedPR[m/hr] as following.

V = π ×(D × 10−3

2

)2× PR

60(3)

Thus, SE[MJ/m3] is defined by the following equa-tion.

S E=EV=

0.24 · fD · PR

· (w1g+ w2) (4)

From the above equation (4), an increase inSEmeansthat its performance becomes lower.

4.4.3 Equivalent angular velocity

　 To apply the evaluation equation (4), an equivalentangular velocity of the double rotation screw is con-sidered. By equating the rotating energies, the equiva-lent angular velocityωS[rad/s] is derived. Here, the

Table 2: Specifications of screw units

L D Mass αSC

SSD 50 mm 50 mm 356-867 g 10 degContra-Rotor 50 mm 50 mm 604 g 10 deg

total energy of rotations is described as follow, ne-glecting the body’s rotation.

12

I1ω21 +

12

I2ω22 =

12

(I1 + I2)ω2S (5)

where,I1[kgm2] is the moment of inertia of the frontscrew,I2[kgm2] is the moment of inertia of the rearscrew,ω1[rad/s] is the angular velocity of the frontscrew andω2[rad/s] is the angular velocity of the rearscrew. Hence, from the above,ωS is derived by thefollowing equation.

ωS =

√I1ω

21 + I2ω

22

I1 + I2(6)

Through the experiments,ωS [rad/s] can be convertedto the rotation speed as following in order to utilizethe above equation (4). Also, the ratios of the angularvelocities and the rotation speed between screws areboth defined as follows.

K =ω1

ω2=

f1f2

(7)

5 Experimental Results

5.1 Results: Non-reaction

　When the SSD driven only the body rotates whilethe remain in place due to the frictional resistancefrom the soil against the screw. It is not really anexcavation or propulsion mode, and the result of theSSD unit indicates the SSD is unsuitable for a bur-rowing robot. In contrast, a reduction of the bodyrotation is confirmed in the case of the contra-rotorscrew. Also, the non-reaction condition is confirmedat aroundK=60. On the other hand, slight wobblingmotion of the body was observed even near the non-reaction condition. This could be the effect of by theconnecting cords or the mass decentering. Alternativ-

Fig.7: Dynamics model of contra-rotor screw

ely, the wobbling could also arise from the skew sym-metry of the screw. This could be resolved by using adual spiral structure. The authors plan to do more ex-periments for measuring the driving torques and con-sider the theoretical approaches to find out the mech-anism. However, the small wobbling behavior is notregarded as a critical problem given the frictional re-sistance against the body underground.

5.2 Results:SE

　 Figure 8 and 9 show the experimental results. Inthe case of the SSD, when the body is free the bodyrotates with any screw rotation. Hence the body isfixed by hands to stop the body reaction in order tomeasure the drilling properties. As shown in Fig.8(a),SE is directly proportional toW and would be sat-urated with increase off in the experiments of theSSD. In Fig.8(a), the blue line denotes the approxi-mate function aboutSEwith constantf and variableW, and the green line indicates averageSEwith con-stantW and variablef. The lower performance withincreasingW is due to the increase of frictional resis-tance. This is expected because an increase ofW isproportional to an increase of normal force betweenthe screw and soils below. This fact is confirmed inFig.8(b), which indicates relationship amongPR, W,andf. Given these results,PR is directly proportionalto f which is equal to the angular velocity andWhas aninsignificant effect onPRduring these experiments. Itis obvious that with screw driving with noW, propul-sion stop. So it is preferable for the burrowing robotto be able to generate arbitrarily an optimalW.　 Next the results of contra-rotor screw are shown inFig.9. The body is fixed by hand in Fig.9(a), the bodyremains free in Fig.9(b), and Fig.9(c) indicates a com-parison of the relationship amongSE, f andPR in (a)and (b). Also in Fig.9, the horizontal axis representsthe ratioK as referred to above under the constantW,and each line denotes the approximates curve associ-ated with the discrete data ofSE, f, andK. As shown inFig.9(a), the propertySEis directly proportional toK,and also,PRandf heavily depends onK and shows asimilar approximate curve. At aroundK=1, SEis sus-tained compared with the SSD data, where the greenline is the estimatedSEof the SSD at the same mass.In other words, the effectiveness is indicated if thenon-reaction state could be achieved. On the otherhand, although the curves shown in Fig.9(b) is verysimilar with the curves in Fig.9(a), and it shows an ob-vious performance reduction at lowerK. Instead, thenon-reaction state is confirmed at aroundK=60, andthe performances of Fig.9(a) and Fig.9(b) indicate in-deed almost the same value near the non-reaction con-dition. Therefore, this result indicates the validity ofnon-reaction mechanism.

(a) Relationship betweenSE, f, andW

(b) Relationship betweenPR, f, andWFig.8: Experimental results of SSD

5.3 Analysis

　 According to the above results, the following re-sults are obtained from the experiments:

• The Penetration speed is proportional to the rota-tion speed

• The best excavating performance condition:K=1

• The Non-reaction condition: aroundK=60

5.3.1 Equation of rotation

　 Here, based on the simplified dynamics model asshown in Fig.7, the equations of rotation are definedas follows.

I0ω0 = −T1 + T2 − sgn(ω0) · TF0 (8)

I1ω1 = T1 − TF1 (9)

I2ω2 = −T2 + TF2 (10)

where,I0[kgm2] is the moment of inertia of the body,ω0[rad/s] is the angular velocity of the body, andsgn(·) is a signum function. The angular velocity indi-cates a positive value when the direction is anticlock-wise direction along the rotation axis passing through

(a) Body fixation

(b) Body free

(c) Comparison between the body is fixed and freeFig.9: Experimental results of contra-rotor screw

the center of the robot (Fig.7). Also,T1[Nm] is thedriving torque for the front screw,T2[Nm] is the driv-ing torque for the rear screw,TF0[Nm] is the fric-tional torque against the body,TF1[Nm] is the fric-tional torque against the front screw andTF2[Nm] isthe frictional torque against the rear screw. Thesetorques are positive values, irrespective of the rotationdirections.

5.3.2 Non-reaction control

　 Next by using above equations (10), this paperdescribes the mechanism of canceling the counter-torque against the body. Given the state that the reac-tion against the body is approximately zero, the workof the friction TF0 would be zero. Thus, the driving

torques for the non-reaction are derived as follows.

ω0(t)→ 0 : T1(t) = T2(t) (11)

On the other hand, when the body rotates, the rela-tionship between the driving torques is expressed asthe following equations.

ω0(t + ∆t) = ω0(t) + ω0(t) · ∆t → 0

...T1(t) − T2(t) =I0ω0

∆t+ sgn(ω0) · TF0 (12)

Here,∆t is the cycle of the input torque, and the re-lationship between torques would be described in thecase of controlling the body’s small reaction withinone cycle input.

5.3.3 Evaluation of DC motor

　 The electric properties of a DC motor are calcu-lated as follows.

VM = IM · RM + ke · ω + VB (13)

T = kt · IM (14)

where,VM[V] is the input power,IM[A] is the electriccurrent of the motor,RM[Ω] is the electric resistanceof the motor with the internal resistance,ke[Vs/rad]is the factor of counter electromotive force,ω[rad/s]is the directed relative angular velocity,VB[V] is thevoltage drop by the friction of the brush,T[Nm] isthe driving torque,kt[Nm/A] is the torque constant.Where, the no-load current of the motor is ignored.In fact, ke is really equal tokt andVB by the metal-lic brush has almost negligibleVB, hence the aboveequation (13) is rewritten as follows.

VM = IM · RM + ke · ω (15)

Also from an absolute coordinate, the motor stator’sdirected angular velocity isωsh[rad/s] and a motorshaft’s directed angular velocity isωsh[rad/s]. So theω is defined as following.

ω = ωsh− ωst (16)

In general, the relationship between the motor torqueand the angular momentumH[kgm2/s] is written asfollows.

T = H = Ishωsh− Istωst (17)

where,Ish[kgm2] is the moment of inertia of the motorshaft andIst[kgm2] is the moment of inertia of the mo-tor body including the stator. Thus, from these consid-erations,T is calculated as follows.

T = ke ·VM − ke · ω

Ra(18)

From the above considerations, Figure 10 shows thesimulation result of an example indicating the DC mo-tor characteristic. Here, the input voltageVM is as-sumed to be constant and the values regarding the fric-

Fig.10: Simulation result of DC motor characteristic

tional resistances, which are given with the ratio be-tween the surface area of the body and the screw,assume much smaller than the torques. Accordingto Fig.10, the frictional resistance reduce directly themotor’s rotation speed with a constant voltage. There-fore the output torque depends on the higher friction,but the another rotation speed keeps accelerating un-til the driving torque would be equal to the resistancetorque.　 In these experiments, the non-reaction state is in-deed observed as a value aroundK=60. However,based on a theoretical analysis, given no-load stateKwould be due around 105 with the gear reduction ra-tio, the moment of inertia and the voltage. Where, thegear reduction ratio of the front screw is 1.875 andthe rear one is 0.5. The ratios are indeed not equiva-lent values tof in Fig.8 or 9. Thereby, the effects offrictional resistance reduce the rotation speed orK asabove considered. Even the ratio between surface ar-eas of screws assumes 1:3, the differential can becomea critical problem for the control. There could be sev-eral other factors, but the most dominating factor isthe frictional resistance. The tendency depends on thefrictional resistance, and more considerations are re-quired with the theoretical analysis. Thus, the theoret-ical approaches are significant future works for anal-ysis of the soil frictional resistance against the screwmotion during the driving of the burrowing robot.

5.3.4 Sustaining the drilling performance

　 To sustain the excavating performance SE, or pro-duce the required propulsive speedPR, the control ofK is necessary as mentioned above. The control lawalso depends on the friction conditions. With the non-reaction control, the absolute values of each motortorque retain same. In other words, the absolute angu-lar accelerations of the motors depend on the torquehistory and the frictional resistances which include auncertainty. So it is surely needed to make the hybridcontrol law with the non-reaction and the performancesustainment, and that is our future work.

6 Conclusion

　 In this paper, the authors have discussed an au-tonomous burrowing robot system for the lunar sub-surface exploration. The authors especially proposeda novel excavation mechanism, called contra-rotorscrew with N-RDM, for the development of the bur-rowing robot for lunar subsurface exploration. In par-ticular, this paper has presented the important andbasic guideline concerning a relationship among thepenetration speed, the rotation speed, the propulsiveforce and the total performanceSE. And then the au-thors have indicated the feasibility and the effective-ness through some experimental analyses. Some ex-periments for the validation of the proposed excavat-ing method are listed as future works. Also, furthertheoretical analysis of the screw mechanism for exca-vating soils and its hybrid control law are in progress.

Acknowledgments

　 Dr. Otsuki, who is an assistant profes-sor at ISAS/JAXA, supported the experiments.Mr.Edmondo, who is a doctoral course student in thelaboratory, helped in writing this paper. Here, the au-thors would like to express my appreciation for them.

References

[1] G. Heiken, D. Vaniman and B. French, ”LunarSourcebook”, Cambridge University Press, 1991.

[2] K. Watanabe, S. Shimoda, T. Kubota and I. Nakatani,”A Mole-Type Drilling Robot for Lunar SubsurfaceExploration”,Proc. of the 7th iSAIRAS, AS-7, 2003.

[3] K. Yoshida, N. Mizuno, T. Yokoyama, Y. Kanamori,M. Sonoyama and T. Watabe, ”Development of Mole-type Robot for Lunar/Planetary Sub-Surface Explo-ration, and its Performance Evaluation” (in Japanese),Proc. of the 20th Annual Conf. of the RSJ, 1J35, 2002.

[4] Y. Liu, B. Weinberg and C. Mavroidis, ”Design andModeling of the NU Smart Space Drilling System(SSDS)”,Proc. of the 10th ASCE Aerospace DivisionInternational Conf. on Engineering, Construction andOperations in Challenging Environments (Earth andSpace 2006), 2006.

[5] R. Campaci, S. Debei, R. Finotello, G. Farziano, C.Bettanini, M. Giacometti, G. Rossi, G. Visentin andM. Zaccariotto, ”Design and Optimization of A Ter-restrial Guided Mole for Deep Subsoil Exploration-Boring Performance Experimental Analysis”,Proc. ofthe 8th iSAIRAS, 2005.

[6] S. P. Gorevan, T. M. Myrick, C. Batting, S. Mukhrrjee,P. Bartlet and J. Wilson, ”Strategies for Future MarsExploration: An Infrastructure for The Near andLonger Term Future Exploration of The Subsurfaceof Mars”, Proc. of the 6th Int. Conf. on Mars, 2003.

[7] K. Nagaoka, S. Tanaka and T. Kubota, ”Study onExcavation Mechanism for Lunar Subsurface Explo-ration by Burrowing Robot”,Proc. of the 17th Work-shop on Astrodynamics and Flight Mechanics, C-21,2007.

[8] The Society of Geotechnical Engineering ed., ”SoilMechanics and Foundation Engineering -Recent con-struction methods-” (in Japanese), The Society ofGeotechnical Engineering, 1967, pp.11-13.

[9] H. Fukada, M. Ootsuka, Y. Tanaka and Y. Shioi, ”Dis-charging Characteristics by Screw Auger of GravelDrain Pile” (in Japanese),JSCE J. of ConstructionEngineering and Management, Vol.62, No.2, 2006,pp.203-212.

[10] H. Raiba, ”Specific Energy as a Criterion for Drill Per-formance Prediction”,Int. J. of Rock Mech. Min. Sci.and Geomech. Abstract, Vol.19, 1982, pp.39-42.