In situ strength profiles along two adjacent vertical drillholes from digitalization of hydraulic rotary drilling

Xuefn Wng,Peng Peng,Zhigng Shn,Zhongqi Yue,*

a Department of Civil Engineering,The University of Hong Kong,Hong Kong,China

b PowerChina Huadong Engineering Corporation Limited,Hangzhou,China

Keywords: Drilling process monitoring (DPM)Hydraulic rotary coring process Constant drilling speed Coring-resistant strength

ABSTRACT Drilling speed and associated analyses from factual field data of hydraulic rotary drilling have not been fully utilized.The paper provides the reference and comparison for the utilization of drilling information from two adjacent vertical drillholes that were formed with the same hydraulic rotary drilling machine and bit.The analysis of original factual data is presented to obtain the constant drilling speed during net drilling process.According to the factual data along two adjacent drillholes,the digitalization results respectively include 461 linear zones and 210 linear zones with their constant drilling speeds and associated drilling parameters.The digitalization results can accurately present the spatial distributions and interface boundaries of drilled geomaterials and the results are consistent with the paralleled site loggings.The weighted average drilling speeds from 2.335 m/min to 0.044 m/min represent 13 types of drilled geomaterials from soils to hard rocks.The quantitative relation between drilling speed and strength property is provided.The digitalization results can statistically profile the basic strength quality grades of III to VI from soils to hard rocks.The thickness distributions of four strength quality grades are presented for each individual type of geomaterials along two drillholes.In total,50.2% of geomaterials from drillhole A are grade IV and 57.4% of geomaterials from drillhole B are grade III.The digitalization results can offer an accurate and cost-effective tool to quantitatively describe the spatial distribution and in situ strength profile of drilled geomaterials in the current drilling projects.

1.Introduction

Quantitative description of ground characterization is the essential and foundation for geotechnical engineering and geoscience to be carried out safely,effectively,and reasonably.Hydraulic rotary drilling is the most common method for ground investigation.The downhole variations on the mechanical and geophysical properties can be quantified by the laboratory measurements and in situ tests for the core samples from hydraulic rotary drilling (Anderson et al.,2002;Bazilevskaya et al.,2013).However,due to the long turn-around cycle,the laboratory measurement is hard to perform real-time testing in the disturbed geomaterials (Yang et al.,2020).The point load test as one of the primary in situ strength measurement methods has limited applications,because the results have the significant difference in conversion coefficients for strength property of various types of rocks (Quane and Russell,2003;Singh et al.,2012).Moreover,the laboratory core measurements and some in situ tests for many hydraulic rotary coring drillholes can be prohibitively expensive and logistically challenging (Flinchum et al.,2018).The accurate and cost-effective methods for profiling the in situ strength property of drilled geomaterials have significant importance.Several researchers attempted to study the drilling information as an in situ test of the drilled geomaterials (Somerton,1959;Schunnesson,1998;Chiang and El?as,2000;Woodhouse,2003;Zang et al.,2008;Li et al.,2014;Rai et al.,2014;BS EN ISO 22476-15:2016,2016;Vezhapparambu and Ellefmo,2020).

However,the relevant techniques and methods have not become a common ground investigation tool in the civil and mining industries because the random variations of calculated penetration rate along drill depth were found in the applications of the relevant techniques (Schunnesson,1998;Rai et al.,2014).Li et al.(2014)surveyed the field of measurement while drilling (MWD) technology and concluded that the random variations of penetration rate cause that the estimation of rock properties quantitatively from drilling data has apparently reached a bottleneck.Yue et al.(2004)pointed out that the random variations of the penetration rate were due to the pre-assigned depth advancement increment method in the recording of the drilling information and proposed the realtime series method to analyze the drilling speed (or penetration rate).By comparing the analysis results of pre-assigned depth interval sampling method and real-time series method,Wang et al.(2021) stated that the measured drilling time by pre-assigned depth interval sampling method contains all the processes including some auxiliary operations which are not belonging to the actual drilling time (or the net drilling time).These auxiliary operations can mainly cause the error or random variations of the drilling speed and they can be recognized by the real-time series method.

Recently,numerous researchers focus on the analysis results of drilling information by real-time series method.Chen and Yue(2015,2016) used the real-time drilling parameters to determine weathering grades of Hong Kong volcanic during the non-coring pneumatic percussive drilling.Wang et al.(2019) conducted the laboratory drilling tests for measuring rock mass characteristics by drilling parameters.He et al.(2019,2020) proposed the empirical method for determining and predicting the mechanical properties of rock mass by drilling information.Yang et al.(2020)studied on the digital drilling test-based rock uniaxial compressive strength (UCS)measurement method.Feng et al.(2020) estimated the optimal drilling efficiency and rock strength by controllable drilling parameters.Jiang et al.(2021) studied the real-time drilling risks monitoring method by laboratory models.Reviewing previous researches,most of them studied the drilling information by laboratory test data and non-coring drilling projects.Further studies on factual field data in real-time series are needed,especially for the hydraulic rotary coring process as the typical ground investigation method.

Furthermore,BS EN ISO 22476-15:2016 (2016) stated that the drilling speed is related to the mechanical strength of drilled formation,but effective change in the characteristics of the ground needs to be further studied.Elkatatny (2021) proposed that predicting the drilling speed plays a key role in the success of the drilling operation.As the important drilling parameter,the drilling speed is the basis for the studies on the drilling information.Table 1 summarizes the researches on drilling information using drilling speed as the main parameter.Although drilling speed by real-time data is the basis of most drilling information researches,the analyses of drilling information still have not become a common in situ test for ground investigation.Because the factual field data of several parameters such as torque are difficult and expensive to collect on site,especially for the hydraulic rotary coring project(Wang et al.,2021).In fact,drilling speed is the key parameter to show the coringresistant strength of drilled geomaterials.Therefore,the accurate and efficient calculation of drilling speed by factual field data and the practicability of associated analysis by drilling speed are important for the applications of drilling information.More studies on quantitative description of drilling speeds and associated analysis results by the factual field data from the traditional coring hydraulic rotary drilling project have been motivated.

Table 1 The researches on drilling information using penetration rate(or drilling speed) as the main parameter.

In this paper,the digital factual data in real-time series along two hydraulic rotary drillholes are presented to calculate the drilling speeds and profile the ground characterization.The digitalization results indicate that the spatial distribution and in situstrength profile can be quantitatively and cost-effectively measured by factual data of current hydraulic rotary drilling project.The comparisons of the factual data along two adjacent drillholes formed by one hydraulic rotary machine show that the results are consistent and accurate.

2.Hydraulic rotary drilling process with digital monitoring system on site

In the tunnel construction project at Hangzhou,the hydraulic rotary drilling was used to offer the core samples and associated test results for ground investigation.For the utilization of drilling information,one hydraulic rotary drilling machine was equipped with digital monitoring system.The system contains three parts:the displacement monitoring part,the pressure monitoring part,and the rotation monitoring part.The three monitoring parts can automatically and continuously record digital factual data as electrical signal in real-time series.The displacement monitoring system measures the downward or upward displacement of the swivel drill chuck head along two vertical hydraulic cylinders during the whole drilling process,including one swivel displacement sensor.The hydraulic pressure monitoring system measures the downward hydraulic pressure and upward hydraulic pressure,including two pressure sensors.The downward hydraulic pressure data represent the downward thrust power to keep the bottom drill bit contacting geomaterial surface and drill down to the target depth and the upward pressure data represent the upward force for the upward movement of drill bit and rods.The rotation monitoring system measures the rotation speed (orRPM),which represents the horizontal force to cut the geomaterial surface.The resolution of each transducer is 1 μm,1 kPa,and 1 r/s,respectively.These drilling parameters are collected and transmitted by the data acquisition unit.It records the four signals simultaneously in the forms of voltage output in real-time series and the sampling interval is 1 s.

The digital monitoring system is portable and convenient for installation and causes few obstacles during drilling process for either the drilling machine or the routine operations on site.In this case,two adjacent vertical drillholes were drilled by one typical XY-1-type hydraulic rotary drilling machine equipped with the digital monitoring system and one polycrystalline diamond compact drill bit with 110-mm diameter.The drilling fluid is bentonite slurry made of SM vegetable gum,bentonite and water with the weight ratio 1:5:100.The circulation of drilling fluid prevents the drillhole from collapsing,cools and lubricates the drill bit.The site photos of digital monitoring system,drillhole locations and the schematic diagram with monitoring system are shown in Fig.1.

Fig.1.Hydraulic rotary drilling machine with digital monitoring system for two drillholes in Hangzhou project: (a) Site photo of drillhole A,(b) Location map,(c) Site photo of drillhole B,and (d) Schematic diagram with monitoring system.

Fig.2.Vertical hydraulic rotary drilling rigs along two drillholes on site:(a)Schematic diagram,(b)Drill rods,(c)Comparison between drill bit and rods,and(d)Casing protection.

Furthermore,the drill rods can hardly contact with the geomaterials surrounding the drillhole because of the drilling rigs and drilling conditions in this case,as shown in Fig.2.The reasons are presented here.First,the diameter of drill bit is 110 mm and larger than the 55 mm diameter of the steel drill rods during the vertical hydraulic rotary drilling.Second,for the total length of the connected drill rods and drill bit is less than 50 m,their rigidity and stiffness are high against bending due to the limited amounts of the vertical thrust and axially rotational loading (Yue et al.,2004).Thus,the drill rods would have negligible bend to contact the surrounding geomaterials.Thirdly,the 6 m casing protection of 114 mm in diameter from the ground surface is used to prevent the surrounding soil collapse since the collapsed upper soil can fill the gap between the rods and the geomaterial surrounding the drillhole.Hence,the chance of a direct contact between the drill rods and the geomaterials is very limited.Such contact can induce additional friction force and affect the drilling speed and drilling process,which needs to be further considered and avoided (Chen and Yue,2010).

The two adjacent drillholes are both located near Qiantang River.The distance of two drillholes is 1.1 km.The strata in the drilled area are mainly Cretaceous Chaochuan Formation,Devonian Xihu Formation,and Quaternary System.The global positioning system (GPS) coordinates of drillhole A is 30°11′34′′N and 120°07′40′′E.According to the manual site logging of drillhole A,there are nine types of geomaterials along the 38.1 m drillhole.They are fill,silty clay,gravelly soil,completely decomposed argillaceous siltstone,highly decomposed argillaceous siltstone,moderately decomposed siltstone,moderately decomposed argillaceous siltstone,highly decomposed tuffaceous glutenite,and moderately decomposed tuffaceous glutenite,respectively.The GPS coordinates of drillhole B is 30°11′52′′N and 120°08′09′′E.According to the manual site logging of drillhole B,there are four types of geomaterials along the 20.2 m drillhole.They are fill,mucky soil,completely decomposed quartz sandstone,and moderately decomposed quartz sandstone,respectively.The selected core samples and corresponding stratigraphic legends by the national standard GB/T 958-2015 (2015) of all the geomaterials along two drillholes are shown in Fig.3.To improve the drilling efficiency,the core samples of three soil strata (fill,silty clay,gravelly soil) were not collected along drillhole A.

3.Digitalization results of net drilling process along two drillholes

3.1.Factual drilling parameters of net drilling process

Along two drillholes in this case,the monitoring system continuously records the four types of factual drilling parametersDPMy(displacement,thrust pressure,upward pressure,and rotation speed) once per second during the full drilling process.The factual digital drilling data in real-time seriesfy(Tx)during the full drilling process are shown in the following equation:

whereyis one of the monitored drilling parameters (including displacement,thrust pressure,upward pressure,and rotation speed);andTxis the sampling time during the full drilling process(x=1;2;3;???;X,in whichXis the last sampling time during the full drilling process along the drillhole),Tx=Tx-1+ΔT,in which ΔTis the time-sampling interval (1 s in this case).

Fig.4 presents the four types of factual drilling parameters in real-time series along drillhole A from 09:29:53 a.m.to 09:39:43 a.m.According to the research by Wang et al.(2021),the factual data of net drilling process can be selected from the complete factual data.The net drilling process means the actual coring operation in which the drill bit breaks the geomaterials and advances into deeper geomaterials.During hydraulic rotary drilling,the operator uses the chuck device to control the drill spindle which is connected to the drill rods and bit.The chuck device can move down and up along the ram stroke length of two vertical hydraulic cylinders.To drill deeper soils,the chuck device clutches the drill spindle and moves drill bit down.The chuck declutches the spindle to return to the start level after completing one ram stroke length,and then clutches the spindle again to drill deeper.Thus,the downward displacement of chuck represents the net drilling process.During the net drilling process,the displacement data decrease with different drilling speeds.Thus,the net drilling process in Fig.4 is expressed as 18 linear segments from zoned1to zoned18.Furthermore,two auxiliary operations can be excluded from the net drilling process.In Fig.4,zonesp1andp2represent the operation of pushing drill chuck downward and zonesu1tou2represent the operation of pulling drill chuck upward.They have the much higher movement speeds than all the drilling speeds along two drillholes.

Fig.3.Nine types of strata from drillhole A and four types of strata from drillhole B with selected core samples and corresponding stratigraphic legends.

Fig.4.Analysis for the hydraulic rotary coring process of original factual data along drillhole A.

3.2.The curve of drill bit advancement with net drilling time and associated constant drilling speed

The linear summation of the chuck displacement during the net drilling process (zonesd1tod18) can represent the total bit advancement during the full process in Fig.4.To analyze the conversion relation,two definitions should be clarified.First,the vertical advancement of chuck can be defined as the total downward displacement of the chuck during the net drilling process along one ram stroke length of the cylinders.One vertical advancement means that the chuck device clutches the drill rods and bit to move them down from the top position to the bottom position along the ram stroke.In Fig.4,there are totally five vertical advancements of chuck along the ram stroke length of the cylinders.Thus,the calculation of the No.kvertical advancement of chuck along the ram stroke length during the net drilling process can be expressed as

whereTkmis themth sampling time along the No.kvertical advancement of chuck,in whichk=1;2;3;???;K,Kis the last vertical advancement of chuck along the whole drillhole,m=0;1;2;???;Mk,andMkis the last sampling time along the No.kvertical advancement of chuck;DPMadvancement(Tkm) is the vertical advancement of chuck along the ram stroke length during the sampling time period ofTk0toTkm;DPMdisplacement(Tkm) is the factual displacement data at themth sampling time along the No.kvertical advancement of chuck;andDPMdisplacement(Tk0) is the factual displacement data at the starting sampling time along the No.kvertical advancement of chuck.

Second,the factual drilling data set in real-time series during the net drilling process can be realigned with a new time sequence of one regular time increment ((i.e.1 s in this case).The new time sequence of drilling data set during the net drilling process can be defined as the net drilling time by

Fig.6.The curve of drill bit advancement with net drilling time and associated drilling parameters by factual data along two drillholes.

wheretis the net drilling time,andt=0;1;2;???;N,in whichNis the last net drilling time along the whole drillhole:TjMjis theMjth sampling time along the No.jvertical advancement of chuck;andMjis the last sampling time along the No.jvertical advancement of chuck.

Because the high rigidity and stiffness of the connected extension rods and drill bit,the drill bit advancement (or the drilling depth) can be represented by the accumulated vertical advancement of chuck along the ram stroke length of the cylinders.The drilling depth with the net drilling time is calculated by

whereDepthDPM(t) is the accumulated drilling depth at the net drilling timet;DepthDPM(0) is the starting depth (the starting depths along two drillholes in this case are both 0 m);andDPMadvancement(TjMj)is the vertical advancement of chuck along the ram stroke length during the sampling time period ofTj0toTjMj.

Therefore,the drilling depth of the full process in Fig.4 is shown as the curve of drill bit advancement with net drilling time in Fig.5.The curve consists of 18 connected linear zones from zone d1to zone d18.Each linear zone has a constant slope gradient or constant drilling speed.The determination for the constant drilling speed of each linear zone can be described as

Fig.5.The curve of drill bit advancement with net drilling time and associated drilling parameters.

whereDrilling speediis the constant drilling speed of theith linear zone;tiis the starting net drilling time of theith linear zone(i=1;2;3;???;n,in whichnis the last linear zone along the drillhole);and Δtiis the total net drilling time of theith linear zone.

In Fig.5,the constant drilling speeds of 18 linear zones(d1tod18)vary from 0.129 m/min to 0.318 m/min.The downward thrust pressure,upward pressure and rotation speed fluctuate in a narrow range with the average values of 0.823 MPa,0.051 MPa and 159 r/min,respectively.The corresponding standard deviations are 0.022 MPa,0.024 MPa and 29 r/min,respectively.During the net drilling process of the hydraulic rotary drilling,the downward thrust pressure is fixed to fluctuate within the certain range of high gear,the upward pressure is fixed to fluctuate within the certain range of standby gear,and the rotation speed is fixed to fluctuate within the certain range of working gear.

3.3.Analysis results of factual drilling data along two drillholes

According to the above-mentioned analysis results,two curves of drill depth with net drilling time and associated parameters along two drillholes are presented in Fig.6a.The drill depth measured by digital data along drillhole A is 38.068 m.The drill depth measured by digital data along drillhole B is 20.125 m.The corresponding drill depths by manual loggings along two drillholes are 38.1 m and 20.2 m with the measurement accuracy of 0.1 m.The differences of depth by digitalization results and depth by manual loggings along two drillholes are 0.032 m and 0.075 m,respectively.The relative differences are 0.08% and 0.37%,respectively.

As a result of digitalization analysis along two drillholes,Fig.6b shows a total of 461 linear zones with different constant drilling speeds along drillhole A and a total of 210 linear zones with different constant drilling speeds along drillhole B.The average thrust pressure,upward pressure and rotation speed of each linear zone are also shown in Fig.6c,d and e,respectively.For the digitalization results of drillhole A,the constant drilling speeds of 461 linear zones change from 0.015 m/min to 2.76 m/min.The average thrust pressure,upward pressure and rotation speed of each linear zone fluctuate within a relatively narrow range of 0.442-1.076 MPa,0.030-0.239 MPa and 102-171 r/min,respectively.For the digitalization results of drillhole B,the constant drilling speeds of 210 linear zones change from 0.006 m/min to 2.9 m/min.The average thrust pressure,upward pressure and rotation speed of each linear zone fluctuate within a relatively narrow range of 0.432-0.91 MPa,0.031-0.113 MPa and 120-167 r/min,respectively.Drilling itself can be considered as an in situ measurement for geomaterial characterization(Somerton,1959;Chiang and El?as,2000;Yue et al.,2002;Woodhouse,2003).Yue et al.(2004)and Yue(2014)proposed that each linear segment with the associated slope gradient can represent the constant drilling speed of a homogeneous geomaterial,and the constant drilling speed is related to the coring-resistant strength property of drilled geomaterial.The linear zones with constant drilling speeds contain rich information about the drilled geomaterials along two drillholes.

3.4.Influencing factors for the constant drilling speeds along two drillholes

To research the influencing factors for the constant drilling speed,the effects of thrust pressure,upward pressure,rotation speed and linear correlation coefficient on the constant drilling speed of each linear zone along two drillholes are presented in Fig.7.The linear correlation coefficient,denotedR2orr2,is a number computed directly from the data that measures the strength of the linear relationship between two variables (Glantz and Slinker,2001).The linear correlation coefficient ranges from 0 to 1.In this case,the better the regression of linear zone with constant drilling speed fits the factual data,the closer the value of linear correlation coefficient is to one.

Fig.7.The relations between constant drilling speed of 461 linear zones along drillhole A and 210 linear zones along drillhole B and corresponding drilling parameters in the same zones: (a) Mean values of downward pressure,(b) Mean values of upward pressure,(c) Mean values of revolution,and (d) Linear correlation coefficient.

In Fig.7a,as the constant drilling speed of each linear zone increases,the corresponding average thrust pressures fluctuate within the range of 0.432-1.076 MPa with the average value of 0.82 MPa and standard deviation of 0.065 MPa from the digitalization results of two drillholes.Theaveragevaluesof thrustpressuresfromdrillholesAand B are 0.808 MPa and 0.845 MPa,respectively.InFig.7b,astheconstant drilling speed of each linear zone increases,the corresponding average upward pressures fluctuate within the range of 0.03-0.239 MPa with the average value of 0.062 MPa and standard deviation of 0.023 MPa from the digitalization results of two drillholes.The average values of upward pressures from drillholes A and B are 0.023 MPa and 0.054 MPa,respectively.In Fig.7c,as the constant drilling speed of each linear zone increases,the corresponding average rotation speeds fluctuate within the range of 102-171 r/min with the average value of 150 r/min and standard deviation of 12 r/min from the digitalization results of two drillholes.The average valuesofrotation speedsfromdrillholes AandBare150r/minand151 r/min,respectively.

Hence,the results indicate that the drilling parameters for each linear zone including the downward thrust pressure,upward pressure and the rotation speed have limited effects on the variations of the constant drilling speed for the same linear zone.As the drilling speeds increase from 0.006 m/min to 2.9 m/min along two drillholes,these three parameters randomly fluctuate within the certain range.During the net drilling process,the downward thrust pressure and the rotation speed are fixed in the working gear and the upward pressure is fixed in the standby gear.

In Fig.7d,all the linearcorrelation coefficients among a total of 671 linear zones are larger than 0.9938 with the average value of 0.9981 and standard deviation of 0.001.It verifies the accuracy of constant drilling speed of each linear zone.The average values of linear correlation coefficients from drillholes A and B are 0.9982 and 0.9979,respectively.The two drillholes were drilled by one XY-1-type hydraulic rotary drilling machine and one polycrystalline diamond compact drill bit.Therefore,the in situ strength properties(or coringresistant strength)mainly cause the variations of drilling speeds.As the drilled geomaterials vary from soil(such as silty clay)to hard rock(such as sandstone),the constant drilling speeds of linear zones decrease from 2.9 m/min to 0.006 m/min along two drillholes.The comparison results along two drillholes reveal the following:

(1) As the constant drilling speed of each linear zone increases,the corresponding thrust pressures,upward pressures and rotation speeds fluctuate within a relative narrow range.

(2) The thrust pressures,upward pressures and rotation speeds have limited effects on the variations of the constant drilling speeds among a total of 671 linear zones along two drillholes.

(3) The constant drilling speed of each linear zone has direct relation with the in situ strength property (or coringresistant strength) of the drilled geomaterials.

In addition,factual field data in Fig.7 and above descriptions show that the thrust pressure and rotation speed along two drillholes are controlled to fluctuate in a limited range.The corresponding digitalization results are analyzed under controlled drilling conditions with fixed operating mode of the drilling rig.In fact,the variations of drilling conditions including thrust pressure and rotation speed can influence the drilling speeds of the same geomaterials.The influence needs to be considered for further studies and wider applications.

4.Quantitative description of the spatial distributions along two drillholes

4.1.Spatial distributions of digitalization results compared with paralleled manual logging along drillhole A

Figs.8 and 9 show the digitalization results along drillhole A with linear zones of Nos.1-461 from 0 m to 38.068 m and the corresponding stratigraphic column by site loggings.Nine types of strata and associated stratigraphic legends along drillhole A are shown in Fig.3.Because each linear zone with the corresponding drilling speed has its individual thickness,the weighted average drilling parameters are the calculations that consider the varying thickness of a series of linear zone as

Fig.8.Relationship between digitalization results and corresponding stratum description along drill depth 0-15.7 m by site loggings from drillhole A.

Fig.9.Relationship between digitalization results and corresponding stratum description along drill depth 15.7-38.1 m by site loggings from drillhole A.

wherenis the number of linear zones to be averaged (461 linear zones along drillhole A in total and 210 linear zones along drillhole B in total);Xiis the value of drilling parameters of theith linear zone;andwiis the thickness of theith linear zone applied toXias the weight.

In Fig.8,the digitalization results with linear zones of Nos.1-27 from ground to 5.512 m show the relatively high drilling speeds,which correspond to the superficial deposits of Quaternary system with the strata thicknesses of 5.5 m by site loggings.The linear zones of Nos.1-3 with weighted average drilling speed of 1.29 m/min correspond to the fill stratum.The linear zones of Nos.4-10 with weighted average drilling speed of 2.335 m/min correspond to the silty clay stratum.The linear zones of Nos.11-27 have the average drilling speed of 1.63 m/min.The digitalization results with linear zones of Nos.28-146 from 5.512 m to 15.628 m correspond to the sedimentary rocks with the strata thicknesses of 10.2 m by site loggings.The stratum of completely decomposed argillaceous siltstone has the weighted average drilling speed of 0.85 m/min with linear zones of Nos.28-46.The stratum of highly decomposed argillaceous siltstone has the weighted average drilling speed of 0.419 m/min with linear zones of Nos.47-62.The stratum of moderately decomposed siltstone has the weighted average drilling speed of 0.116 m/min with linear zones of Nos.63-92.The stratum of moderately decomposed argillaceous siltstone has the weighted average drilling speed of 0.293 m/min with linear zones of Nos.93-146.

In Fig.9,the digitalization results with linear zones of Nos.147-461 from 15.628 m to 38.068 m correspond to the tuffaceous glutenite strata of Cretaceous Chaochuan Formation with the thicknesses of 22.4 m by site loggings.The stratum of highly decomposed tuffaceous glutenite has the weighted average drilling speed of 0.467 m/min with linear zones of Nos.238-252.There are two strata of moderately decomposed tuffaceous glutenite with the drill depths of 15.628-21.263 m and 23.233-38.068 m,which have the weighted average drilling speeds of 0.213 m/min and 0.174 m/min,respectively.

According to the digitalization results and site loggings in Figs.8 and 9,each stratum among a total of ten different strata along drillhole A can have several linear zones calculated by Eqs.(2)-(5).Each linear zone has a constant drilling speed.The geomaterial zone in the curve of drill bit advancement with net drilling time can be defined as the set of a series of linear zones for one stratum.The weighted average drilling speed and associated drilling parameters of one geomaterial zone can be calculated by Eq.(6) considering the different thicknesses of a series of linear zones in one geomaterial zone.The weighted average drilling speeds of geomaterial zones can represent the strata strength in a large scale of drilling depth.The corresponding linear zones in one geomaterial zone can show more details on the geomaterials in a small scale of drilling depth such as the characterization of weak zone (Chen and Yue,2016),the presence of silt inter-bedding(Wang et al.,2021),and the heterogeneity of one rock stratum.Drillhole A has ten geomaterial zones representing the ten strata of silty clay to moderately decomposed siltstone.Their weighted average drilling speeds varying from 2.335 m/min to 0.116 m/min and associated weighted average drilling parameters are shown in Fig.10.

In addition,Fig.11 shows the core samples of seven rock strata from 5.5 m to 38.1 m by site loggings along drillhole A.Among a total of ten strata along drillhole A,the paralleled site loggings verify that the different average drilling speeds of linear zones can represent the nine types of geomaterials with their corresponding in-site coring resistant strength.The detailed digitalization results along drillhole A are summarized in Table 2.

Table 2 Comparisons of manual loggings and digitalization results along two drillholes.

Table 3 The digitalization results of constant drilling speed for each geomaterial along two drillholes.

Fig.10.Digitalization results of 10 geomaterial zones and corresponding stratum description along drillhole A.

Fig.11.Seven types of rock strata and corresponding core samples along drill depth 5.5-38.1 m by site loggings from drillhole A.

Fig.12.Relationship between digitalization results and corresponding stratum description along drill depth 0-8 m by site loggings from drillhole B.

4.2.Spatial distributions of digitalization results compared with paralleled manual logging along drillhole B

Figs.12 and 13 show the digitalization results along drillhole B with linear zones of Nos.1-210 from 0 m to 20.125 m and the corresponding stratigraphic column by site loggings.Four types of strata and associated stratigraphic legends along drillhole B are shown in Fig.3.The weighted average drilling parameters are calculated by Eq.(6).The linear zones of Nos.1-16 with weighted average drilling speed of 2.169 m/min correspond to the fill stratum.The linear zones of Nos.17-38 with weighted average drilling speed of 1.284 m/min correspond to the mucky soil stratum.The digitalization results with linear zones of Nos.39-210 from 7.186 m to 20.125 m correspond to the quartz sandstone strata of Devonian Xihu Formation with the thickness of 13 m by site loggings.The linear zones of Nos.39-45 with weighted average drilling speed of 0.493 m/min correspond to the completely decomposed quartz sandstone.The linear zones of Nos.46-210 with weighted average drilling speed of 0.044 m/min correspond to the moderately decomposed quartz sandstone.

Fig.13.Relationship between digitalization results and corresponding stratum description along drill depth 8-20.2 m by site loggings from drillhole B.

Fig.14.Digitalization results of 4 geomaterial zones and corresponding stratum description along drillhole B.

Fig.15.Four types of strata and corresponding core samples along drill depth 0-20.2 m by site loggings from drillhole B.

As above-mentioned geomaterial zones in Section 4.1,drillhole B has four geomaterial zones representing the four strata of fill to moderately decomposed sandstone.Their weighted average drilling speeds of 2.169 m/min to 0.044 m/min and associated weighted average drilling parameters are shown in Fig.14.The weighted average drilling speed and associated drilling parameters of each geomaterial zone are calculated by Eq.(6) considering the thicknesses of a series of linear zones in each geomaterial zone.

Fig.16.The weighted average constant drilling speeds and corresponding standard deviations of different geomaterials along two drillholes.

In addition,Fig.15 shows the core samples of four strata from 0 m to 20.2 m by site loggings along drillhole B.The paralleled site loggings show that the stratum along drillhole B varies from the top layer of fill to the second layer of mucky soil to the third layer of completely decomposed quartz sandstone,and then to the bottom layer of moderately decomposed quartz sandstone.As the drilled geomaterials vary from soil(such as fill)to hard rock(such as quartz sandstone),the weighted average constant drilling speeds decrease from 2.169 m/min to 1.284 m/min to 0.493 m/min,and then to 0.044 m/min,respectively.Among a total of four strata along drillhole B,the paralleled site loggings also verify that the different average drilling speeds of linear zones can represent the four types of geomaterials with their corresponding in situ coring resistant strength.The detailed digitalization results along drillhole B are summarized in Table 2.

5.Quantitative description of the in situ strength profile by digitalization results

5.1.Constant drilling speed for profiling the geomaterial strength along two drillholes

According to the digitalization results,13 different geomaterials along two adjacent drillholes and the corresponding weighted average drilling speeds are shown in Fig.16 and Table 3.In general,five soil strata have the relatively high constant drilling speeds with the weighted average values of 1.284-2.335 m/min.Four completely decomposed or highly decomposed strata have the relatively medium constant drilling speeds with the weighted average values of 0.419-0.85 m/min.Four moderately decomposed strata have the relatively low constant drilling speeds with the weighted average values of 0.044-0.293 m/min.The digitalization results show that the constant drilling speeds of linear zones can quantitatively describe the in situ strength profiles or in situ coring resistant strength.

Table 4 Criteria for basic strength quality classification of rock masses or ground geomaterials from the standard GB/T 50218-2014(2014)and the corresponding digitalization results.

Table 5 Percentage distribution of strata thicknesses with the four strength quality grades measured by digitalization results for the geomaterials along two drillholes.

Moreover,in Fig.16,the moderately decomposed quartz sandstone has the lowest average drilling speed of 0.044 m/min with 165 linear zones,corresponding to the zone thicknesses of 12.123 m.The associated weighted average thrust pressure,upward pressure and rotation speed are 0.852 MPa,0.045 MPa and 155 r/min,respectively.The silty clay has the highest average drilling speed of 2.335 m/min with seven linear zones,corresponding to the zone thicknesses of 2.296 m.The associated weighted average thrust pressure,upward pressure and rotation speed are 0.762 MPa,0.103 MPa and 133 r/min,respectively.The lowest average drilling speed of moderately decomposed quartz sandstone corresponds to the higher average thrust pressure and higher rotation speed than the values of silty clay with the highest average drilling speed.The fact can further indicate that the linear zones with lower drilling speeds represent the stronger or less easily drillable geomaterials.

Fig.17.Laboratory test equipment and the test samples.

Fig.18.Comparison between the rock UCS Rc by laboratory test and the corresponding drilling speed by factual data along two drillholes.

Fig.19.Comparisons of estimated strength property by digital results and measured strength property by laboratory test along two drillholes.

UCS is a basic parameter by laboratory test to represent the strength property of core samples.Currently,effective methods to obtain the rock strength property in real-time on-site are scarce(Yang et al.,2020).The strength property of the rock core samples by UCS test result is further compared with the weighted drilling speeds of linear zones at the same depth.The beginning depth and ending depth of each core sample were recorded on site.Then the depth of each standard specimen with a height of 10 cm can be confirmed.The depth of each specimen corresponds to one or several linear zones with different thicknesses at the same depth.If the depth of one specimen belongs to a part of one linear zone,the specimen has the corresponding drilling speed of the linear zone.If the depth of one specimen corresponds to several linear zones,the weighted average drilling speed of these linear zones by Eq.(6) is the corresponding drilling speed of the specimen.Therefore,each UCS value corresponds to one drilling speed.Forty-seven core samples along drillhole A and fifteen core samples along drillhole B were tested for the UCS by GB/T 50218-2014(2014).The laboratory test equipment and fifteen test samples along drillhole B are shown in Fig.17.The comparison between the strength property by test results and the corresponding drilling speeds by digital data along two drillholes is shown in Fig.18.The results indicate that the strength property of drilled geomaterials increases as the corresponding constant drilling speed decreases,as shown in Eq.(7).With Eq.(7),the estimated values of strength property by digitalization results can be obtained by the corresponding drilling speed.

For the individual digitalization results from two adjacent drillholes,the weighted average constant drilling speeds of 0.116-2.335 m/min along drillhole A correspond to the different geomaterials varying from moderately decomposed strata to highly decomposed strata to completely decomposed strata and then to soil strata.Along drillhole B,the weighted average constant drilling speeds of 0.044-2.169 m/min also correspond to the different geomaterials varying from moderately decomposed strata to highly decomposed strata to completely decomposed strata and then to soil strata.According to Fig.18,the three moderately decomposed strata along drillhole A with the weighted average drilling speeds of 0.293 m/min,0.183 m/min and 0.116 m/min have the corresponding average UCS values of 6 MPa,12.4 MPa and 38.6 MPa,respectively.The moderately decomposed stratum along drillhole B with the weighted average drilling speed of 0.044 m/min has the corresponding average UCS value of 76.5 MPa.For the individual factual data from each drillhole,the constant drilling speed decreases with the strength property of drilled geomaterial increases from soils to hard rocks.After integrating the data from two drillholes together,the results show the same relationship between constant drilling speeds and strength property of drilled geomaterials.

Furthermore,the estimated strength property using Eq.(7) are close to the measured strength property from the UCS tests,as shown in Fig.19.As such,Eq.(7)proposes fair estimates of the UCSs of the drilled geomaterials.The estimated results are consistent with Eq.(8) proposed by Huang and Wang (1997).To build a generalized estimation method based on factual drilling data for wider applications,more studies on various drill machines,drill bit and geomaterial types are required.

whereaandbare the constant coefficients for different drill machines and drill bits.

5.2.Distribution of linear zone thickness with drilling speed for statistically profiling the basic strength grades

For the estimation of strength property of rock mass,several rock mass classifications have been produced during the last 50 years,including rock quality designation (RQD),rock mass rating(RMR),Q-system(Q),geological strength index(GSI),and rock mass quality rating (RMQR) (He et al.,2019).The digitalization results provide a way to statistically profile the basic strength grades by the distribution of linear zone thickness and corresponding drilling speed.Deere (1988) defined RQD as the borehole core recovery percentage incorporating pieces of solid core that are longer than 100 mm in length measured along the centerline of the core.In this case,the thickness and constant drilling speed of each linear zone along one drillhole can be obtained by the factual data.We arrange the thickness and constant drilling speed of each linear zone(VAi;HAi)along drillhole A to form then-pair array from smallest to largest:(VA1;HA1),(VA2;HA2),…,(VAn;HAn),whereVA1≤VA2≤…≤VAn.Along drillhole A,461 linear zones have the constant drilling speeds from 0.015 m/min to 2.76 m/min.Along drillhole B,210 linear zones have the constant drilling speeds from 0.006 m/min to 2.9 m/min.Based on the drilling process monitoring results along each drillhole,theRQD(VDPM) can be defined as the percentage ratio of accumulated linear zone thicknesses with the constant drilling speed less than a given valueVDPMover the whole drill depth along one drillhole:

whereVDPMis the given value of drilling speed,andVX1≤VDPM≤VXn,in whichVX1≤VX2≤…≤VXn,VX1is the smallest drilling speed of each linear zone along drillholeX(VA1=0?015 m/min andVB1=0?006 m/min),VXnis the largest drilling speed of each linear zone along drillholeX(VA461=2?76 m/min andVB210=2?9 m/min);k=1,2,3,…,K,VXKis the drilling speed of the No.Klinear zone along drillholeXwhich is the maximum value in the range of[VX1;VDPM],HXKis the corresponding zone thickness of the No.Klinear zone;and Σ=20?125 m.

Fig.20 shows the distributions of the linear zone thickness with constant drilling speed for statistically profiling the strength quality grades.The vertical axis is theRQD(VDPM)value from Eq.(9)and the horizontal axis is the corresponding linear zone drilling speed.The relation between the distributions of linear zone thicknesses and the constant drilling speeds can be expressed by

Fig.20.Distributions of the linear zone thickness with drilling speed for statistically profiling the strength quality grades by the factual data along two drillholes.

wherepandqare the constant parameters,varying from different drillholes.In drillhole A,a=24.27 andb=78.64.In drillhole B,a=17 andb=79.82.

Compared with the basic strength quality classification of rock masses by the traditional method from GB/T 50218-2014 (2014),the curves along two drillholes in Fig.20 are divided into the following four sections as the drilling speed increases along the horizontal axis:

(1) Section III means that the basic quality grade of drilled geomaterials along two drillholes is mainly grade III by site loggings and laboratory test,corresponding to the drilling speed varying from 0.006 m/min to 0.11 m/min.The strength property can be estimated by Eq.(2) with the values of 36.5 MPa-85.8 MPa.TheRQD(VDPM) values which are the percentage numbers of linear zone thickness with the drilling speed less than the upper bound value of this section(i.e.0.11 m/min)are about 8.7%along drillhole A and 57.4%along drillhole B.It means that the linear zone thickness of geomaterials with the basic strength grade III along drillhole A is less than the thickness along drillhole B.

(2) Section IV means that the basic quality grade of drilled geomaterials along two drillholes is mainly grade IV by site loggings and laboratory test,corresponding to the drilling speed varying from 0.11 m/min to 0.393 m/min.The estimated strength property has the values of 3.6-36.5 MPa.The percentage numbers of linear zone thickness with the drilling speed less than the upper bound value of this section(i.e.0.393 m/min) are about 58.9% along drillhole A and 60.9%along drillhole B.It means that 8.7% and 50.2% of geomaterials along drillhole A have the basic quality grades of III and IV,respectively.Along drillhole B,57.4% and 3.5% of geomaterials have the basic quality grades of III and IV,respectively.

Fig.21.Variations of linear zone thicknesses with their constant drilling speeds and strength quality grades.

Fig.22.Distributions of the linear zone thickness with drilling speed for statistically profiling different geomaterials along drillhole A.

(3) Section V means that the basic quality grade of drilled geomaterials along two drillholes is mainly grade V by site loggings and laboratory test,corresponding to the drilling speed varying from 0.393 m/min to 0.645 m/min.The estimated strength property has the values of 0.5-3.6 MPa.The percentage numbers of linear zone thickness with the drilling speed less than the upper bound value of this section (i.e.0.645 m/min) are about 79.8% along drillhole A and 62.2%along drillhole B.

(4) Section VI (or soil) means that the geomaterials along two drillholes are mainly soils by site loggings and laboratory test,corresponding to the drilling speed varying from 0.645 m/min to 2.9 m/min.The estimated strength property has the values of 0-0.5 MPa.The percentage numbers of linear zone thickness with the drilling speed less than the upper bound value of this section (i.e.2.9 m/min) are both 100% along drillholes A and B.The 20.2% and 37.8% of geomaterials along drillholes A and B are mainly different soils:fill,silty clay,gravelly soil and mucky soil.

The criteria for basic strength quality classification of rock masses from the standard GB/T 50218-2014 (2014) and the associated digitalization results are further summarized in Table 4.Fig.21 shows the variations of linear zone thickness with their constant drilling speeds on dual logarithmic coordinate diagram.Along two drillholes,the zone thicknesses of 671 linear zones are from 0.001 m to 0.439 m,and have the average and median values of 0.087 m and 0.055 m.A total of 671 linear zones with their constant drilling speeds and zone thicknesses are divided into four basic strength quality grades for statistically profiling the in situ strength property or coring-resistant strength of the drilled geomaterials.

Fig.23.Estimated nonlinear regression models of thickness distribution with drilling speed for different geomaterials along drillhole A.

Table 6 Estimated nonlinear regression models of thickness distribution with drilling speed by digitalization results for the different geomaterials along two drillholes.

5.3.Statistical profiles of each geomaterial along two drillholes by digitalization results

The distributions of thicknesses with constant drilling speeds for each geomaterial are statistically profiled by digitalization results.The distribution for each geomaterial along drillholes A and B can be expressed as one nonlinear regression model,and the corresponding parameters vary from different geomaterials.

Fig.22 and Table 5 present the detailed distributions of the linear zone thickness with drilling speed for statistically profiling each of the nine types of geomaterials along drillhole A.The three soil strata (fill,silty clay,gravelly soil) are considered as the soil layer in Fig.22.Among the total thickness of 5.512 m for soil layer along drillhole A,99.3% of soil corresponds to the grade VI by digitalization results,and 85.1% of completely decomposed argillaceous siltstone also corresponds to the grade VI.Most of highly decomposed tuffaceous glutenite,which has a total thickness of 1.97 m,corresponds to the basic strength quality grade V.The 74.8% of highly decomposed argillaceous siltstone with the total thickness of 1.159 m correspond to the basic strength quality grades of IV and V.For moderately decomposed argillaceous siltstone with the total thickness of 5.154 m,94.7%corresponds to the basic strength quality grades of IV and V.For moderately decomposed tuffaceous glutenite and siltstone,they have the total thicknesses of 20.47 m and 1.822 m,respectively.The 83.2% and 100% of the two geomaterials correspond to the basic strength quality grades of III and IV,respectively.Along drillhole A with the whole depth of 38.068 m,the thickness distributions of four basic quality grades of III to VI are 8.7%,50.2%,20.9% and 20.2%,respectively.

Seven curves of different geomaterials along drillhole A in Fig.22 can be expressed as the nonlinear regression models in Fig.23.Along drillhole A,the observational data are modeled by Eq.(11) which is a nonlinear combination of the model parameters and depends on three independent variables.The detailed regression models and corresponding parameters are shown in Table 6.

Fig.24.Distributions of the linear zone thickness with drilling speed for statistically profiling different geomaterials along drillhole B.

Fig.25.Estimated nonlinear regression models of thickness distribution with drilling speed for different geomaterials along drillhole B.

wherezis the horizontal asymptote of the curve,xis the parameter that affects the horizontal translation of the curve,yis the parameter that affects the steepness of the curve,and the sigmoid midpoint can be represented as (z/2 lnx/y).

Fig.24 and Table 5 present the detailed distributions of the linear zone thickness with drilling speed for statistically profiling each of the four types of geomaterials along drillhole B.Among the total thickness of 7.186 m for fill and mucky soil layers along drillhole B,all of them correspond to the grade VI.The 84.9% of completely decomposed quartz sandstone corresponds to the grades of V and VI.For moderately decomposed quartz sandstone with the total thickness of 12.123 m,97% corresponds to the basic strength quality grade III.Along drillhole B with the whole depth of 20.125 m,the thickness distributions of four basic quality grades of III to VI are 57.4%,3.5%,1.3% and 37.8%,respectively.

Four curves of different geomaterials along drillhole B in Fig.24 can be expressed as the nonlinear regression models of Eq.(11) in Fig.25.The detailed regression models and corresponding parameters along drillhole B are also shown in Table 6.

6.Conclusions

The paper presents the utilization of digital factual data in realtime series along two adjacent drillholes.The analysis results of filed factual drilling data explain the real-time series method to obtain the accurate drilling speed during net drilling process.The digitalization results of constant drilling speed quantitatively and continuously describe the spatial distribution and in situ strength profile of drilled geomaterials.

According to the factual data in real-time series,the curve of drill bit advancement with net drilling time is presented along each drillholes.The drill depths measured by digital data along two drillholes are consistent with the site loggings.The curves along two drillholes respectively consist of 461 linear zones and 210 linear zones with their constant drilling speeds and associated drilling parameters.The in situ strength property (or coringresistant strength) of drilled geomaterials mainly causes the variations of drilling speeds from 0.006 m/min to 2.9 m/min along two drillholes.As the drilled geomaterials vary from soil to hard rock,the weighted average constant drilling speeds of geomaterial zones decrease from 2.335 m/min to 0.044 m/min.

Compared with the manual loggings and core samples on site,the digitalization results can show the detailed spatial distributions and interface boundaries of the drilled geomaterials along two drillholes.For drillhole A,a total of ten different strata with the corresponding linear zone thicknesses from 0.688 m to 14.835 m are identified by the digital factual data.For drillhole B,a total of four different strata with the corresponding linear zone thicknesses from 0.816 m to 12.123 m are identified by the digital factual data.The empirical correlation between drilling speeds and UCS values provides a way to quantitatively describe the in situ strength of drilled geomaterials.

Furthermore,four basic strength quality grades of III to VI can be statistically profiled by the constant drilling speed,estimated strength property,and the linear zone thickness designationRQD(VDPM).The 8.7%of all the drilled geomaterials along drillhole A and 57.4% of all the drilled geomaterials along drillhole B correspond to the basic quality grades of III.The 50.2%along drillhole A and 3.5%along drillhole B correspond to the basic quality grades of IV.The 20.9% along drillhole A and 1.3% along drillhole B correspond to the basic quality grades of V.The 20.2% along drillhole A and 37.8%along drillhole B correspond to soils.The distribution for each geomaterial along drillholes A and B can be statistically expressed as one nonlinear regression model.

The digitalization results along two adjacent drillholes in the paper show that the spatial distribution and in situ strength profile can be effectively and objectively measured and estimated by factual drilling data.The paper provides the valuable reference and comparison for the utilization of drilling information and the quantitative description of in situ ground characterization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The paper was partially supported by grants from the Research Grant Council,Hong Kong Special Administrative Region,P.R.China(Project Nos.HKU 17207518 and R5037-18).The authors thank the four reviewers for their time and constructive comments.The first author also thanks the University of Hong Kong for scholarship for his PhD studies.