Application of wave equation theory to improve dynamic cone penetration test for shallow soil characterisation

Miguel Angel Benz Nvrrete ,Pierre Breul ,Rolnd Gourvès

aSol Solution Géotechnique Réseaux,ZA des Portes de Riom Nord,23 Avenue Georges Gershwin,Riom Cedex,63204,France

b UniversitéClermont Auvergne,Institut Pascal,UMR CNRS 6602,Clermont-Ferrand,63000,France

c Polytech Clermont-Ferrand Campus des Cézeaux,2 Avenue Blaise Pascal,Aubière Cedex,63178,France

Keywords:In situ test Dynamic cone penetrometer P.A.N.D.A.Wave equation Wave decoupling Dynamic cone load-penetration(DCLT)curve

ABSTRACT Among the geotechnical in situ tests,the dynamic penetration test(DPT)is commonly used around the world.However,DPT remains a rough technique and provides only one failure parameter:blow count or cone resistance.This paper presents an improvement of the dynamic cone penetration test(DCPT)for soil characterisation based on the wave equation theory.Implemented on an instrumented lightweight dynamic penetrometer driving with variable energy,the main process of the test involves the separation and reconstruction of the waves propagating in the rods after each blow and provides a dynamic cone load-penetration(DCLT)curve.An analytical methodology is used to analyse this curve and to estimate additional strength and deformation parameters of the soil:dynamic and pseudo-static cone resistances,deformation modulus and wave velocity.Tests carried out in the laboratory on different specimens(wood,concrete,sand and clay)in an experimental sand pit and in the field demonstrated that the resulting DCLT curve is reproducible,sensitive and reliable to the test conditions(rod length,driving energy,etc.)as well as to the soil properties(nature,density,etc.).Obtained results also showed that the method based on shock polar analysis makes it possible to evaluate mechanical impedance and wave velocity of soils,as demonstrated by the comparisons with cone penetration test(CPT)and shear wave velocity measurements made in the field.This technique improves the method and interpretation of DPT and provides reliable data for shallow foundation design.

1.Introduction and state-of-the-art

Among in situ tests,the dynamic probing(ISO-22476-2,2005)or dynamic penetration test,noted DPT,is the oldest geotechnical characterisation method(Massarch,2014).DPTs are widely used around the world due to their quick set-up,affordable cost and adaptability to all soil types.However,DPTs provide a single failure parameter:the blow count(N)or the dynamic cone resistance(qd).This value is not an intrinsic parameter of the soil and its interpretation is still largely empirical.

Indeed,to evaluate dynamic cone resistance,the pile driving formulae are usually employed(Lowery et al.,1968;Sanglerat,1972;ISO-22476-2,2005).These are derived from a Newtonian analysis to relate driving energy and cone penetration to the ultimate strength of the soil.Although the result of the pile driving formulae is a good estimator of the soil strength,application of these expressions presents some theoretical limits(Gonin,1996,1999).It is known that penetrometer driving is not a simple problem which can be only solved by Newton’s shock theory and nowadays it is well accepted that it is better represented by the wave equation solution.

In fact,Isaacs(1931)and Smith(1960)suggested applying this theory for the study of concrete pile driving,and subsequently many authors worked on the numerical and practical implementation of the wave equation in order to improve the bearing capacity prediction of driven piles(Smith,1960;Aussedat,1970;Rausche,1970;Rausche et al.,1971,1972,1985;Meunier,1974;Goble et al.,1975,1980;Gonin,1979,1996;Middendorp and Weele,1986;Holeyman,1992;Hussein and Goble,2004).

Fig.1.The P.A.N.D.A.3 instrumented DPT device(Benz Navarrete,2009):(a)Field equipment,and(b)General principle and description of instrumented lightweight dynamic penetrometer.

Notwithstanding the analogy with driven piles,few studies have implemented the wave equation solution to improve the interpretation of DPT.In fact,after the first theoretical and practical experiments published by Palacios(1977),Schmertmann(1978,1979),and Schmertmann and Palacios(1979),numerous works were carried out to evaluate energy transmission in standard penetration test(SPT)and obtain the correctedNSPTnumber for an energy ef ficiency of 60%(N60)(Seed et al.,1985;Skempton,1986;Sy and Campanella,1991;Goble and Aboumatar,1992,1994;Aboumatar and Goble,1997;Butler et al.,1998;Farrar,1998;Farrar et al.,1998;Batilas et al.,2016).

Among the rare works,Aussedat(1970)in France was certainly the first,by means of a laboratory penetrometer,to obtain stressstrain relation of soil using wave equation and experimental measurements.Later,Chen(1991),Goble and Aboumatar(1992,1994),and Liang and Sheng(1993)attempted to determine soil parameters with a laboratory instrumented penetrometer in order to improve the pile bearing capacity prediction by wave equation.Nazarian et al.(1998),Kianirad et al.(2011),and Byun and Lee(2013)instrumented lightweight dynamic penetrometers and applied the same approach to correct cone index value by energy transfer and evaluate the soil strength.Recently,ˇZarˇzojus et al.(2013)and Keleviˇsius andˇZarˇzojus(2016)instrumented a dynamic penetrometer super high(DPSH)(ISO-22476-2,2005)with an accelerometer to improve penetration measurements and blow count.

However,none of these works has made it possible to improve systematically the technology associated with DPT either to implement new methods of measurements and analysis,or to obtain in situ soil stress and strain necessary for the most current geotechnical problems.Although some numerical works on measurement,wave equation interpretation as well as dynamic penetration mechanism in granular media have been published recently(Breul et al.,2009;Escobar Valencia et al.,2013;Quezada et al.,2014;Kotrocz et al.,2016;Poganski et al.,2016,2017;2017;Tran et al.,2016,2017,2018,2019;Zhang et al.,2019),these have not also been implemented in practice.

This paper presents the development of a lightweight dynamic penetrometer based on the principle of P.A.N.D.A(Gourvès,1991;Gourvès and Barjot,1995;Zhou,1997),which currently incorporates dynamic measurements,signal processing and wave equation analysis to continuously provide a dynamic cone loadpenetration(DCLT)curve(Benz Navarrete,2009;Benz Navarrete et al.,2013;Escobar Valencia,2015;Escobar Valencia et al.,2016a,b).A simple interpretation method of this curve makes it possible to directly estimate additional strain and strength parameters of soils as well as the mechanical impedance and wave velocity of soils by means of the method proposed by Aussedat(1970).

2.Dynamic measurements and wave equation analysis

The P.A.N.D.A.,which meanspenetrometerautonomousnumericaldynamicassisted(from Frenchpénétromètreautonomenumériqueassistéparordinateur),is an instrumented lightweight dynamic penetrometer(Gourvès,1991;Gourvès and Barjot,1995;Zhou,1997;Langton,1999).It is composed of rods with 14 mm in diameter and 500 mm in length and of over flowing conical tips with a cross-section of 2 cm2or 4 cm2(15.9 mm or 22.5 mm in diameter,respectively).According to the standard ISO-22476-2(2005),the apex angle of cones is 90°.As shown in Fig.1a,the driving energy is provided manually by means of a hand-hammer mass hitting the instrumented anvil.Driving energy can be thus adapted according to the soil stiffness variations without the measurement being in fluenced by the impact force or being operator-dependent,since for each blow the energy supplied is directly measured.As per ISO-22476-2(2005),in the classic version of P.A.N.D.A.,the dynamic cone resistance(qd)is obtained by means of the modi fied Dutch formula.

A new version of the device was designed by Benz Navarrete(2009),the P.A.N.D.A.3(Benz Navarrete et al.,2013;Escobar Valencia,2015),hereinafter called the instrumented DPT(Fig.1).It is based on the same functional principle of the device developed by Gourvès(1991),but incorporates new sensors.These are installed on the penetrometer’s anvil and used to measure the strainε(x,t)and accelerationa(x,t)variations caused within the rods by the compressional wave created immediately after each hammer blow.The instrumentation of the anvil is composed of strain gauges with a measurement range of±45 kNand installed in a Wheatstone bridge that compensates lateral deformations.The wave force,F(t),is calculated from the measured strainε(x,t)using Hooke’s law.Miniature piezoresistive high-gshock accelerometers with a measurement range of±20,000gare equally installed close to the strain gauges(1g=9.81 m/s2).A displacement sensor is also installed in the central acquisition unit(UCA,from Frenchunité centraled’acquisition).It is connected to the instrumented anvil to measure simultaneously the cone penetration displacements(t)per blow(Fig.1).

The UCA is placed at ground level during the penetration test and continuously records the signals measured by each sensor,which are sampled up to a 250 kHz frequency at 24-bit resolution.Time record per blow is either 100 ms or 200 ms.After each hammer blow,the UCA sends all data to the transfer dialog data(TDD)box which conditions,processes,and stores each measured signal by means of a specially designed software containing the algorithms presented below.The signal processing of raw measurement includes a baseline correction and a signal filtering by means of a low-pass finite impulse response(FIR)filter using a rectangular window and a cut-off frequency of 25 kHz.An example of a measurement recorded during the test is shown in Fig.2.

From a point of view of the penetrometer driving phenomenon,when the hammer,animated by a speedvm,strikes the anvil,a compressional waveu(x,t)is generated in the rods and propagates at a constant velocityctowards the cone of the penetrometer.Afterwards,whenu(x,t)reaches the cone/soil interface,a part of it is transmitted to the soil,causing its deformation.The second part of the wave is re flected upwards into the rods and travels to the top of the penetrometer,where a new downward wave re flection occurs.The phenomenon becomes thus cyclical during cone penetration.

Considering an elastic rod with both uniform sectionAtand lengthLt,if external forces(e.g.skin friction)along the rods are negligible,the waveu(x,t)propagation is described by Jean le Rond d’Alembert’s equation,known as the wave equation:

Fig.2.Example of a raw measurement of force F(t)(black line),acceleration a(t)(grey line)and displacement s(t)(grey dashed line)recorded for one blow during the penetrometer driving.

Being for the case of the penetrometer a one-dimensional propagation phenomenon and according to the method of characteristics(Abbott,1966;Middendorp and Weele,1986;Verruijt,2010),the general and most used solution to this equation is given by the overlap of downwarduf(x-ct)and upwardug(x+ct)waves,whereufandugare the arbitrary respective functions:

Knowing theufandugwaves at a pointxAin the rods,it is possible to determine for eachxpoint along the rods,the stressσ(x,t),strainε(x,t),velocityv(x,t)as well as displacementu(x,t).In fact,for a plane wave and single mode propagation,stress,strain,velocity,and displacement can be expressed in terms of the Fourier transforms and as a function of these waves:

whereA(ω)andB(ω)are the Fourier components of the downwardufand upwardugwaves,respectively;E*(ω)is the complex Young’s modulus;andωis the angular frequency.The wave numberξ(ω)is a complex function de fined byξ(ω)=k(ω)+iα(ω),wherekandαare the real and imaginary components.The two parameters,E*(ω)andξ(ω),depend only on the rod characteristics,geometry and material(Bussac et al.,2002;Lodygowski and Rusinek,2014;Othman,2014).

The general problem is thus reduced to determine the Fourier componentsA(ω)andB(ω),which is the same as determiningufandugin the time domain from Eq.(2).In practice,dynamic measurements during penetrometer driving can be performed by means of strain gauges and accelerometers.However,decoupling waves and the assessment ofufandugcomponents are not an easy task.This is because these waves are noisy and often superimposed in recorded signal,especially in the case of a penetrometer where steel and short rods are employed(wave velocity in steel is about 5200 m/s).Therefore,it is necessary to separate them by means of adapted and precise methods.

2.1.Wave decoupling and cone signal reconstruction

Wave decoupling can be performed by different methods.These are distinguished on the types and number of sensors used as well as initial and boundary conditions.Without underestimating the signal processing methods developed during the last 30 years for pile dynamic test(Goble et al.,1980;Hussein and Goble,2004;Middendorp and Verbeek,2006),actually,the most precise and effective methods for wave decoupling and waveform calculation have been developed for rapid shocks tests,split Hopkinson pressure bar(SPHB)tests as well as solving percussion problems of rocks(Zhao and Gary,1997;Park and Zhou,1999;Bussac et al.,2002;Casem et al.,2003;Jung et al.,2006;Othman,2014),as shown in Lodygowski and Rusinek(2014).

In the present instrumented DPT,the used method is based on a singlexApoint measurement on the rod,at the instrumented anvil,where strainεA(t)and accelerationaA(t)are recorded,from which the velocityvA(t)is calculated.In the pointxAof measurements,the downward and upward waves are separated fromεA(t)andvA(t)recorded signals by

whereεf(x-ct)andεg(x+ct)are the strains of the downward and upward waves,respectively;εA(t)andvA(t)are the strain and velocity records at measurement pointxA;andcis the wave velocity in the steel rods(～5200 m/s).Alternatively,the Bussac-Collet-Gary-Othman(BCGO)method(Bussac et al.,2002)can be used to obtain the Fourier componentsA(ω)andB(ω)of Eq.(3)from which and through an inverse Fourier transformεf(x-ct)andεg(x+ct)signals can be finally obtained.

Once the wavesεf(x-ct)andεg(x+ct)are separated at measurement pointxA,the next step is to reconstruct the strain,stress,velocity and displacement signals at penetrometer’s cone,located at a distance(xJ-xA)below the measurement pointxA.Assuming that there are neither variation in external forces or mechanical impedance along the rods,the iterative method presented in Eq.(5)and proposed by Lundberg and Henchoz(1977),Karlsson et al.(1989),and Carlsson et al.(1990)is suitable to rebuild stressσn(t)and velocityvn(t)for eachxnsection along the rods.impedance changes along the rod string must be solved in advance.

In the case of the current instrumented DPT,where rods are elastic and homogenous,and considering there are no impedance changes at the connection sections as well as no external skin forces along the rods,the major impedance change takes place at the rod/cone and cone/soil sections(represented byCandJin Fig.3).Wave attenuation caused by connectors and length of rods is negligible.In fact,it has been largely studied for the SPTand it was estimated that the effects of energy losses in the rod string to depths of up to 30 m were not signi ficant and less than 1.5%(Palacios,1977;Farrar,1998;Farrar et al.,1998;Odebrecht et al.,2005).Thus,cone signals are calculated by two iterations of Eq.(5):

(1)In the first iteration,we calculate the stressσC(t)and velocityvC(t)for sectionC(notedn)(Fig.3)fromσA(t)andvA(t)recorded in the measurement sectionA(notedn-1)by using Eq.(5).

(2)In the second iteration,stressσJ(t)and velocityvJ(t)for sectionJ(notedn)(Fig.3)are calculated from stress and velocity records that were calculated previously for sectionC(notedn-1).

This method has the advantage of being suitable for a wide

whereΔtn-(n-1)=(xn-1-xn)／candΔZn=(En／c),in whichZnandEnare the mechanical impedance and Young’s modulus at the sectionn,respectively.As represented in Fig.3,according to this method,if the geometry and the distance between impedance change planes are known,the stress and velocity at the lower extremityncan be calculated from previous measurement point(n-1)where stress and velocity were known.In Fig.3,a longitudinal rod having different impedance changes represents the penetrometer.SectionArepresents the pointxAwhere strain gauges and accelerometers are installed while the cross-sectionJ(if the skin friction along the rod string is negligible)represents the soil/cone interface,where stress,force,velocity and displacement must be established(Carlsson et al.,1990).SectionJis chosen to represent cone/soil interaction because it integrates all forces that the soil exerts on the cone(shaft and base)during penetration per blow.To compute stress,force and velocity for the cone/soil sectionxJfrom the signals recorded atxA,each range of impact velocities and the results obtained are theoretically accurate.In addition,there is no limitation for geometry along the rods of the penetrometer if the measurement sensors are installed in a uniform section where the waves are as uniform as possible.Once the stressσJ(t)and velocityvJ(t)signals are calculated for the penetrometer cone,strainεJ(t)and forceFJ(t)are calculated by means of elasticity relationships presented in Eq.(3).DisplacementuJ(t)can be also calculated thought numerical integration of velocityvJ(t).

An example of raw measurements,forceF(t)and velocityv(t),carried out throughout the test and made at the measurement pointxAare presented in Fig.4a.Here,velocity is multiplied by the mechanical impedance of the rod(Z=EA/c,whereEis the steel Young’s modulus andAis the rod section)to express it in terms of force.From these signals(Fig.4a)and by applying the presented formulations(Eq.(4)),decoupled forces of the upward and downward waves are obtained(Fig.4b).Calculated cone signals ofvelocityvp(t),displacementsp(t)and total soil resistanceqd(t),obtained using Eq.(5),are also presented.The calculated velocityvp(t)as well as displacementsp(t) of the cone is presented simultaneously in Fig.4c.The stressqd(t)mobilised during the cone penetration at the cone/soil interface is presented in Fig.4d.In addition,assuming that there is equal stress and displacement at the cone/soil interface during cone penetration,it is possible to plot the DCLTcurve.Theoretical,numerical as well as practical reliability of these method has been demonstrated recently by Benz Navarrete et al.(2013),Escobar Valencia et al.(2013,2016a,b),Tran et al.(2017,2019),and Zhang et al.(2019).

2.2.Assessment of soil mechanical impedance,wave velocity and strain using shock polar curves

To assess soil mechanical impedance,wave velocity as well as strain,the shock polar curve method is applied(Aussedat,1970;Meunier,1974;Oularbi,1989;Oularbi and Levacher,2009;Lodygowski and Rusinek,2014;Omidvar et al.,2014;Iskander et al.,2015;Tran et al.,2019).As shown in Fig.5,the polar shock curve represents the relationship between stress(σ)and particular velocity(v)generated by the mechanical wave which propagates in a de fined material.In this method,it is assumed that a plane and unidirectional elastic shock wave propagates from a medium A(rods)to a medium B(soil).Both media have different mechanical impedances,and in our case,the mechanical impedance of the rods is greater than that of the soil.The main purpose here is to obtain the soil shock polar curve from decoupled waves in the measurement sectionxAof the penetrometer,close to the anvil.

Considering the penetrometer and the soil at rest,just after the blow,the penetrometer rods are crossed by the compression incident waveuf(t).After its passage,the relationship between the stressσfand particular velocityvfcan be expressed according to Eq.(6),which is represented by the grey straight line with a slope positive ofZt(Fig.5).When the incident wave reaches the soil/cone interface,a transmitted waveuT(t)into the soil occurs while a reflected waveug(t)is returned upwards into the rods.The stress resulting after its passage can be expressed as

The pair of pointsA(σf,vf)andC(σg,vg)in Fig.5 belong to the rod polar shock curve de fined by the slopeZ=±ρc,whereρis the density of the steel rod.In the soil,immediately after the passage of the transmitted waveuT(t),the stressσTas well as the particular velocityvTincreases proportionally(Eq.(8)).At the soil/cone interface,the incident and re flected wave overlap and resulting stressσTand particular velocityvTcan be expressed as a function of these waves according to Eqs.(9)and(10).Thus,the pointB(σT,vT)belongs to the soil polar shock curve(Fig.5).In Fig.5,black straight line represents the rod polar curve,characterised by its mechanical impedanceZt(de fined from the material properties),the Young’s modulusE(2.1×1011Pa in our case)and the wave velocityc(～5200 m/s).The grey dashed curve represents the soil shock polar curve,intercepting the polar curve of the rods at pointBwhere the stress and velocity of incident,re flected and transmitted waves converge.Once this point is identi fied,the shock polar curve of the soil and consequently its mechanical impedanceZscan be determined.

According to Fig.5,for the case of steel penetrometer rods,the polar shock curve is a straight line de fined by the slopeZ=±ρc;while for the soil,the shape of this curve remains unknown and must be determined experimentally.In practice,a part of soil polar shock curve can be obtained from penetrometer measurements and for the time intervalt0+2L/cas follows,wheret0is the trigger time andLis the rod length:

(1)Consider decoupled incident and re flected waves(Eq.(4));

(2)Compute stress and velocity for incident and re flected waves(Eq.(6)and(7));

(3)Compute stress and velocity of transmitted wave(Eq.(9)and(10));and

(4)Plot transmitted stressσTas a function of velocityvTand fitting the curveσT=ZsvT.

Furthermore,knowing the impedance of the soilZsand considering the short load rise time of wave during the first arrival of the wave-front at the soil-cone interface(less than 400μs,as shown in Fig.4),it can be accepted that the soil behaviour is almost elastic,and it has no time to deform radially.The deformation during this short time is mainly axial and thus it is possible to assess the soil compressional wave velocitycpand the strainεxxby

Nevertheless,in the practical case of in situ soil characterisation and if the penetrometer driving energy is high,it is important to note that the value of compressional wave velocity(Eq.(11))determined through this method can be affected by the presence of the groundwater table.In all cases,the soil under dynamic compression loading will behave in undrained condition,which means that its Poisson’s ratio will be close to 0.5,especially for the first wave-front arrival(Verruijt,2010).In such cases,the values obtained should be carefully considered.

3.DCLT curve:Proof of concept

3.1.Experiments on different materials:Sensitivity and repeatability tests

The first experiments conducted aim to determine the DCLT curve for different materials:wood,concrete,sand and sandy clay(Fig.6).The main purposes of these experiences are to evaluate the repeatability and the sensitivity of DCLT curves obtained with a simpli fied test con figuration.In addition,it aims to assess whether Aussedat(1970)’s method can be used to determine the mechanical impedance as well as wave velocity of soil.

For wood,concrete and sand,the tests were performed in laboratory with variable driving energy using a 1726-g hand hammer.The wood measurements(Douglas fir)were carried out parallel to the fiber direction on a sample with dimensions of 500 mm×300 mm×180 mm.For concrete,the measurements were performed directly on a 240-mm thickness slab;while the sand sample was prepared and compacted in a cylindrical mould with a diameter of 160 mm and a height of 320 mm.The height of each sample was adapted in order to avoid,as much as possible,the effect of the bottom re flection on the first re flection wave coming from the cone/sample interface,as proposed by Aussedat(1970).For measurement on sand as well as wood and concrete samples,variable driving energy was used.

To evaluate the repeatability and accuracy of this method,the tests performed on the natural sandy clay were carried out at a constant driving energy,by dropping a hammer from a constant height(hammer mass of 5 kg and a fall height of 500 mm).For this purpose,a classic DPTdriving systemwas adapted to the device and a 4-cm2cone section was employed to avoid any skin friction along the rods.

All the tests were carried out with two assembled rods of 14 mm in diameter and 500 mm in length(total length of rod was 1000 mm).The rods were strongly screwed together without any speci fic connection element that could generate modi fication of the waves that propagate inside them.For each material,at least five blows were recorded and analysed.

DCLT curves obtained for a series of recorded blows on each sample are presented in Fig.6.Firstly,the good repeatability of curves obtained can be observed as well as its sensitivity to the type of material tested:concrete,wood,sandy clay and sand.Indeed,DCLT curves obtained for concrete and wood(Fig.6a and b)show a good agreement with those reported for similar tests in the literature(split Hopkinson pressure bar(SHPB),static indentation hardness test,etc.)(Ross et al.,1986;Widehammar,2004;Lodygowski and Rusinek,2014;Omidvar et al.,2014,2015;Iskander et al.,2015).Additionally,from the results obtained for natural sandy clay,performed with a constant driving energy,a very good repeatability can be observed(Fig.6c).In this case,the curves obtained are almost identical for each blow.

Concerning the curves obtained for sand at variable driving energy(Fig.6d),it can be noted that the cone load increases proportionally to the displacement,following a nonlinear trend,as usually observed on base load-displacement response of piles in sand.It can also be observed that a maximum soil penetration resistance remains almost constant for each blow independently of driving energy,while total penetration increases proportionally.In addition,for driving energy employed here to obtain sand’s DCLT curves,no signi ficant rate effects on cone resistance were observed in our experiences,such as found in other similar experimental cases(Eiksundand Nordal,1996).

For the case of soils,once cone resistanceqd(t)reaches a threshold value(close to the maximum stress),the soil deforms plastically and the cone resistanceqd(t)remains almost constant until the maximum penetration is reached.At this moment,the energy contained in the waves propagating inside the rods is not enough to continue deforming the soil and the unloading phase begins.After,a series of unloading and reloading cycles can be observed in some cases(Fig.6c and d).

On the other hand,the experiences carried out in laboratory and results obtained have been employed to compute the polar shock curve and evaluate in this way the interest of this method.For each recorded blow and the first-round trip cycle(t0tot0+2L/c,the shock polar curve of each material has been obtained and presented in Fig.7a.Here,the polar curve of penetrometer rod is also plotted.

Moreover,to evaluate the sensitivity of Aussedat(1970)’s method,supplementary tests have been carried out on different natural soil samples:marlaceous clay,Allier sand(low and high density)and Fontainebleau sand.The results obtained are presented simultaneously with those achieved on sandy clay and sand samples(Fig.7b).From presented curves(Fig.7),the good agreement can be observed as well as repeatability of each analysed blowand its sensitivity to the type of material.Furthermore,as can be expected,the mechanical impedance(Z)obtained for rigid materials(steel and concrete)is higher than those obtained for other soil materials(Fig.7a).

Additionally,a summary of results obtained from the interpretation of each shock polar curve achieved on each material is provided in Table 1.Here,the maximumvalues of force and velocity for incident(Ff,vf),re flected(Fg,vg)and transmitted waves(FT,vT)are presented.For each material,the average of mechanical impedance(Zs),compressional wave velocitycpand equivalent strainεp(Eqs.(11)and(12))has been calculated assuming the linear elasticity for each tested material.

Table 1Experimental results of mechanical impedance and wave velocity assessment obtained from the polar shock curves for different materials and some recorded blows(Fig.7).

Table 2Comparison of the mean value of cone resistances obtained with the instrumented DPT and conventional methods(CPT and DPT)for the two layers of the sand fill pit.

It can be noted that the obtained values of the compressional wave velocity are in good agreement with those found in the literature:2800-3600 m/s for concrete,3500-6000 m/s for wood,1200-3000 m/s for marlaceous clay and 200-2200 m/s for dry/wet sands.In this way,the method proposed by Aussedat(1970)to evaluate the mechanical impedance(Zs)as well the wave velocity of soils seem to be a reliable and interesting means to characterise shallow soils.

Fig.7.Experimental shock polar curves obtained in the laboratory:(a)Comparison for different materials(concrete,clean sand,wood and steel rods),and(b)Comparison for various types of soils(compacted clayey sand,Fontainebleau sand and Allier compacted and loose sand).

3.2.Interpretation of DCLT curves

Besides applying the Aussedat(1970)’s method,a simple analytical method was proposed to analyse DCLT curves obtained during penetrometer driving,as shown in Fig.8,based on simplified pile model(Benz Navarrete,2009;Benz Navarrete et al.,2013,2014;Escobar Valencia,2015;Escobar Valencia et al.,2016b).

The experimental DCLT curves can be separated into three phases(Fig.8a):full dynamic penetration,plastic shear penetration and unloading/reloading cycles.Full dynamic penetration is mainly inertial and penetration rate dependent,while plastic shear penetration is penetration rate and displacement dependent.The unloading/reloading cycle,which follows the moment when the rate penetration becomes zero(at this moment,represented by the pointAin Fig.8,the energy to penetrate the soil is not enough),is mainly elastic displacement dependent.

The DCLT is modelled as a simplistic elasto-viscoplastic model(Fig.8a).Here,the total soil resistanceqd(t)is modelled with both viscous dynamic(qdyn)and pseudo-static(qs)components(Eq.(13)).The total soil resistance is thus the sum of the spring reaction(qs)and the radiation dashpot reaction(qdyn)(Salgado et al.,2015).These two components can be separated from each DCLT curve.Pseudo-static resistanceqsis displacement dependent and then independent of penetration rate.This is modelled by an elastic perfectly plastic law and determined experimentally when average penetration rate is zero(Eq.(14)).Knowing pseudo-static resistance value,viscous dynamic resistance(qdyn)is determined from dynamic loading curves as the average resistance mobilised in the penetration interval between elastic settlementseand maximum measured plastic penetrationsponce pseudo-static resistance is subtracted(Eq.(15)).

whereνis the Poisson’s ratio of the soil,dpis the cone diameter,andkMis the embedding Mindlin’s coef ficient.

To summarize,in practice,at the end of the dynamic penetration test according to the method presented,the following log pro files were produced:dynamic and pseudo-static cone resistance,unloading and reloading moduli,and compressional wave velocity.Shear wave velocity can be also determined by assuming the Poisson’s ratio of the soil.As previously stated,considering dynamic compression as well as undrained condition,Poisson’s ratio will be close to 0.5.

3.3.Laboratory tests in a sand fill

A second experiment was carried out in an experimental sand pit to evaluate the reliability of the measurements,especially the soil resistance obtained from the DCLT curve(Fig.9).

The results are compared with those obtained,firstly,with a cone penetration test(CPT)(Gouda)providing cone resistanceqc,and secondly,with dynamic penetrometer P.A.N.D.A providing the dynamic cone resistanceqdobtained through modi fied Dutch formula(Gourvès,1991;Gourvès and Barjot,1995;Langton,1999).In this way,total soil resistanceqd(t)(Eq.(13))is compared with dynamic cone resistanceqd(from P.A.N.D.A)while pseudo-static resistanceqs(Eq.(14))is compared with CPT results(qc).

This experiment aims also to evaluate the relevance and the adaptability of the new method to obtain DCLT curves in different conditions,more precisely,at different depths,up to 3.4 m,with different rod lengths and in a same material compacted at different degrees.

As shown in Fig.9,the external dimensions of pit are 4 m×2.1 m×2.9 m,and the filling material is an alluvial sand(from the Allier river,central France).A summary of the general characteristics as well as the location of each test are shown in Fig.9a.The filler sand was deposited arbitrary in two layers(Fig.9b).The loose-density lower layer of 2 m thick was deposited by pluviation,at low drop height with no mechanical compaction.The upper layer of 1.45 m thick was compacted with a vibrator plate compactor in 0.2 m thick layers.

Conventional DPT(P.A.N.D.A.)was carried out close to the current instrumented DPT(Fig.9b).The tests were performed at 60 cm from each other and 60 cm from the pit edges,in order to reduce the effects of the boundary conditions considering a ratio between in fluence area of the test and the cone diameter at least of 50(Schnaid and Houlsby,1991;Bolton and Gui,1993;Balachowski and Kurek,2008;Wachiraporn et al.,2018).To avoid the skin friction along the rods,the tests were conducted with an over flowing cone of 4 cm2in cross-section(22.6 mm in diameter).In addition,as the rod length is 500 mm,DPT tests have been carried out with 2-4 rods within the top layer and 4-8 rods for the case of the bottom layer.As the test progresses in depth,rods were added and strongly screwed together without any additional connectors to ensure continuity and homogeneity of rod string.

Concerning the proposed instrumented DPT,three measurements of the DCLT curve were carried out at approximately every stage of 0.2 m between the depths of 0.3 m and 3.2 m.A total of 45 measurements were recorded.Some examples of DCLT curves are presented in Fig.10.From each curve,total(qd(t))and pseudo-static(qs)soil resistances are obtained.The mean values(grey triangles and black circles)of the three consecutive measurements at each stage are plotted in Fig.9c.The logs of the dynamic(qd)and static(qc)cone resistances obtained respectively from conventional DPT(P.A.N.D.A.)using the Dutch driving formula and the CPT(Gouda)are also plotted(Fig.9c).

Fig.9.Experimental results obtained in a laboratory sand pit fill:(a)Allier sand properties;(b)Diagram of experimental pit filled with Allier sand in two different layers,general view of penetration test position;and(c)Cone resistance pro files:dynamic cone resistance q d obtained with conventional DPT(P.A.N.D.A.),static cone resistance q c obtained with a CPT and q s and q d(t)(pseudo-static and total soil resistances)obtained from DCLT curves performed at different depths through the present method.

Fig.10.Example of DCLT curves obtained in a laboratory sand pit fill for 3 consecutive blows at different depths:(a)In the upper layer at 0.3 m and 0.7 m depths,and(b)In the bottom layer at 1.6 m and 3.2 m depths.

The results of the cone resistances obtained by means of the proposed instrumented DPT show a good agreement(Fig.9c)with those obtained with conventional devices(Table 2).Indeed,about pseudo-static and static(CPT)cone resistances,the mean values as well as the standard deviations for two layers are very similar,as shown by Odebrecht et al.(2005),and Schnaid et al.(2007,2009,2017).Regarding the total(qd(t))and dynamic(qd)cone resistances,the values obtained from dynamic load curves are slightly higher than the values obtained with the driving formulae.

Furthermore,in Fig.10,some DCLT curves for successive blows are presented.These curves were smoothed using a low-pass FIR filter(Hamming windows)with a cut-off frequency varying from 900 Hz to 300 Hz to attenuate the natural modes of rods.A good repeatability of the curves for each layer can be observed as well as a sensitivity to the sand compaction degree.In both cases,elastic deformation,plasticity threshold and unloading/reloading cycles can be identi fied.Nevertheless,due to the low resistance of the lower sand layer,unloading/reloading cycles after the main penetration were not observed.In this case,when very soft soils are tested,it seems more appropriate to adapt the driving energy to the minimum.

4.Full-scale tests

A final test was carried out to assess the feasibility of the proposed method in the field.The test site is located in the vicinity of Castellód’Empúries in the Alt Empordà,close to the Costa Brava,north of Barcelona,Spain.This is an alluvial plain mostly formed by deposits of the Fluviàand Muga rivers.In this site,the Holocene deposits reach a thickness of about 20-30 m in the area,with alternating sand dominated deposits and silt-clay deposits.At the surface of this site,a very compacted back fill of approximately 1.5 m thick was built(Perez et al.,2013;Arroyo et al.,2015).The groundwater table was located at a depth of 2.4 m below the ground surface.

Concerning the measurements performed with the instrumented DPT,a total of six soundings were conducted.These were dropped to an average depth of 7.2 m,while minimal and maximal depth reached were 5.7 m and 10.1 m,respectively.Steel rods of 500 mm in length and 14 mm in diameter,screwed tightly together during probing,were used.No additional connectors between two rods were employed.

To reduce the skin friction along the rods,over flow cones of 4 cm2in cross-section has been used.Because the ratio between cone and rod diameters is greater than 1.6,the skin friction can be signi ficantly reduced.Indeed,the skin friction was checked each 1 m of driving by means of the torque measurement.This was negligible in all cases,which was con firmed additionally by using the methods developed in dynamic pile load test to identify the shaft forces(Rausche,1970;Goble et al.,1980;Goble and Aboumatar,1992).

Each test was driven by variable driving energy using a hand hammer,adapting the power of blow to the soil resistance.Stress,acceleration,and displacement measurements were performed continuously blow by blow for all tests.In total,5932 blows were recorded,which represents an average of 135 blows/m.In this way,a dynamic cone penetration curve was obtained almost every 7.5 mm of penetration.

The results obtained for each parameter are plotted as a function of the depth in Fig.11.Here,the logs of total soil resistanceqd(t),pseudo-static cone resistanceqs,compressional(cp)and shear(cs)wave velocities,unloadingand reloadingpenetrometric moduli are presented.Considering undrained condition of soil and dynamic loading,Poisson’s ratio of 0.49 was employed.

The average value for each parameter is also presented(grey continuous line)as a function of the depth.The dotted horizontal grey line indicates the groundwater table(at 2.4 m depth).Thus,the information available and the resulting pro files can be used to easily identify two shallow layers:a sandy gravel fill up to 1.2 m deep,followed by silty clay and soft sandy clay.

As different geotechnical tests(CPT,pressuremeter(PMT),seismic dilatometer(sDMT),multi-channel analysis of surface waves(MASW),etc.)have been carried out in previous investigations(Perez et al.,2013;Arroyo et al.,2015),a comparison of the available values for CPTu’s cone resistance as well as S-wave velocities(sDMT and MASW)measured on site with the static cone resistance and S-wave velocity obtained with the instrumented DPT is presented(Fig.12).Although for the first meter(compacted back fill layer),a difference is observed in terms of cone resistance,it can be noted that the obtained values in deeper layer,either for cone resistances or for wave velocities,are in good agreement with the values measured previously on this site and published by Perez et al.(2013).The differences observed,especially in near surface and at 5.4 m depth,can be explained by the soil heterogeneity and the uncertainty of data provided by each method compared here(geometry,inversion method,observation scale,representative elementary volume,vertical resolution,wave damping in rods,etc.).Finally,compressional and shear wave velocities under the groundwater table must be considered carefully,even though the results obtained seem in agreement with the values reported in the literature.

Fig.11.Results of experimental tests performed in the vicinity of Castellód’Empúries(Spain):log10z curves of(a)total soil resistance q d(t),(b)pseudo-static cone resistance q s,(c)compressional wave velocity c p,(d)shear wave velocity c s,(e)unloading penetrometric modulus E dp3,and(f)reloading penetrometric modulus E rp3.

Fig.12.Results of experimental tests performed in the vicinity of Castellód’Empúries(Spain):comparison of(a)the cone resistances and(b)shear wave velocity measured from the new instrumented DPT with previous conventional measurements carried out on the same site(cf.Perez et al.,2013;Arroyo et al.,2015).

5.Conclusions

DPTs are widely used around the world and currently provide a single failure parameter whose interpretation is still largely empirical.Several authors proposed to improve the interpretation of the DPT by using the wave equation.However,none of these works have been implemented in practice to obtain in situ soil stress and strain relationship necessary for the most current geotechnical problems.

In this work,a lightweight dynamic variable energy penetrometer has been instrumented to measure the strainε(x,t),accelerationa(x,t)and displacements(t)variations caused within the rods by the compressional wave created immediately after each hammer blow and during penetrometer driving.By using a wave decoupling and reconstruction method,it has been possible to obtain the DCLT curve of the soil at each blow.

As demonstrated by a series of tests on different materials,the resulting DCLT curve is reproducible,sensitive,and reliable to the test conditions as well as to the soil conditions.Moreover,the implementation of the method based on a linear viscoelastic model and the Smith(1960)approach makes it possible to compute total,dynamic and pseudo-static soil resistances as well as the deformability moduli from DCLT curve.Finally,the application of the method proposed by Aussedat(1970)makes it possible to determine the soil impedance or shock polar curve,from which the soil compressional wave velocity can be calculated.

It is important to note that the test proposed here,manually driven with adapted energy,is not affected by the subsequent hammer rebounds as noted in previous SPT energy measurement works.The technical feasibility of the method as well as the reliability of the results has been proved in situ by a series of tests with continuous recordings up to a depth of 7 m.

Considering that for one linear meter of sounding,almost 200 hammer blows are provided and that from each curve,a series of parameters is produced,the amount of information collected during a field test is highly signi ficant and in the long-term will facilitate implementation of statistical analysis methods for the data analysis.

The method proposed here is not P.A.N.D.A.speci fic and can be applied to the other DPTs by being vigilant to avoid the skin friction along the rods.This can be achieved by using cones with larger diameters than those of the rods or most traditional techniques as mud injection or outer casing,as described in ISO-22476-2(2005).Anyway,if skin friction is present,back analysis or fitting methods commonly used in pile loading test(Rausche,1970;Rausche et al.,1972;Goble et al.,1980;Loukidis et al.,2008;Salgado et al.,2015,2017,2017;Poganski et al.,2016,2017)can be adapted to obtain cone response.

Also,it should be noted that if the penetrometer driving energy is too high for low-consistency and saturated soils or for the tests performed below the groundwater table,the assessment of compressional waves obtained through the present method can be highly affected.In such cases and according to the current state of knowledge regarding dynamic signal processing,the values obtained are likely to be higher and should be carefully considered.

Despite the results obtained,the soil behaviour subjected to cone penetration remains poorly understood.Indeed,this is a nonhomogeneous loading test,and given its nonlinearity,the soil behaviour after blow is complex.This is why interpretation of the DCLT curve is a complex matter and should be the subject of future studies to improve its understanding,and to develop methods in order to estimate intrinsic soil parameters governing stress-strain behaviour under dynamic penetration.

Declarationofcompetinginterest

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