Free fall ball penetrometer with a booster

Abstract

A free fall ball penetrometer with a booster is dynamically penetrated into the seabed through its kinetic and potential energies. The main measuring instrument is a ball penetrometer, which is subject to end bearing resistance, drag force, and soil buoyant force during the dynamic penetration process within the soil. Based on the measured data from the accelerometer and load cell, the soil strength parameters including the undrained shear strength and strain-rate parameter can be back-analyzed. The added booster can: (1) effectively increase the penetration depth of the ball penetrometer and hence enlarge the range of measured penetration depths; and (2) improve the directional stability and avoid the rotation of the ball penetrometer during the falling process. The force data measured from the load cell, together with the acceleration data from the accelerometer, can further improve the measured accuracy.

Claims

1. A free fall ball penetrometer with a booster, comprising: a ball penetrometer and a connecting rod used to connect the ball penetrometer and the booster; the ball penetrometer is equipped with a pore water pressure transducer sealed to an equator of the ball penetrometer to measure dissipation of a pore water pressure after a dynamic penetration of the ball penetrometer; the ball penetrometer and a first side of the connecting rod are connected using a load cell, and the load cell is used to measure a resistance of the ball penetrometer during the dynamic penetration within a soil; a second side of the connecting rod is connected to the booster through threads; the connecting rod forms a certain distance between the ball penetrometer and the booster in order to avoid influence of the booster on a flow mechanism of the soil around the ball penetrometer, and a sectional area of the connecting rod is determined based on a criterion that a measured soil resistance on the ball penetrometer is not influenced by the connecting rod; the booster is used to increase a penetration depth of the ball penetrometer; the booster comprises a cylindrical shaft with an ellipsoidal tip and a streamlined rear to reduce a resistance on the booster during a free fall in water and dynamic penetration within the soil; a length of the cylindrical shaft varies based on practical measuring requirement; a rear of the cylindrical shaft is set with four rear fins to improve a directional stability of the booster during the free fall, and sizes of the rear fins are adjusted based on practical requirement; a tip of the booster is provided with internal threads to connect external threads on the connecting rod; a rear of the booster is reserved an internal space to accommodate an accelerometer, an internal data acquisition card, and a power supply device; the accelerometer is sealed in the internal space towards the rear of the booster; a wire of the accelerometer is extended from the rear of the booster and is connected to an external data acquisition instrument; an installation line and a retrieval line are attached to the rear of the booster; the booster and the ball penetrometer are retrieved by pulling the retrieval line up after measurement, and recorded data are exported to a computer for analysis.

2. The free fall ball penetrometer with the booster of claim 1, wherein the connecting rod comprises a single-shaft type connecting rod and a three-shaft type connecting rod, and the three-shaft type connecting rod owns an improved ability of resisting bending moment and disturbance.

3. The free fall ball penetrometer with the booster of claim 1, a distance between the ball penetrometer and the booster is four times a diameter of the ball penetrometer.

4. The free fall ball penetrometer with the booster of claim 1, a ratio of a sectional area A.sub.shaft of the connecting rod to a projected area A.sub.t of the ball penetrometer is less than 0.1.

5. The free fall ball penetrometer with the booster of claim 3, a ratio of a sectional area A.sub.shaft of the connecting rod to a projected area A.sub.t of the ball penetrometer is less than 0.1.

6. An operation method using the free fall ball penetrometer with the booster of claim 1, comprising: step 1, screw the booster and the ball penetrometer through threads; make sure that a gravitational center of the ball penetrometer is in line with a central axis of the booster in order to improve a directional stability of the ball penetrometer during the free fall in water and the dynamic penetration in the soil, and to avoid large inclination of the ball penetrometer, and hence to increase an impact velocity and the penetration depth of the ball penetrometer; connect wires of the accelerometer, the pore water pressure transducer and the load cell to the internal data acquisition card and the external data acquisition instrument; step 2, release the ball penetrometer with the booster to a determined height above a seabed through the installation line, and release the retrieval line to a seabed surface; and turn on the internal date acquisition card and the external data acquisition instrument and prepare to collect data when the ball penetrometer with the booster is steady in water; step 3, release the installation line, allowing the ball penetrometer with the booster to freely fall in a water column and dynamically penetrate within the seabed until the ball penetrometer with the booster is rest in the soil; and after the dynamic penetration, the ball penetrometer with the booster is allowed to be left in the soil for a period of time, during which dissipation of the pore water pressure in the soil surrounding the ball penetrometer is measured; step 4, retrieve the ball penetrometer with the booster by pulling the retrieval line up after measurement, and export recorded data from the internal data acquisition card and the external data acquisition instrument for analysis; first, a velocity and a penetration depth of the ball penetrometer are analyzed based on recorded data from the accelerometer; and the velocity of the ball penetrometer is obtained by Eq. (1) and the penetration depth of the ball penetrometer is obtained by Eq. (2):
v=.sub.0.sup.tadt(1)
s.sub.t=.sub.0.sup.tvdt(2) where a is a vertical acceleration of the ball penetrometer measured by the accelerometer, v is a vertical velocity of the ball penetrometer, s.sub.t is a vertical displacement of the ball penetrometer; a soil undrained shear strength is back-analyzed based on recorded data from the load cell and the accelerometer, and specific procedures comprise: forces acting on the ball penetrometer during the dynamic penetration within the seabed is written in Eq. (3):
(m+m)a=W.sub.b+F.sub.mF.sub.NF.sub.DF.sub.b(3) where m is a mass of the ball penetrometer, a is a vertical acceleration measured by the accelerometer, W.sub.b is a submerge weight of the ball penetrometer in water, F.sub.m is a measured force by the load cell, F.sub.N is a soil end bearing resistance on the ball penetrometer during the dynamic penetration within the seabed, F.sub.D is a soil drag force on the ball penetrometer during the dynamic penetration within the seabed, F.sub.b is a soil buoyancy on the ball penetrometer, which is expressed as a product of a displaced soil volume by the ball penetrometer and a soil effective unit weight ; and an added mass, m is expressed in Eq. (4):
m=C.sub.mm.sub.soil(4) where C.sub.m is an added mass coefficient, which is valued as C.sub.m=0.5, m.sub.soil is a displaced soil mass by the ball penetrometer, which is described in Eq. (5):
m.sub.soil=V.sub.ball.sub.soil(5) where V.sub.ball is a displaced soil volume by the ball penetrometer, and .sub.soil is a density of the soil; when a soil strain-rate effect is taken into consideration during the dynamic penetration of the ball penetrometer, the soil end bearing resistance, F.sub.N, in Eq. (3) is expressed in Eq. (6):
F.sub.N=R.sub.fN.sub.cs.sub.uA.sub.t(6) where N.sub.c is an end bearing capacity factor of the ball penetrometer, s.sub.u is a measured soil undrained shear strength under a reference shear strain-rate, A.sub.t is a projected area of the ball penetrometer, R.sub.f is a soil strain-rate factor, which is expressed using a power law expression shown in Eq. (7): $\begin{array}{cc}{R}_f={\left(\frac{\stackrel{.}{}}{{\stackrel{.}{}}_{\mathrm{ref}}}\right)}^{}={\left(\frac{v/D}{{\stackrel{.}{}}_{\mathrm{ref}}}\right)}^{}& \left(7\right)\end{array}$ where {dot over ()} is a shear strain-rate defined as a ratio of the vertical velocity, v, of the ball penetrometer to a diameter, D, of the ball penetrometer, {dot over ()}.sub.ref is a reference shear strain-rate, is a strain-rate parameter usually ranging 0.0340.14; the soil strain-rate factor R.sub.f is expressed by Eq. (8):
R.sub.f=f.sub.1(v,,,R.sub.en)(8) a non-Newtonian Reynolds number, R.sub.en, in Eq. (8) is described as Eq. (9): $\begin{array}{cc}{R}_{\mathrm{en}}=\frac{{}_{\mathrm{soil}}{v}^2}{s_u}& \left(9\right)\end{array}$ hence the soil strain-rate factor, R.sub.f, is expressed as:
R.sub.f=f(v,,,.sub.soil,s.sub.u)(10) the end bearing capacity factor of the ball penetrometer, N.sub.c, depends on a frictional coefficient, , and is described as Eq. (11):
N.sub.c=f.sub.2()=A.sub.1+A.sub.2+A.sub.3.sup.2(11) where A.sub.1A.sub.3 are undetermined parameters which are determined by numerical simulations; the soil drag force of the ball penetrometer during its penetration within the soil in Eq. (3) is defined by Eq. (12):
F.sub.D=C.sub.D.sub.soilv.sup.2A.sub.t(12) where C.sub.D is a drag coefficient; the drag coefficient of the ball penetrometer is expressed as Eq. (13):
C.sub.Df.sub.3(,R.sub.en)=f.sub.3(,.sub.soil,v,s.sub.u)(13) based on Eqs. (313), the measured soil undrained shear strength under the reference shear strain-rate back-analyzed based on the vertical acceleration, a, and the measured force, F.sub.m, is expressed by Eq. (14): $\begin{array}{cc}{s}_u=\frac{\begin{array}{c}{W}_b+F_m-\left(m+C_m{m}_{\mathrm{soil}}\right)a-\\ 0.5f_3\left(,{}_{\mathrm{soil}},v,s_u\right){}_{\mathrm{soil}}{v}^2{A}_t-F_b\end{array}}{A_t.Math.f_2\left(\right).Math.f_1\left(v,,,{}_{\mathrm{soil}},s_u\right)}& \left(14\right)\end{array}$ where associated parameters in f.sub.1, f.sub.2 and f.sub.3 are determined from numerical simulations; in Eq. (14), W.sub.b and F.sub.b are calculated, F.sub.m and a are measured by the load cell and the accelerometer, v is obtained by integrating measured data of the accelerometer, and , , and s.sub.u are unknown parameters which are back-analyzed based on a least-squares regression scheme; for typical clayey seabed, the measured soil undrained shear strength under the reference shear strain-rate increases linearly with depth, hence s.sub.u is expressed as:
s.sub.u=s.sub.u0+kz(15) where s.sub.u0 is a soil undrained shear strength at a mudline, z is a distance from a soil surface, k is a soil strength gradient; based on measured data from the accelerometer and the load cell during the dynamic penetration of the ball penetrometer, soil strength parameters (s.sub.u0, k), the strain-rate parameter (), and the frictional coefficient () are back-analyzed using Eqs. (1415).

Description

DESCRIPTION OF DRAWINGS

(1) FIG. 1a Booster and ball penetrometer with single-shaft type connecting rod and wireless data acquisition method.

(2) FIG. 1b Booster and ball penetrometer with three-shaft type connecting rod and wireless data acquisition method.

(3) FIG. 2a Booster structure with single-shaft type connecting rod and wireless data acquisition method.

(4) FIG. 2b Booster shaft and rear fins with single-shaft type connecting rod and wireless data acquisition method.

(5) FIG. 2c Booster structure with three-shaft type connecting rod and wireless data acquisition method.

(6) FIG. 3a Details of ball penetrometer and connecting rod with single-shaft type connecting rod.

(7) FIG. 3b Details of ball penetrometer and connecting rod with three-shaft type connecting rod.

(8) FIG. 3c Diagram of cross section of the three-shaft type connecting rod.

(9) FIG. 4a Booster and ball penetrometer with single-shaft connecting rod and external data acquisition method.

(10) FIG. 4b Booster and ball penetrometer with three-shaft connecting rod and external data acquisition method.

(11) FIG. 5a Details of booster with single-shaft connecting rod and external data acquisition method.

(12) FIG. 5b Details of booster with three-shaft connecting rod and external data acquisition method.

(13) FIG. 6 Forces acting on the ball penetrometer.

(14) FIG. 7 Acceleration during the dynamic penetration of the penetrometer.

(15) FIG. 8 Velocity during the dynamic penetration of the penetrometer.

(16) In the Figures: 1. Ball penetrometer; la. Pore water pressure transducer; 2. Connecting rod; 2a. External threads; 2b. Load cell; 3. Booster; 3a. Internal threads; 3b. Booster shaft; 3c. Accelerometer; 3d. Rear fins of booster; 3e. Power supply; 3f Internal data acquisition card; 3g. Retrieval line; 3h. Installation line; 4. External data acquisition instrument.

DETAILED DESCRIPTION

(17) The operation procedures using the present free fall ball penetrometer with a booster are detailed shown as follows, with reference to the drawing sand technical solutions.

(18) Step-1. The booster 3 and ball penetrometer 1 are connected through threads. Note the gravitational center of the ball penetrometer 1 is in line with the central axis of booster 3 to improve the directional stability and avoid large inclination of the ball penetrometer 1 during its free fall in water and dynamic penetration in the soil, and hence to increase the impact velocity and penetration depth of the ball penetrometer 1. Then connect the wires of all transducers to the internal data acquisition card 3f or external data acquisition instrument 4.

(19) Step-2. Release the assembled penetrometer to the determined height above the seabed through the installation line 3h, and release the retrieval line 3g to the seabed surface. When the penetrometer is steady in water, turn on the internal data acquisition card or the external data acquisition instrument, and prepare to start collecting data.

(20) Step-3. Release the installation line 3h, allowing the ball penetrometer 1 to freely fall in the water column and dynamically penetrate within the seabed until the ball penetrometer is rest in the soil. After the dynamic penetration, the ball penetrometer 1 is allowed to be left in the soil for a period of time, during which the dissipation of the pore water pressure in the soil around ball 1 is measured.

(21) Step-4. After measurement, retrieve the ball penetrometer 1 by pulling the retrieval line 3g up. Then the recorded data from the internal data acquisition card 3f or external data acquisition instrument 4 are exported to a computer for analysis.

(22) First, the velocity and penetration depth of the ball penetrometer 1 are analyzed based on the recorded data from the accelerometer 3c. The velocity of the ball penetrometer 1 can be obtained by Eq. (1), and the penetration depth of the ball penetrometer 1 can be obtained by Eq. (2).
v=.sub.0.sup.tadt(1)
s.sub.t=.sub.0.sup.tvdt(2)
where a is the vertical acceleration of the penetrometer measured by accelerometer 3c, v is the vertical velocity of the penetrometer, s.sub.t is the vertical is placement of the penetrometer.

(23) The soil undrained shear strength can be back-analyzed based on the measured data of load cell 2b and accelerometer 2c, and the specified procedures are listed as below.

(24) The forces acting on the ball penetrometer 1 during the dynamic penetration process within the seabed are depicted in FIG. 6 and can be written in Eq. (3).
(m+m)a=W.sub.b+F.sub.mF.sub.NF.sub.DF.sub.b(3)
where m is the mass of ball penetrometer 1, a is the acceleration measured by accelerometer 3c, W.sub.b is the submerge weight of ball penetrometer 1 in water, F.sub.m is the measured force by load cell 2b, F.sub.N is the soil end bearing resistance on ball penetrometer 1 during its dynamic penetration within the seabed, F.sub.D is the soil drag force on ball penetrometer 1 during its dynamic penetration within the seabed, F.sub.b is the soil buoyancy on ball penetrometer 1, which is expressed as the product of displaced soil volume by ball penetrometer 1 and soil effective unit weight (). Morton et al. suggested that during the acceleration (or deceleration) of the ball penetrometer 1, the surrounding soil around the ball moves and accelerates (or decelerates) together with the ball. Hence it is necessary to consider the added mass, m, can be expressed in Eq. (4).
m=C.sub.mm.sub.soil(4)
where C.sub.m is the added mass coefficient, which is usually valued as C.sub.m=0.5, m.sub.soil is the displaced soil mass by the ball penetrometer 1, which can be described in Eq. (5).
m.sub.soil=V.sub.ball.sub.soil(5)
where V.sub.ball is the displaced soil volume by the ball penetrometer 1, and .sub.soil is the density of the soil.

(25) If the soil strain-rate effect during the dynamic penetration of the ball penetrometer 1 within the soil is taken into consideration, the soil end bearing resistance, F.sub.N, in Eq. (3) can be expressed in Eq. (6).
F.sub.N=R.sub.fN.sub.cs.sub.uA.sub.t(6)
where N.sub.c is the end bearing capacity factor of the ball penetrometer 1, s.sub.u is the measured soil undrained shear strength under the reference shear strain-rate, A.sub.t is the projected area of the ball penetrometer 1, R.sub.f is the strain-rate factor, which is expressed using the power law shown in Eq. (7).

(26) $\begin{array}{cc}{R}_f={\left(\frac{\stackrel{.}{}}{{\stackrel{.}{}}_{\mathrm{ref}}}\right)}^{}={\left(\frac{v/D}{\stackrel{.}{}{\mathrm{ref}}_{}}\right)}^{}& \left(7\right)\end{array}$
where {dot over ()} is the shear strain-rate defined as the ratio of the velocity, v, to the diameter, D, of the ball penetrometer 1, {dot over ()}.sub.ref is reference shear strain-rate, is the strain-rate parameter usually ranging 0.0340.14.

(27) Liu et al. indicated that the strain-rate factor, R.sub.f, of a free fall cone penetrometer depends on the velocity, v, strain-rate parameter, , non-Newtonian Reynolds number, R.sub.en, and frictional coefficient, , based on numerical simulations. Moreover, the expression of the strain-rate factor, R.sub.f, can be fitted based on numerical simulating results. Therefore, the factor R.sub.f is expressed by Eq. (8).
R.sub.f=f.sub.1(v,,,R.sub.en)(8)
The non-Newtonian Reynolds number, R.sub.en, in the above equation can be expressed as Eq. (9).

(28) $\begin{array}{cc}{R}_{\mathrm{en}}=\frac{{}_{\mathrm{soil}}{v}^2}{s_u}& \left(9\right)\end{array}$
Therefore, the strain-rate factor R.sub.f is expressed as:
R.sub.f=f.sub.1(v,,,.sub.soil,s.sub.u)(10)
The end bearing capacity factor, N.sub.c, of the ball penetrometer 1 depends on the frictional coefficient, , and can be described as Eq. (11).
N.sub.c=f.sub.2()=A.sub.1+A.sub.2+A.sub.3.sup.2(11)
where A.sub.1A.sub.3 are undetermined parameters which can be determined from numerical simulations. For example, Liu et al. established the relationship between the end bearing capacity factor and frictional coefficient of the free fall cone penetrometer based on numerical simulations.

(29) The soil drag force during the penetration process of the ball penetrometer 1 in the soil shown in Eq. (3) can be described by Eq. (12).
F.sub.D=C.sub.D.sub.soilv.sup.2A.sub.t(12)
where C.sub.D is the drag coefficient. Liu et al. indicated that the drag coefficient of a free fall cone penetrometer depends on the frictional coefficient, , and non-Newtonian Reynolds number, R.sub.en, and the expression of C.sub.D can be determined from numerical simulating results. Therefore, the factor C.sub.D can be expressed as Eq. (13).
C.sub.Df.sub.3(,R.sub.en)=f.sub.3(,.sub.soil,v,s.sub.u)(13)

(30) Based on Eqs. (313), the soil undrained shear strength back-analyzed based on the measured acceleration, a, and force, F.sub.m, is expressed by Eq. (14).

(31) $\begin{array}{cc}{s}_u=\frac{\begin{array}{c}{W}_b+F_m-\left(m+C_m{m}_{\mathrm{soil}}\right)a-\\ 0.5f_3\left(,{}_{\mathrm{soil}},v,s_u\right){}_{\mathrm{soil}}{v}^2{A}_t-F_b\end{array}}{A_t.Math.f_2\left(\right).Math.f_1\left(v,,,{}_{\mathrm{soil}},s_u\right)}& \left(14\right)\end{array}$

(32) where the associated parameters in f.sub.1, f.sub.2 and f.sub.3 can be determined from numerical simulations. In Eq. (14), W.sub.b and F.sub.b are directly calculated, F.sub.m and a are measured by load cell and accelerometer, v is obtained by integrating the data of the accelerometer, and , , and s.sub.u are unknown parameters which can be back-analyzed based on a least-squares regression scheme.

(33) For typical clayey seabed, the soil undrained shear strength increases linearly with depth. Hence s.sub.u can be expressed as:
s.sub.u=s.sub.u0+kz(15)
where s.sub.u0 is the soil undrained shear strength at the mudline, z is the distance from the soil surface, k is the soil strength gradient. Based on the measured data from the accelerometer and load cell during the dynamic penetration process of the ball penetrometer, the soil strength parameters (s.sub.u0, k), strain-rate parameter (), and frictional coefficient () are back-analyzed using Eqs. (1415).

(34) FIG. 7 and FIG. 8 show the variation of acceleration and velocity with penetration depth. A series of acceleration (a.sub.1, a.sub.2, . . . , a.sub.n) and velocity (v.sub.1, v.sub.2, . . . , v.sub.n) data with different depths are obtained from the measured data. Then the soil strength parameters (s.sub.u0, k), strain-rate parameter (), and frictional coefficient () are back-analyzed based on Eq. (14) through a least-squares regression scheme.

(35) As shown in FIGS. (1a3c), the free fall ball penetrometer with a booster primarily comprises a ball penetrometer 1 and booster 3. The ball penetrometer 1 and booster 3 are connected by a connecting rod 2. The booster 3 comprises a cylindrical shaft 3b with ellipsoidal tip and retracted rear to reduce the drag force during the dynamic penetration process. The booster rear is set with rear fins 3d to improve the directional stability and reduce the inclination of the penetrometer during the falling process. The rear fins 3d are fixed to the booster 3 by being inserted into the slots reserved at the booster rear. The booster tip is provided with internal threads 3a to connect the external threads 2a of the connecting rod 2. If using wireless data acquisition and storage method, the internal space in the booster 3 is equipped with accelerometer 3c, power supply 3e, and internal data acquisition card 3f to collect associated data during the falling process. The internal data acquisition card 3f, which is connected to the power supply 3e, is used to record the data from the load cell, accelerometer, and pore water pressure transducer. If using external data acquisition and storage method, the wires of the load cell, accelerometer, and pore water pressure transducer are connected to the external data acquisition instrument 4. The length of the booster 3 can be adjusted based on practical requirement. In order to obtain a deep penetration depth, along and heavy booster may be used. For a long fall distance in water, the rear fins 3d of the booster should be enlarged to improve the directional stability in water. While with a low fall distance in water, the rear fins 3d can be replaced with smaller ones to reduce the water and soil resistance on the booster. One side of the connecting rod 2 is used to connect the ball penetrometer 1, and the other side of the connecting rod 2 is provided with external threads 2a to connect the booster 3. The axes of booster 3, connecting rod 2 and ball penetrometer 1 should be collinear to improve the directional stability of the whole system and avoid large inclination during the falling process. A load cell 2b between the ball penetrometer 1 and connecting rod 2 is used to measure the resistance of the ball penetrometer 1 during the dynamic penetration within the soil. A pore water pressure transducer 1a is configured in the equator of the ball penetrometer 1 to measure the pore water pressure in the soil around the ball. After measurement, the whole system is retrieved by pulling the retrieval line 3g up.