**4. Experimental results**

The rheological characterization (rheometry) has classified the mixtures into two distinct groups as it was illustrated in Fig. 5. Based on that approach, all data and results obtained through experimental work were compared in order to establish groups with similar properties. A total of 15 parameters divided into seven categories were used to fully characterize and distinguish each group: geometry, rheology, analysis of mean vertical profiles, time-series of data, internal dynamics of the flow, depositional features and, nondimensional parameters as seen in Fig. 6.

After applying this method of analysis, it was possible to identify six regions (or groups) of similar sediment gravity flows generated experimentally. Each one has typical properties and characteristics in terms of rheology, geometry, hydrodynamic and depositional processes along time and space. Moreover, the relationship with initial properties (concentration and clay content) demonstrates the cause-consequence of the experiments (from source to deposit) and the entire dynamic involved. The Fig. 7 illustrates this diagramphase with delimited boundaries amongst the regions.

Each region properties will be completely described below from non-cohesive dominated flows (regions I, II and III) to cohesive dominated flows (regions IV, V and VI). The averaged vertical profiles will be discussed apart (item 4.6).

Sediment Gravity Flows: Study Based on Experimental Simulations 273

Fig. 7. Six regions (or groups) of similar sediment gravity flows generated experimentally

Sediment gravity flows generated considering the properties of the region I (Newtonian, low-volumetric concentration (< 5%) regardless of the amount of clay) reproduces a classic behaviour of turbidity currents widely discussed in the literature (Kneller & Buckee, 2000; Middleton, 1966; Simpson, 1997). The current accelerates (waxing flow – Kneller, 1995) due to the buoyancy flux with clearly defined head at the front. The thickness of the head is greater than the body, indicating the flow undergoes a large resistance of the ambient fluid and also from gravitational forces acting over the body. As consequence, a large billow

The body presents the peak of velocity and after this point the flow starts to decelerate gradually (waning flows - Kneller, 1995). Concomitantly, the concentration of sediment within the flow follows the velocity behaviour. In the head, sediments are held in suspension by virtue of the high-turbulence intensity (no depositional zone) and then, the suspended sediments start to settle (fall out) with the decrease in velocity. The current becomes diluted and finally there is only the sedimentation of finer particles by

In these currents the main mechanism of grain support is turbulence (inertial forces) with high Reynolds numbers along the entire current (despite the low concentration of mixtures) except for the final stages of the flow (tail). The evaluation of the turbulent intensity (*root mean square* - RMS) shows that turbulence occurs mainly in the head and particularly in the vortex generated behind the head whilst in the body, turbulence occurs around shear layer (mixing zone). Along the vertical profile there was absence of high RMS values near the

decantation (very long time for cohesive particles because of low settling velocity).

**4.1 Region I - Turbidity currents like sediment gravity flows** 

(shear vortex) takes place behind the head (high mixing zone).

Fig. 6. Results obtained through the experimental simulations

Fig. 6. Results obtained through the experimental simulations

Fig. 7. Six regions (or groups) of similar sediment gravity flows generated experimentally

### **4.1 Region I - Turbidity currents like sediment gravity flows**

Sediment gravity flows generated considering the properties of the region I (Newtonian, low-volumetric concentration (< 5%) regardless of the amount of clay) reproduces a classic behaviour of turbidity currents widely discussed in the literature (Kneller & Buckee, 2000; Middleton, 1966; Simpson, 1997). The current accelerates (waxing flow – Kneller, 1995) due to the buoyancy flux with clearly defined head at the front. The thickness of the head is greater than the body, indicating the flow undergoes a large resistance of the ambient fluid and also from gravitational forces acting over the body. As consequence, a large billow (shear vortex) takes place behind the head (high mixing zone).

The body presents the peak of velocity and after this point the flow starts to decelerate gradually (waning flows - Kneller, 1995). Concomitantly, the concentration of sediment within the flow follows the velocity behaviour. In the head, sediments are held in suspension by virtue of the high-turbulence intensity (no depositional zone) and then, the suspended sediments start to settle (fall out) with the decrease in velocity. The current becomes diluted and finally there is only the sedimentation of finer particles by decantation (very long time for cohesive particles because of low settling velocity).

In these currents the main mechanism of grain support is turbulence (inertial forces) with high Reynolds numbers along the entire current (despite the low concentration of mixtures) except for the final stages of the flow (tail). The evaluation of the turbulent intensity (*root mean square* - RMS) shows that turbulence occurs mainly in the head and particularly in the vortex generated behind the head whilst in the body, turbulence occurs around shear layer (mixing zone). Along the vertical profile there was absence of high RMS values near the

Sediment Gravity Flows: Study Based on Experimental Simulations 275

next to boundary between regions I and II), other depositional processes start to play in the

In non-cohesive flows, the sediment in suspension settled down creating a concentrated near-bed layer that was constantly fed by sediments from the top (fall out). As consequence, the space between grains became more restricted causing rapid deposition of sediments (high depositional rate in the first stages of the flow where there was insufficient time for the natural segregation of the grains). Hence, the deposit generated *partially graded beds*, i.e., massive (coarse size) deposits at the bottom followed by fining upwards particles on the top

Despite the presence of clay in the mixtures gives the impression to modify the mechanism of deposition of these currents, again, for this group of experiments the deposits show a clear division between the non-cohesive grains (at the bottom) and cohesive grains (at the top).

The region III corresponds to Newtonian flows with high-concentration and low presence of clay (up to maximum of 20%). The hydrodynamics followed the processes described before (region II), considering the higher values of velocity (amongst all regions) and also the flux of buoyancy, which does not allow the grains settled down in the early stages of the flow. The magnitude of forces acting over the head (mainly buoyancy) and over the body (mainly gravitational) was similar reducing the head height. Once more the flow generates a very wavy concentrated layer close to the bottom, creating a bipartite flow which caused sudden deposition (high-depositional rate) of large amount of sediments. Then, the diluted current

The support mechanism of grain in these flows is basically turbulence generated at the head (high values of RMS) as well as the upper and lower surfaces. However, additional sediment-support mechanisms as hindered settling and dispersive pressure may occur within the concentrated near-bed layer (mainly non-cohesive). On the other side, the mechanism of deposition for these flows represents an evolution of the processes described in region II. Since the suspended load of sediment becomes progressively concentrated towards the bottom, the continuous supply of the grain from the top (fall out) compress the inner layer reducing space for grains to move. At this point, there is a rapid deposition of grains. This process may be a first signal of frictional freezing, where non-cohesive grains settle quickly (collapse) without segregating grains by size. As a result, deposit is partially graded; being massive graded near the bottom and normally graded (fining upward) on the

The flows classified as region IV are non-Newtonian, which consequently leads to changes in hydrodynamic properties, such as sediment-support mechanism and depositional

In this class of flows dominated by cohesive particles, the hydrodynamic processes are closely related to the region II. The head of the current is the local of high velocity, turbulent intensity and mixing, whilst the viscous forces play a significant role on the body causing deceleration and then, the early stage of deposition. It was also verified the formation of a concentrated layer (mainly dominated by clay) at the bottom. The presence of this deformable clay/mud near-bed layer is followed by a constant value of inner concentration.

flows regarding the amount of clay in the mixture.

(final stages of flow with low depositional rate).

flows over the bed previously deposited (low-depositional rate).

**4.3 Region III** 

top.

**4.4 Region IV** 

processes, mainly because of the yield strength.

bottom, which may explain the initiation of the deposition just after the passage of the front. For the flows of this region, the presence of cohesive sediments at low concentrations (< 5%) implies in no significant changes on the flow behaviour.

During the flow movement, the main mechanism of deposition was by individual particles (grain-to-grain) falling out from suspension by gravity (decelerating flow). Consequently, the dissipation of turbulence caused the lost of sediment-transport capacity of the flow and the grains segregated naturally, i.e. the coarse grains (high setting velocity) were deposited first followed by fine grains and then by colloidal particles (after the stop indeed). As a result, the deposits generated normal gradation (decreasing mean grain size towards to the top - fining upward). For the flows containing clay in suspension, the deposit is characterized by a non-cohesive layer of grains near the bottom with a layer of clay (as a resulted of settling) at the top. The contact between the non-cohesive and cohesive grains is very sharp, clearly indicating different stages of deposition. Despite the fact that clay may form flocs, due to the cohesion of their particles, there was no evidence of the formation of large flocs. The depositional rate for this class of flows was linear (deposit thickness increased at constant rate) starting just after the passage of the head.

#### **4.2 Region II**

The Newtonian sediment gravity flows originated by the increase in concentration and the presence of clay (around 50%) showed differences in the properties of the flow dynamics and deposition. Both velocity and buoyancy flux increased in the flow causing a decreased in the head height. As a result, the average velocities of the body and head were almost identical, showing that buoyancy forces present in the head are in balance with gravitational forces. Yet, the head of the current is slightly higher then the body and is characterized by intense mixing zone. The main difference comparing with region I can be noticed after the peak of velocity in the body, since the flow rapidly decelerates reaching low values of velocity until completely stopped (tail). The quick deceleration is related to formation of an inner layer of grains more concentrated near the bottom. For a short time the flow becomes stratified (bipartite) changing the velocity and concentration profile instantly and implying in different mechanisms of deposition.

The sediment-support mechanism of the non-cohesive flows (low content of clay) is driven by the turbulence of the flow (in the head), Kelvin-Helmholtz instabilities behind the head and along the mixture layer at the upper and the bottom surfaces. The high values of turbulence intensity were measured throughout vertical profile explaining a period of no deposition at early stages of the flow. Also, the concentrated near-bed layer (mainly noncohesive) is characterized by high turbulence intensity and its internal undulations are closely related to instabilities at the upper surface.

The flows generated from experiments adjacent to rheological threshold in Fig. (7), the increase of amount of clay and/or concentration caused a decrease in turbulence intensity. Also, not only the turbulence plays a key role on these flows but also the influence of the matrix strength and cohesive interaction of the grains started to become relatively significant. This fact is reflected on the behaviour of near-bed layer (mainly cohesive) which is characterized by undulations and deformations, although not as considerable as those presented by pure non-cohesive flows.

The mechanism of deposition in such flows differs from region I. Besides the grain-to-grain sedimentation caused by dissipation of the turbulence intensity (typical behaviour of flows next to boundary between regions I and II), other depositional processes start to play in the flows regarding the amount of clay in the mixture.

In non-cohesive flows, the sediment in suspension settled down creating a concentrated near-bed layer that was constantly fed by sediments from the top (fall out). As consequence, the space between grains became more restricted causing rapid deposition of sediments (high depositional rate in the first stages of the flow where there was insufficient time for the natural segregation of the grains). Hence, the deposit generated *partially graded beds*, i.e., massive (coarse size) deposits at the bottom followed by fining upwards particles on the top (final stages of flow with low depositional rate).

Despite the presence of clay in the mixtures gives the impression to modify the mechanism of deposition of these currents, again, for this group of experiments the deposits show a clear division between the non-cohesive grains (at the bottom) and cohesive grains (at the top).

#### **4.3 Region III**

274 Hydrodynamics – Natural Water Bodies

bottom, which may explain the initiation of the deposition just after the passage of the front. For the flows of this region, the presence of cohesive sediments at low concentrations (< 5%)

During the flow movement, the main mechanism of deposition was by individual particles (grain-to-grain) falling out from suspension by gravity (decelerating flow). Consequently, the dissipation of turbulence caused the lost of sediment-transport capacity of the flow and the grains segregated naturally, i.e. the coarse grains (high setting velocity) were deposited first followed by fine grains and then by colloidal particles (after the stop indeed). As a result, the deposits generated normal gradation (decreasing mean grain size towards to the top - fining upward). For the flows containing clay in suspension, the deposit is characterized by a non-cohesive layer of grains near the bottom with a layer of clay (as a resulted of settling) at the top. The contact between the non-cohesive and cohesive grains is very sharp, clearly indicating different stages of deposition. Despite the fact that clay may form flocs, due to the cohesion of their particles, there was no evidence of the formation of large flocs. The depositional rate for this class of flows was linear (deposit thickness

The Newtonian sediment gravity flows originated by the increase in concentration and the presence of clay (around 50%) showed differences in the properties of the flow dynamics and deposition. Both velocity and buoyancy flux increased in the flow causing a decreased in the head height. As a result, the average velocities of the body and head were almost identical, showing that buoyancy forces present in the head are in balance with gravitational forces. Yet, the head of the current is slightly higher then the body and is characterized by intense mixing zone. The main difference comparing with region I can be noticed after the peak of velocity in the body, since the flow rapidly decelerates reaching low values of velocity until completely stopped (tail). The quick deceleration is related to formation of an inner layer of grains more concentrated near the bottom. For a short time the flow becomes stratified (bipartite) changing the velocity and concentration profile instantly and implying

The sediment-support mechanism of the non-cohesive flows (low content of clay) is driven by the turbulence of the flow (in the head), Kelvin-Helmholtz instabilities behind the head and along the mixture layer at the upper and the bottom surfaces. The high values of turbulence intensity were measured throughout vertical profile explaining a period of no deposition at early stages of the flow. Also, the concentrated near-bed layer (mainly noncohesive) is characterized by high turbulence intensity and its internal undulations are

The flows generated from experiments adjacent to rheological threshold in Fig. (7), the increase of amount of clay and/or concentration caused a decrease in turbulence intensity. Also, not only the turbulence plays a key role on these flows but also the influence of the matrix strength and cohesive interaction of the grains started to become relatively significant. This fact is reflected on the behaviour of near-bed layer (mainly cohesive) which is characterized by undulations and deformations, although not as considerable as those

The mechanism of deposition in such flows differs from region I. Besides the grain-to-grain sedimentation caused by dissipation of the turbulence intensity (typical behaviour of flows

implies in no significant changes on the flow behaviour.

increased at constant rate) starting just after the passage of the head.

**4.2 Region II** 

in different mechanisms of deposition.

presented by pure non-cohesive flows.

closely related to instabilities at the upper surface.

The region III corresponds to Newtonian flows with high-concentration and low presence of clay (up to maximum of 20%). The hydrodynamics followed the processes described before (region II), considering the higher values of velocity (amongst all regions) and also the flux of buoyancy, which does not allow the grains settled down in the early stages of the flow. The magnitude of forces acting over the head (mainly buoyancy) and over the body (mainly gravitational) was similar reducing the head height. Once more the flow generates a very wavy concentrated layer close to the bottom, creating a bipartite flow which caused sudden deposition (high-depositional rate) of large amount of sediments. Then, the diluted current flows over the bed previously deposited (low-depositional rate).

The support mechanism of grain in these flows is basically turbulence generated at the head (high values of RMS) as well as the upper and lower surfaces. However, additional sediment-support mechanisms as hindered settling and dispersive pressure may occur within the concentrated near-bed layer (mainly non-cohesive). On the other side, the mechanism of deposition for these flows represents an evolution of the processes described in region II. Since the suspended load of sediment becomes progressively concentrated towards the bottom, the continuous supply of the grain from the top (fall out) compress the inner layer reducing space for grains to move. At this point, there is a rapid deposition of grains. This process may be a first signal of frictional freezing, where non-cohesive grains settle quickly (collapse) without segregating grains by size. As a result, deposit is partially graded; being massive graded near the bottom and normally graded (fining upward) on the top.

#### **4.4 Region IV**

The flows classified as region IV are non-Newtonian, which consequently leads to changes in hydrodynamic properties, such as sediment-support mechanism and depositional processes, mainly because of the yield strength.

In this class of flows dominated by cohesive particles, the hydrodynamic processes are closely related to the region II. The head of the current is the local of high velocity, turbulent intensity and mixing, whilst the viscous forces play a significant role on the body causing deceleration and then, the early stage of deposition. It was also verified the formation of a concentrated layer (mainly dominated by clay) at the bottom. The presence of this deformable clay/mud near-bed layer is followed by a constant value of inner concentration.

Sediment Gravity Flows: Study Based on Experimental Simulations 277

Fig. 8. Mean vertical profiles of velocity, concentration and sediment flux for the six regions

Concerning the flows classified as Newtonian (regions I, II and III), the velocity profile presented the classical behaviour of turbidity current (see description section 1.1) with a maximum velocity point located at some distance from the bottom and two distinct zones: an inner zone near the wall and an outer zone up to the top surface (Fig 8, top-left). Applying the model developed by Michon et al., (1955) and modified by Altinakar, (1988) it was possible to establish analytical equations for non-dimensional velocity profiles in terms

The model consists in a relationship between a non-dimensional velocity and geometry parameters and also separates the velocity profile in two zones (the threshold is height of maximum velocity - hm). The equations below present the results of applied methodology for the inner zone (z < hm) including the parameters fitted for this group of experiments.

> *u z = U h* max max

*u h h e*

.

Those equations can be applied to a wider range of currents with different behaviours as the first approximation of the non-dimensional velocity profile for Newtonian sediment gravity

*U*

max

*0.4*

1 9

.

2 7 *<sup>m</sup> t m z h*

(7)

(8)

of sediment gravy flows.

**4.6.1 Velocity profiles** 

of initial concentration of the flow.

And for the outer zone (z > hm) is,

The sediment-support mechanism is influenced by the content of clay once the turbulence is damped within the current (being only verified in the head of the flow). The cohesive matrix begins to act internally changing the hydrodynamic behaviour of the current. The buoyancy of the interstitial fluid (water and clay) and pore-pressure also contribute to keep the grains in suspension inside the clay/mud near-bed. This behaviour differs from Newtonian noncohesive flows (regions II and III). In region IV, the concentration has not yet reached the gelling concentration for cohesive mixtures (Winterwerp, 2002).

During the flow, it was possible clearly identify the shear-like flow near the bed and pluglike flow above that, which is dominated by viscous forces acting on the flow. However, the flow can not be classified as completely laminar, since spots of turbulence (high intensity) can be generated within this layer. Also, in the plug-like flow, fluid shear stress is lower than yield strength of the mixture, generating an instantaneously mass deposit (cohesive freezing). As it occurs suddenly, there is no segregation (selection) of the grains. On the other side, the shear stress at the bed is higher enough to allow the settled of non-cohesive sediments. As a result, the final deposit is divided into three distinct depositional layers: low-content clay (~ 5%) bottom layer (shear-like flow); an intermediate ungraded matrix of sand and clay/mud layer (plug-like flow) and; a clay dominant layer on the top (tail and settling deposition).

#### **4.5 Region V and Region VI - Debris flow like sediment gravity flow**

Regions V and VI have very similar behaviour with high concentration and high amount of cohesive material (Herschel-Bulkley rheological model). This region represents the other extreme of sediment gravity flows evolution and their transformations.

The hydrodynamic of the current was influenced by the clay content presenting a strong waxing flow-phase (high-turbulence intensity only at the head) and abrupt deceleration, after the arrival of deformable clay/mud near-bed layer (for Region V) and practically not undulating/deformable (for region VI). The plug-like flow in the body induced cohesive freezing, in which a large amount of sediments are deposited in few seconds (highdepositional rate). In this region, the content of clay in the mixture at high concentrations is influenced by the gelling concentration. According to the literature, this occurs at concentrations of clay between 80 and 180 g/l, equivalent to a solid volume fraction of 0.03 and 0.07 (Whitehouse et al., 2000; Winterwerp, 2001, 2002). The mixtures simulated in the regions V and VI correspond to this range of values. Therefore, the cohesive forces acting on these deposits are transmitted to all mass deposited and not only to each single particle causing a thick ungraded chaotic deposit.

The sediment-support mechanism is highly influenced by the increased of apparent viscosity of the mixture and matrix strength which is induced by electrostatic interactions of clay particles. Thus, turbulence is damped throughout the flow, with local spots of high-turbulence intensity close to the bottom (high values), as well as at the interface between the deposit generated by clay/mud near-bed layer and the remaining flow (body and tail). This final stage of the flow generates a normally graded deposit (coarse-tail grading on the top) associated to the mechanism of deposition described in the region I (turbidity currents like flows).

#### **4.6 Mean vertical profiles**

Based on the experimental results, Fig. (8) illustrated the idealized pattern for each region concerning the average velocity, concentration and sediment flux vertical profiles.

Fig. 8. Mean vertical profiles of velocity, concentration and sediment flux for the six regions of sediment gravy flows.

#### **4.6.1 Velocity profiles**

276 Hydrodynamics – Natural Water Bodies

The sediment-support mechanism is influenced by the content of clay once the turbulence is damped within the current (being only verified in the head of the flow). The cohesive matrix begins to act internally changing the hydrodynamic behaviour of the current. The buoyancy of the interstitial fluid (water and clay) and pore-pressure also contribute to keep the grains in suspension inside the clay/mud near-bed. This behaviour differs from Newtonian noncohesive flows (regions II and III). In region IV, the concentration has not yet reached the

During the flow, it was possible clearly identify the shear-like flow near the bed and pluglike flow above that, which is dominated by viscous forces acting on the flow. However, the flow can not be classified as completely laminar, since spots of turbulence (high intensity) can be generated within this layer. Also, in the plug-like flow, fluid shear stress is lower than yield strength of the mixture, generating an instantaneously mass deposit (cohesive freezing). As it occurs suddenly, there is no segregation (selection) of the grains. On the other side, the shear stress at the bed is higher enough to allow the settled of non-cohesive sediments. As a result, the final deposit is divided into three distinct depositional layers: low-content clay (~ 5%) bottom layer (shear-like flow); an intermediate ungraded matrix of sand and clay/mud layer (plug-like flow) and; a clay dominant layer on the top (tail and

Regions V and VI have very similar behaviour with high concentration and high amount of cohesive material (Herschel-Bulkley rheological model). This region represents the other

The hydrodynamic of the current was influenced by the clay content presenting a strong waxing flow-phase (high-turbulence intensity only at the head) and abrupt deceleration, after the arrival of deformable clay/mud near-bed layer (for Region V) and practically not undulating/deformable (for region VI). The plug-like flow in the body induced cohesive freezing, in which a large amount of sediments are deposited in few seconds (highdepositional rate). In this region, the content of clay in the mixture at high concentrations is influenced by the gelling concentration. According to the literature, this occurs at concentrations of clay between 80 and 180 g/l, equivalent to a solid volume fraction of 0.03 and 0.07 (Whitehouse et al., 2000; Winterwerp, 2001, 2002). The mixtures simulated in the regions V and VI correspond to this range of values. Therefore, the cohesive forces acting on these deposits are transmitted to all mass deposited and not only to each single particle

The sediment-support mechanism is highly influenced by the increased of apparent viscosity of the mixture and matrix strength which is induced by electrostatic interactions of clay particles. Thus, turbulence is damped throughout the flow, with local spots of high-turbulence intensity close to the bottom (high values), as well as at the interface between the deposit generated by clay/mud near-bed layer and the remaining flow (body and tail). This final stage of the flow generates a normally graded deposit (coarse-tail grading on the top) associated to

Based on the experimental results, Fig. (8) illustrated the idealized pattern for each region

the mechanism of deposition described in the region I (turbidity currents like flows).

concerning the average velocity, concentration and sediment flux vertical profiles.

gelling concentration for cohesive mixtures (Winterwerp, 2002).

**4.5 Region V and Region VI - Debris flow like sediment gravity flow** 

extreme of sediment gravity flows evolution and their transformations.

settling deposition).

causing a thick ungraded chaotic deposit.

**4.6 Mean vertical profiles** 

Concerning the flows classified as Newtonian (regions I, II and III), the velocity profile presented the classical behaviour of turbidity current (see description section 1.1) with a maximum velocity point located at some distance from the bottom and two distinct zones: an inner zone near the wall and an outer zone up to the top surface (Fig 8, top-left). Applying the model developed by Michon et al., (1955) and modified by Altinakar, (1988) it was possible to establish analytical equations for non-dimensional velocity profiles in terms of initial concentration of the flow.

The model consists in a relationship between a non-dimensional velocity and geometry parameters and also separates the velocity profile in two zones (the threshold is height of maximum velocity - hm). The equations below present the results of applied methodology for the inner zone (z < hm) including the parameters fitted for this group of experiments.

$$\frac{\mu}{\mu L\_{\text{max}}} = \left(\frac{z}{h\_{\text{max}}}\right)^{0.4} \tag{7}$$

And for the outer zone (z > hm) is,

$$\frac{\mu}{\mu L\_{\text{max}}} = c^\* \left[ {}^{-2.7 \left( \frac{z - h\_m}{h\_t - h\_m} \right)}^{1.9} \right] \tag{8}$$

Those equations can be applied to a wider range of currents with different behaviours as the first approximation of the non-dimensional velocity profile for Newtonian sediment gravity

Sediment Gravity Flows: Study Based on Experimental Simulations 279

Fig. 9. Concentration profiles measured and fitted curves for the two groups of sediment

The evaluation of the reduced flux of sediments gives the idea of the mass conservation during the flow, since velocity, concentration and, initial properties of the flow (reduced gravity) are taken into account (eq. 10). Through the evaluation of this parameter, it is possible to check which zone within the flow the sediments are being transported as seen in

m a Flux vol mean mean

The differences among all classes of sedimentary gravity flows simulated were evidenced, particularly, the influence of the cohesive particles (non-Newtonian regions), which

The limitations of the simulations in terms of the length of the tank do not allow a complete study on spatial variability of the sediment gravity flows from their origin to the final deposit. Nonetheless, the full characterization of the main parameters involved in the flow such as time series, vertical profiles, rheology, deposition and so on, may be applied in order to extrapolate the results to natural ambient. Based on that, a detailed spatial analysis was

Concerning the flows from regions I and II, both concentration and presence of clay increased sediment capacity of transport of the flow, indicating the current could flow further. At the early stages (near the source) the gravity flow is more concentrated with high buoyancy flux and high-turbulence. As the flow propagates downstream, the hydrodynamic

(10)

a S g Ch u

 

accomplished and the flow evolution for each region will be described below.

implying in a great amount of sediments at the bottom of the current.

**5. Spatial evolution of the sediment gravity flows** 

gravity flows simulated: a) regions I, II and III; b) regions IV, V and VI.

**4.6.3 Reduced Flux of Sediment** 

the experimentally-derived profiles in Fig. 8.

flows. However, in order to extrapolate the results to natural fields, it must take into consideration the maximum velocity value and its location within the current.

For the flows classified as non-Newtonian (regions IV, V and V) the velocity profile changes drastically and can be divided in four zones (Fig. 8 top-right): the *shear-like flow* zone (near the bottom), strongly influenced by viscous sublayer; the *plug-like flow zone:* occurs when the value of the shear stress is lower than yield strength; and the *other two zones* from the remaining diluted current (similar to Newtonian flows described above). The first two zones involve the evaluation of the shear stress at the wall (viscous sublayer) and the thickness of the plug. For the last two zones above the plug-like flow the model of Michon et al., (1955) can be adjusted adding the plug-like flow velocity and its thickness.

The velocity profiles measured for the high-density currents were similar to those cited by (McCave & Jones, 1988; Postma et al., 1988, Talling et al., 2007). To express these profiles in terms of equations require a detailed analysis of stress distribution along the vertical profiles (to establish the shear zone and plug zone) as well as the estimative of the thickness of the near–bed layer (inner flow). In nature those parameters are not easily estimated. The detailed evaluation of these parameters can be found in Manica, (2009).

#### **4.6.2 Concentration profile**

The mean concentration profile measured in the experiments show the transition between the six regions of sediment gravity flows (Fig. 8). For flows classified as Newtonian (regions I, II and III) the profile is practically more invariable along the vertical (region I) with a slight increase (creating an inflexion point) at the concentration values near the bottom. The curve is similar to an exponential trend (regions II and III), corresponding typical profiles of open-channel flows (e.g. rivers). An empirical exponential law can be fit in such type of curves considering non-dimensional parameters defined as: local concentration divided by concentration measured at 5% of the total height of the flow (concentration of reference – Cr); and the distance from the bottom divided by total height of the current (z/ht). The equation fitted for the experimental results is expressed by

$$\frac{C(z)}{C\_r} = 1.22 \cdot e^{\left(-4.0 \frac{z}{h\_t}\right)}\tag{9}$$

Considering the non-Newtonian sedimentary gravity flows (regions IV, V and VI), the vertical profile of concentrations is strongly influenced by the clay/mud inner layer, which generates high-levels of concentration and, practically stratified the profile into two regions (threshold is the inner layer thickness – see Fig. 1). In terms of analytical adjustment of these peculiar curves, the definition of this threshold point is crucial, once it can be presumed for z < hi that concentration assumes the value of concentration of reference. Above the clay/mud inner layer, equation (9) can be applied.

The methodology presented here to obtain the non-dimensional concentration profiles (Fig. 9) was straightforward in order to simplify at maximum the input parameters. Methodologies found in literature such as (Graf & Altinakar, 1998, Parker et al., 1987) were tested and applied showing very similar results.

flows. However, in order to extrapolate the results to natural fields, it must take into

For the flows classified as non-Newtonian (regions IV, V and V) the velocity profile changes drastically and can be divided in four zones (Fig. 8 top-right): the *shear-like flow* zone (near the bottom), strongly influenced by viscous sublayer; the *plug-like flow zone:* occurs when the value of the shear stress is lower than yield strength; and the *other two zones* from the remaining diluted current (similar to Newtonian flows described above). The first two zones involve the evaluation of the shear stress at the wall (viscous sublayer) and the thickness of the plug. For the last two zones above the plug-like flow the model of Michon et al., (1955) can be adjusted adding the plug-like flow velocity and its

The velocity profiles measured for the high-density currents were similar to those cited by (McCave & Jones, 1988; Postma et al., 1988, Talling et al., 2007). To express these profiles in terms of equations require a detailed analysis of stress distribution along the vertical profiles (to establish the shear zone and plug zone) as well as the estimative of the thickness of the near–bed layer (inner flow). In nature those parameters are not easily estimated. The detailed evaluation of these parameters can be found in Manica, (2009).

The mean concentration profile measured in the experiments show the transition between the six regions of sediment gravity flows (Fig. 8). For flows classified as Newtonian (regions I, II and III) the profile is practically more invariable along the vertical (region I) with a slight increase (creating an inflexion point) at the concentration values near the bottom. The curve is similar to an exponential trend (regions II and III), corresponding typical profiles of open-channel flows (e.g. rivers). An empirical exponential law can be fit in such type of curves considering non-dimensional parameters defined as: local concentration divided by concentration measured at 5% of the total height of the flow (concentration of reference – Cr); and the distance from the bottom divided by total height of the current (z/ht). The equation fitted for the experimental

> 4 0 1 22 *<sup>t</sup>*

 

*e*

. ( ) .

Considering the non-Newtonian sedimentary gravity flows (regions IV, V and VI), the vertical profile of concentrations is strongly influenced by the clay/mud inner layer, which generates high-levels of concentration and, practically stratified the profile into two regions (threshold is the inner layer thickness – see Fig. 1). In terms of analytical adjustment of these peculiar curves, the definition of this threshold point is crucial, once it can be presumed for z < hi that concentration assumes the value of concentration of reference. Above the

The methodology presented here to obtain the non-dimensional concentration profiles (Fig. 9) was straightforward in order to simplify at maximum the input parameters. Methodologies found in literature such as (Graf & Altinakar, 1998, Parker et al., 1987) were

*r C z*

*C*

clay/mud inner layer, equation (9) can be applied.

tested and applied showing very similar results.

*z h*

(9)

consideration the maximum velocity value and its location within the current.

thickness.

**4.6.2 Concentration profile** 

results is expressed by

Fig. 9. Concentration profiles measured and fitted curves for the two groups of sediment gravity flows simulated: a) regions I, II and III; b) regions IV, V and VI.

#### **4.6.3 Reduced Flux of Sediment**

The evaluation of the reduced flux of sediments gives the idea of the mass conservation during the flow, since velocity, concentration and, initial properties of the flow (reduced gravity) are taken into account (eq. 10). Through the evaluation of this parameter, it is possible to check which zone within the flow the sediments are being transported as seen in the experimentally-derived profiles in Fig. 8.

$$\mathbf{S}\_{\rm Flux} = \mathbf{g} \cdot \left(\frac{\rho\_{\rm m} - \rho\_{\rm a}}{\rho\_{\rm a}}\right) \cdot \mathbf{C}\_{\rm vol} \cdot \mathbf{h}\_{\rm mean} \cdot \mathbf{u}\_{\rm mean} \tag{10}$$

The differences among all classes of sedimentary gravity flows simulated were evidenced, particularly, the influence of the cohesive particles (non-Newtonian regions), which implying in a great amount of sediments at the bottom of the current.

### **5. Spatial evolution of the sediment gravity flows**

The limitations of the simulations in terms of the length of the tank do not allow a complete study on spatial variability of the sediment gravity flows from their origin to the final deposit. Nonetheless, the full characterization of the main parameters involved in the flow such as time series, vertical profiles, rheology, deposition and so on, may be applied in order to extrapolate the results to natural ambient. Based on that, a detailed spatial analysis was accomplished and the flow evolution for each region will be described below.

Concerning the flows from regions I and II, both concentration and presence of clay increased sediment capacity of transport of the flow, indicating the current could flow further. At the early stages (near the source) the gravity flow is more concentrated with high buoyancy flux and high-turbulence. As the flow propagates downstream, the hydrodynamic

Sediment Gravity Flows: Study Based on Experimental Simulations 281

deposit. From region IV to V, a concentrated inner layer presents a high deformation and undulation over time, with a shear–like flow near the bottom and a plug-like flow above (generating the three layer deposit commented on section 4.4). On the other side, from region V to VI (Fig. 13), the near-bed layer is practically a solid mass of mixture flowing

downstream, generating a thick clay/muddy deposit at proximal zone.

Fig. 11. Spatial evolution scheme of the sediment gravity flow for regions II and III.

Fig. 12. Spatial evolution scheme of the sediment gravity flow for regions VI and V

processes (e.g. entrainment of ambient water at the upper surface) and depositional processes (e.g. deposition of sediment over time and space) take place, transforming the inner properties of the flow. As a result, the current become more diluted due to deceleration of the flow, losing their capacity of transport (grains settled down) and then, tend to stop. The final deposit shows coarse grains in the proximal areas, due to deposition by gravity (high-settling velocity) and a gradually grain size thinning towards to downstream (low-settling velocity). The Fig. 10 illustrates a model of propagation for flows from region I to region II, also considering their transition points.

Fig. 10. Spatial evolution scheme of the sediment gravity flow for regions I and II.

In the flows characterized by high concentration and high content of clay (regions II and III) the hydrodynamic properties of the flow change during the run by virtue of the presence of concentrated near-bed layer. The suspended sediment rapidly settled down after the formation of this concentrated layer, causing a reduction in buoyancy flux. As consequence, the remaining diluted current is not able to travel further. This process occurs mainly in the proximal and intermediate zones, where the final deposit is, basically, massive graded. After this zone, the deposits were mainly generated by settling of the grains (gravity) up to distal zone (Fig. 11).

The spatial evolution of the deposit for non-Newtonian mixtures (regions IV, V and VI) showed a distinct behaviour. The increase of flow sediment capacity of transport by reason of high concentration and high presence of clay was counter-balanced by viscous forces, which dominated the flow dynamics and consequently, the generation of the clay/mud near-bed layer. Thus, the bulk of sediment from regions IV, V and VI was not able to travel long distances. Within the plug-like flow, the shear stress of the flow was not enough to prevail over the yield strength of the mixture. As a result, the deposit showed a great quantity of sediment in the proximal zone, whilst only a remaining diluted current flows (with more fine particles) moving to distal zones. The Fig. 12 illustrates this idealized model. The main difference between the idealized transition models of evolution to non-Newtonian sediment gravity flow regards the dynamic of the clay/mud near-bed layer and the final

processes (e.g. entrainment of ambient water at the upper surface) and depositional processes (e.g. deposition of sediment over time and space) take place, transforming the inner properties of the flow. As a result, the current become more diluted due to deceleration of the flow, losing their capacity of transport (grains settled down) and then, tend to stop. The final deposit shows coarse grains in the proximal areas, due to deposition by gravity (high-settling velocity) and a gradually grain size thinning towards to downstream (low-settling velocity). The Fig. 10 illustrates a model of propagation for flows

from region I to region II, also considering their transition points.

Fig. 10. Spatial evolution scheme of the sediment gravity flow for regions I and II.

zone (Fig. 11).

In the flows characterized by high concentration and high content of clay (regions II and III) the hydrodynamic properties of the flow change during the run by virtue of the presence of concentrated near-bed layer. The suspended sediment rapidly settled down after the formation of this concentrated layer, causing a reduction in buoyancy flux. As consequence, the remaining diluted current is not able to travel further. This process occurs mainly in the proximal and intermediate zones, where the final deposit is, basically, massive graded. After this zone, the deposits were mainly generated by settling of the grains (gravity) up to distal

The spatial evolution of the deposit for non-Newtonian mixtures (regions IV, V and VI) showed a distinct behaviour. The increase of flow sediment capacity of transport by reason of high concentration and high presence of clay was counter-balanced by viscous forces, which dominated the flow dynamics and consequently, the generation of the clay/mud near-bed layer. Thus, the bulk of sediment from regions IV, V and VI was not able to travel long distances. Within the plug-like flow, the shear stress of the flow was not enough to prevail over the yield strength of the mixture. As a result, the deposit showed a great quantity of sediment in the proximal zone, whilst only a remaining diluted current flows (with more fine particles) moving to distal zones. The Fig. 12 illustrates this idealized model. The main difference between the idealized transition models of evolution to non-Newtonian sediment gravity flow regards the dynamic of the clay/mud near-bed layer and the final deposit. From region IV to V, a concentrated inner layer presents a high deformation and undulation over time, with a shear–like flow near the bottom and a plug-like flow above (generating the three layer deposit commented on section 4.4). On the other side, from region V to VI (Fig. 13), the near-bed layer is practically a solid mass of mixture flowing downstream, generating a thick clay/muddy deposit at proximal zone.

Fig. 11. Spatial evolution scheme of the sediment gravity flow for regions II and III.

Fig. 12. Spatial evolution scheme of the sediment gravity flow for regions VI and V

Sediment Gravity Flows: Study Based on Experimental Simulations 283

The experiments simulated a single catastrophic event and do not consider a continuous sediment supply from rivers (for instance, plumes and hyperpycnal flows among others) which can change some properties of the flow along time and space. Moreover, the limit of maximum value of volumetric concentration was 35% by volume. In this case, regions III (see Amy et al., 2006) and region VI (see e.g. Hampton, 1972; Ilstad et al., 2004; Marr et al., 2001; Mohrig et al., 1999; Mohrig & Marr, 2003) were left with an open boundary to further experiments and perhaps the creation of a complementary experimental-derived

classification of sediment gravity flows.

%Clay clay content in the mixture (%) Cr concentration of reference (%) Cvol volumetric concentration (%)

g acceleration of gravity (m/s²)

hi inner layer thickness (m),

hmean mean current height (m),

 consistence coefficient n power law coefficient Sflux sediment flux (m³/s³) u current velocity (m/s),

*Greek letters* 

ht or H overall height of the current (cm),

Umax maximum current velocity (m/s), umean mean current velocity (m/s), Z or z distance to bottom (cm)

 dynamic viscosity coefficient (Pa.s) ap apparent viscosity coefficient (Pa.s) a density of ambient fluid (kg/m³) m density of mixture (kg/m³)

i yield strength - critical shear stress (Pa)

lam laminar component of shear stress (Pa) turb turbulent component of shear stress (Pa)

0 shear stress at the bottom (Pa)

x shear stress (Pa)

**8. Acknowledgement** 

C(z) volumetric concentration at the point z (%),

hm height of the point of maximum velocity (m),

coefficient of dynamic viscosity of pure water (Pa.s)

A grateful thanks to: CNPq – Brazilian National Council for Scientific and Technological Development - to support my PhD "sandwich" program at University of Leeds; the head of

**7. Nomenclature** 

∂u/∂z strain rate (1/s)

hb body height (m), hh head height (m),

Fig. 13. Spatial evolution scheme of the sediment gravity flow for regions V and VI
