Adv. Geosci., 39, 1–7, 2014 www.adv-geosci.net/39/1/2014/ doi:10.5194/adgeo-39-1-2014

© Author(s) 2014. CC Attribution 3.0 License.

Advances in Geosciences

Open Access

Acoustic measurements of a liquefied cohesive sediment bed under waves

R. Mosquera, V. Groposo, and F. Pedocchi

Instituto de Mecánica de los Fluidos e Ingeniería Ambiental (IMFIA), Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay

Correspondence to: R. Mosquera (rmosquer@fing.edu.uy)

Received: 1 October 2013 – Revised: 31 December 2013 – Accepted: 13 January 2014 – Published: 1 April 2014

Abstract. 

In this article the response of a cohesive sediment deposit under the action of water waves is studied with the help of laboratory experiments and an analytical model. Un- der the same regular wave condition three different bed re- sponses were observed depending on the degree of consoli- dation of the deposit: no bed motion, bed motion of the upper layer after the action of the first waves, and massive bed mo- tion after several waves. The kinematic of the upper 3 cm of the deposit were measured with an ultrasound acoustic profiler, while the pore-water pressure inside the bed was si- multaneously measured using several pore pressure sensors. A poro-elastic model was developed to interpret the experi- mental observations. The model showed that the amplitude of the shear stress increased down into the bed. Then it is possible that the lower layers of the deposit experience plas- tic deformations, while the upper layers present just elastic deformations. Since plastic deformations in the lower lay- ers are necessary for pore pressure build-up, the analytical model was used to interpret the experimental results and to state that liquefaction of a self consolidated cohesive sedi- ment bed would only occur if the bed yield stress falls within the range defined by the amplitude of the shear stress inside the bed.

1. Introduction

   The erosion of cohesive sediment deposits presents signifi- cant differences with the erosion of non-cohesive deposits. One of the main differences is the strong dependence of the cohesive bed erosion on the previous consolidation process. Mehta (1991) characterized the erosion mechanisms of co- hesive sediment beds into three types: surface erosion, whenthe flocs or aggregates are entrained one by one as a result of the hydrodynamic lift and drag; Mass erosion, when a slip surface is generated inside the deposit and all the material above this surface is mobilized; and Destabilization of the sediment-water interface, when processes within the bed in- duce the formation of fluid mud.Two mechanism for the formation of fluid mud have been proposed in the literature, sudden failure due to the large shear stresses imposed by “large" waves on a “soft bed" and progressive pore pressure build-up under the successive ac- tion of “small" waves on a “partially consolidated bed". This article explores the necessary conditions that would lead to the occurrence of each of these mechanisms. The second of these two mechanisms is technically described as lique- faction of the bed due to pore pressure build-up. Terzaghi et al. (1996) established that the stress at any location inside a sediment-water mixture has two components: one compo- nent is a hydrostatic stress state that acts with equal intensity in every direction, which is associated to the pore-water pres- sure. The other component, called effective stress, is associ- ated with the stress supported by the solid phase. The solid phase is considered the skeleton of the mixture and provides its shearing resistance.Liquefaction of a sediment-water mixture is related to the increase of pore-water pressure and the corresponding de- crease of the effective stress. When liquefaction occurs, the water-sediment mixture loses its shearing resistance and be- haves as a dense fluid. During liquefaction, the mechanical characteristics of the sediment bed change so dramatically that marine structures fail, buried pipelines emerge, and nav- igation channels get silted in a matter of hours. Under the action of waves, liquefaction is a major concern in sedimentbeds with low permeability such as silt, clay or very fine sand (De Groot et al., 2006; Jeng, 2003).Silt and clay water mixtures are usually referred as mud. For analytical purposes, mud can be considered to be a visco- elastic material, having an elastic response for small defor- mations and shear stresses, and a viscous response for large deformations (for an extense review see de Wit et al., 1994). These large deformations are associated with shear stresses τ overpassing a certain threshold, called yield stress τY. Under oscillatory flow, the shear stresses could overpass the yield stress during part of the wave cycle producing non-elastic deformations in some regions of the bed. In high porosity and low permeability deposits, this non-elastic deformations may induce the progressive reorganization of sediment par- ticles and the reduction of pore volume. This reduction may progressively lead to the increase (build-up) of the pore pres- sure and the associated reduction of the effective stresses, eventually triggering liquefaction (see for example the work of Sumer and Fredsøe, 2002, for non-cohesive sediments).In this article we explore the liquefaction mechanism in a cohesive-sediment bed under the action of regular waves.For this aim we ran experiments in a laboratory wave flume,stress anymore. However, the elastic model can be used to qualitatively explore the necessary conditions for liquefac- tion and interpret the experimental observations.Yamamoto et al. (1978) studied the response of a poro- elastic semi-infinite bed under regular water waves using a quasi-static model. Here the same set of equations is used, but for studying the response of a finite thickness poro-elastic bed. Furthermore, the equations are expressed in dimension- less form, defining a set of dimensionless parameters, which facilitates the psychical interpretation of the different terms in the equations, and their relevance for the occurrence of liq- uefaction. The case of a finite thickness poro-elastic bed was studied before by Spierenburg (1987). However, Spierenburg solutions were approximate, while the harmonic solutions presented here are exact. The detailed deduction of these ex- act harmonic solutions exceeds the scope of this article and can be found in Mosquera (2013).Based on the model developed by Biot (1941) and assum- ing that the pore-water flow follows Darcy’s law, the follow- ing equation for the conservation of pore-water can be writ- tenand simultaneously registered the pore pressure and the mudk n∆p =∂p ∂‹+ , (1)bed velocity. To our knowledge this is the first time these si- γKr ∂t ∂tmultaneous measurements are performed, making it possible to clearly differentiate the two mechanisms that can generate fluid mud under the action of waves: sudden shear failure in soft deposits, and progressive pore pressure build-up in par- tially consolidated ones. For this second mechanism, a theo- retical model that only considers elastic deformations of the bed is used to estimate the deformations within the bed, and to predict regions where non-elastic deformations of the bed and pore pressure build-up may occur.where k is the coefficient of permeability of the soil, γ is the unit weight of the pore-water, p is the pore-water pressure, n is the porosity, Kr is the apparent bulk modulus of pore- water, t is the time, and ‹ is the volume strain of the porous medium. Considering that the mud behaves in an elastic way, the equations of equilibrium may be expressed asG ∂‹ ∂pG∆u + 1 — 2ν ∂x = ∂x , (2)G ∂‹ ∂p

2. ‌Theoretical model

   In order to have non-elastic deformations and pore pressure build-up, shear stress τ must be larger than the yield stress τY in some regions of the bed during part of the wave cycle.G∆w + 1 — 2ν ∂z = ∂z , (3)‌where u and w are the horizontal and vertical components of the mud displacement, respectively; ν is the Poisson’s ratio of the mud and G is its shear modulus. Remembering the definition of the volume strainIf the sediment grains are loosely packed, the shear stresses generated by the successive waves will gradually rearrange the grains, reducing of the pore volume, and if the perme-∂u‹ = +∂x∂w , (4)∂zability of the soil is low, increasing the pore-water pressure (Sumer and Fredsøe, 2002). To study this necessary condi- tion for liquefaction, the shear stresses inside the bed are es- timated assuming an elastic response of the bed. If τ remains smaller than τY during the whole cycle, only elastic deforma- tions would occur, the pore volume would not change after anow we have four equations from Eqs. (1) to (4), one for each unknown variable (p, u, w and ‹). Additionally, effec- tive stresses within the bed can be related to the bed strains using Hooke’s lawσ r = 2G ∂u +   ν    ‹ , (5)complete wave cycle, and pore pressure build-up would not xtake place. However, if τ becomes larger than τY at somer∂x∂w1 — 2ν   ν    point during the cycle, a permanent deformation of the bed will occur, the pore-water pressure may build-up and lique-σz = 2G+ ‹∂z 1 — 2ν, (6)faction would be eventually observed. Once liquefaction hasτ = G ∂u + ∂w , (7)xzoccurred, the elastic model is not able to predict the actual∂z ∂xwhere σ r and σ r are the effective normal stress in horizontal dλ is the geometric ratio between the bed thickness and thex zand vertical directions respectively and τxz is the shear stress on a vertical or horizontal plane.In order to solve the mud motion and the pore-water pres- sure field, it is necessary to know the boundary conditions of the problem. A dynamic condition is used for the water- mud interface. Since cohesive sediment beds can be consid- ered smooth, the shear stress friction factor is relatively low. For the experimental conditions considered in this article, it can be shown that tangential stresses are at least one orderwave length, κ is the ratio between the water compressibility and sediment bed compressibility, and δ is the ratio between the ability of the water to flow within the bed and the pore pressure variation along the wave cycle. For a cohesive sedi- ment bed saturated with water, both permeability k and shear modulus G are small, and therefore both κ and δ can be con- sidered small quantities.Length scales for u and w can be conveniently defined as1 — 2ν  P0  of magnitude smaller than τY, and as a first approximation waves can be considered to just impose normal stresses on the bed.U0 =and1 — ν2Gλ, (19)Assuming that the pressure varies continuously from the1 — 2ν dP0water column into the top pores of the bed, the boundary conditions at the mud-water interface are obtainedW0 =1 — ν2G , (20)zσ r = 0, (8)τxz = 0, (9)p = P0 cos(λx — ωt), (10)where λ is the wave number and ω the angular frequency of the surface waves, and P0 is the pressure amplitude imposed by the waves on the bed surface. P0 is calculated using the Airy wave theory asrespectively.Finally a system of equations and boundary conditions in dimensionless form can be solved for a given set of the four dimensionless numbers (ν = 0.3, dλ = 0.512, κ = 2.65 · 10—4, δ = 1.80 · 10—3). These numbers were obtained from Eqs. (16) to (18) using the following characteristics for the mud bed: k = 10—6 ms—1, n = 0.3, ν = 0.3, G =4.8 · 105 Nm—2, γ = 9800 Nm—3, Kr = 1.9 · 108 Nm—2, andd = 0.15 m; under the following wave forcing: h = 0.176 m,ω = 4.24 rads—1, H = 0.10 m, giving λ = 3.41 m—1, P0 =γ HP0 = 2 cosh(λh). (11)413 Pa, U0 = 7.20 · 10—5 m and W0 = 3.69 · 10—5 m. All the characteristics are considered uniform within the bed. TheThe lower boundary of the mud deposit is considered rigid and impermeable, allowing for no vertical displacement and no vertical pore-water flux. Additionally, two possible condi- tions for this boundary are considered: complete adherence at the rigid boundary and a perfectly slipping boundary.numerical values were taken from the literature and are con- sidered representative of the experimental conditions dis- cussed here.Under these conditions it was possible to determine theprofiles of p, u, w and the effective stress state (σ r , σ r andx zFor the complete adherence caseu = 0, (12)and for the perfect-slip plane caseτxz = 0. (13)The first two boundary conditions at the lower boundary arew = 0, (14)∂p= 0. (15)∂zTaking scales for the different variables, it could be shown that, apart from the Poisson’s ratio ν, the problem is defined by three dimensionless numbers‌dλ, (16)τxz) for the two possible bottom boundary conditions. Fig- ure 1 shows the dimensionless amplitude profiles of these magnitudes. Once the stress state is known, the amplitude of the maximum shear stress at a point for any plane direction τ can be computed. For both bottom boundary conditions the τ profile is found to be non-zero at the top layer of the de- posit, where τ = τ0. For the complete adherence case, the τ profile has a local maximum and a local minimum, finally in- creasing toward the bottom of the deposit, where τ = τd. For the perfect slip case, the τ profile monotonically increases toward the bottom of the deposit. It is interesting to note that τ reaches higher values for the perfect-slip case that for the complete adherence case showing the relevance of the phase shift among the different components of the shear stress ten- sor.Although the τ profile was found under the hypothesis of pure elastic motion, some relevant observations can be made1 — ν κ = 1 — 2ν1 — ν2nGKr , (17)2kG‌regarding the possible occurrence of liquefaction in regions where the maximum shear stress exceeds the mud yield stress τY, and non-elastic deformations may occur. Comparing theδ = 1 — 2ν γ d2ω. (18)κ + 1mud yield stress τY with the shear stress profile τ , three sce-( ) narios may be defined:p˜A u˜A w˜ Ap˜Su˜S w˜ Sσ˜Axσ˜Azτ˜Axzσ˜Sxσ˜Szτ˜Sxzτ˜A τ˜S

0 0 0

−0.1

−0.1

−0.1

−0.2

−0.2

−0.2

−0.3

−0.3

−0.3

−0.4

−0.4

−0.4

z d

−0.5

−0.6

−0.7

−0.8

−0.9

−1

0 0.5 1

−0.5

−0.6

−0.7

−0.8

−0.9

−1

0 0.2 0.4 0.6

−0.5

−0.6

−0.7

−0.8

−0.9

−1

0 0.2 0.4 0.6

‌|p|

|u|

|w|

|σ r |

|σ r |

|τ |

Fig. 1. Non dimensional profiles of p˜ =

, u˜ =

, w˜ =

, σ˜ r =  x , σ˜ r =  z , τ˜xz =  xz and maximum shear stress amplitude for

P0 U0

W0 x P0 z P0 P0

both bottom boundary conditions, complete adherence (A) and perfect slip (S).

• If τ0 > τY the top layers of the deposit will flow during part of the wave cycle. This behavior will be observed immediately after the first wave acts on the deposit. Since the top layers are flowing, it is easier for pore- water to liberate its pressure, reducing the chances of pressure build-up.
• If τd > τY > τ0, plastic deformations are observed in the lower layers where τ > τY. In this region the per- manent deformations will lead to the reorganization of the soil skeleton and, depending on the mud perme- ability, pore pressure build-up would take place.
• If τ < τY over the whole deposit, only elastic deforma- tions will be expected and no pore pressure build-up can occur.

1. Methods

   Previous laboratory work regarding liquefaction focused on measuring pore-water pressure, due to the importance of this variable on the phenomena. For the experiments shown here a laboratory acoustic velocity meter was used to mea- sure the mud flow simultaneously with the pore pressure. These velocity meter have high spatial and temporal resolu- tion, and are practically non-intrusive. Most acoustic instru- ments are designed to measure in water, but it is possible to use them to perform velocity measurements in concentrated sediment mixtures (Gratiot et al., 2000; Salehi and Strom, 2011). For the present experiments, velocity measurements through the water column and inside the upper layers of the deposit (first 3 cm) were performed using an Ultrasonic Ve- locity Profiler (UVP) produced by MetFlow (Pedocchi and García, 2011) equipped with a 2 MHz transducer. The trans-ducer was placed 12 cm above the mud deposit at a 55◦ an- gle with the horizontal. It should be pointed out that the UVP measures the projection of the velocity vector on the direc- tion of the sensor. However, in shallow waters the water mo- tion can be considered horizontal near the bed and the projec- tion of the velocity measured by the UVP can be considered a good proxy for the actual velocity.The experiments presented here were performed in a wave flume located at the Instituto de Mecánica de los Fluidos e Ingeniería Ambiental (IMFIA). The flume is 0.51 m wide,0.76 m deep, and 16 m long. The flume bottom was modi- fied by placing a false bottom of 15 cm high. The false bot- tom covered the entire flume, with the exception of a 1.8 m gap in the middle of the flume (Fig. 2). At the front of the wavemaker, a 2.8 m long ramp allowed a smooth transition from the flume bottom towards the false bottom. At the op- posite end of the flume a permeable beach absorbed the incident waves. The beach reflection in terms of the wave energy was close to 1 % (Mosquera and Pedocchi, 2013). All five experiments described next were performed under the same hydrodynamics conditions: regular waves gener- ated by a piston-type wavemaker oscillating with a period T = 1.48 s, and producing H = 10 cm hight waves in a wa- ter depth h = 17.6 cm.Seven wet-wet pore pressure transducers, model 26PCAFA6D produced by Honeywell, were mounted at different locations inside the mud bed as shown in Fig. 2. PVC tubing, 3/16 inch (4.8 mm) internal diameter and 9/32 inch (7.1 mm) external diameter, was used to connect the measurement points P# with the pressure transducers. The measuring range of the pressure transducers was±0.70 mH2O (±6.9 KPa). Iron pieces were attached to theflume bottom to strongly hold the piping and avoid their motion. The air from inside the tubing was carefully drained

   ‌Fig. 2. Scheme of the wave flume and the experimental set-up, showing the location of the UVP transducer and the seven pore pres- sure sensors.

   in order to obtain high quality measurements. At the end of each tubing a filter was placed to prevent sediments from flowing into the measuring system and care was taken to avoid the filters from getting clogged with sediment.Artificial kaolinite clay was used for the mud deposits. The sediment density was 2635 kg m—3. Its granulometry was de- termined by two different techniques, with ASTM (2007a) standard method and with a laser diffraction technique us- ing a Mastersizer 2000 produced by Malvern. Results were in good agreement, giving a mean diameter of 7.1 µm and a standard deviation of 0.2 mm. Also ASTM (2007b) and ASTM (2007c) standards where applied for the determina- tion of a liquid limit of 24 and a plastic limit of 18, an inor- ganic clay of low plasticity according to Casagrande (1932) classification. The density of the mud was determined before the experiments by extracting a sample of the upper layers of the deposit, and applying the ASTM (2010) and ASTM (2009) standards, with the help of a LJ16 Infrared Dryer pro- duced by Mettler Toledo.In order to produce beds that would develop different re-sponses under the same wave forcing several mud deposits were prepared as follows. After the flume was filled with wa- ter, the sediments were mixed with the water in the water column. Two partition walls were used to prevent the sed- iment mixture from flowing away from the bottom depres- sion area during the mixing, sedimentation, and consolida- tion of the bed. Different consolidation times, ranging from days to weeks, were used to generate deposits with different densities and yield stresses. Experiment # 1 had a bed den- sity of 1548 kg m—3, #2 1599 kg m—3, #3 1738 kg m—3, #41608 kg m—3 and #5 1660 kg m—3. Experiment #3 was per- formed over the bed left by Experiment #2.

2. Results and discussion

   Figure 3 summarizes the results of the experiments. The top colored charts in this figure show the velocity profile series measured with the UVP during sixty waves. The black an‌Fig. 3. From top to bottom: Experiment #1 (ρb = 1548 kg m—3), progressive motion of the bed starting from the upper lay-ers, corresponding to the τY < τ0 condition. Experiment #4 (ρb = 1608 kg m—3), liquefaction of the bed due to pore pressure build-up, corresponding to the τd > τY > τ0 condition. Experiment#3 (ρb = 1738 kgm—3), no mobilization of the bed, correspondingto the τY > τd condition. The colored charts show the velocity pro- file series measured with the UVP at each experiment during sixty waves, the black line indicates the location of the top of the bedat the beginning of the experiment, cold colours indicate velocities towards the sensor and warm colours away from the sensor, grey zones indicate low quality data due to low acoustic backscatter in- tensity. The black an white charts shows the period-averaged pore- water pressure for two different heights (2.3 cm and 5.3 cm below the initial mud-water interface).white charts show the period-averaged pore-water pressure for two different heights (2.3 cm and 5.3 cm below the ini- tial mud-water interface). For the present experiments the maximum shear stress at the upper layer was of the order of τ0 = 50 Pa. Three types of bed response were observed in the experiments: motion of the upper layers of the deposit, start- ing with the first waves; liquefaction of the bed, after several waves had pass over the deposit; and “no motion”.The first response (motion of the upper layers) was ob- served during Experiment #1 (ρb = 1548 kg m—3), which had the lowest bed density. The bed motion started on the upper layers with the first wave and slowly progressed down into the deposit. Figure 1 illustrates this response, which corre- sponds to the τ0 > τY case presented at the end of Sect. 2. For this case the shear stress overpasses the yield stress and the top layer fails as the first wave travels over the bed. As the first layer fails, the elastic model does not apply to that layer anymore. However, it may still be applied to the next layer down, which will also fail. This process can therefore progress, slowly mobilizing successive layers of the deposit as it was observed in this experiment. A slight build-up of pore-water pressure was observed during Experiment #1 on both sensors but it was not large enough to produce liquefac- tion.The second response (liquefaction of the bed) was ob-served in Experiments #2 and #4 (ρb = 1599 kg m—3 and ρb = 1608 kg m—3 respectively). A gradual build-up of pore pressure was measured by the pressure sensors and no mo- tion on the top layers was measured by the UVP. These ex- periments can be considered to fall in the τY > τ0 class. The shear stresses near the surface were only able to produce elas- tic deformations. However, as the shear stress increases with depth, the lower layers suffered plastic deformations. Then, the successive action of waves slowly reduced the voids vol- ume in these layers increasing the pore-water pressure. After tens of waves had passed over the bed, the entire bed abruptly started to move and the pore pressure at 2.3 cm sensor de- scended to a value near the recorded value by the 5.3 cm depth sensor. The difference between Experiments #2 and #4 was the number of waves that induced liquefaction, in Ex- periment #2 (not shown here) only ten waves were needed. It is interesting to note that the 2.3 cm sensor presented a faster pore pressure build-up. This can be explained in part because the yield stress of the bed probably increases with depth, instead of being constant as supposed here. Addition- ally, if complete adherence at the bottom of the deposit is considered, Fig. 1 shows that this sensor was located close to τ ’s local maximum, where the largest plastic deformations should be expected.Finally, during Experiments #3 and #5 (ρb = 1738 kg m—3and ρb = 1660 kg m—3 respectively) neither bed motion nor significant pore-water pressure built up were observed, even after hundreds of waves had passed over the bed. These two experiments are considered to had fallen in the τd < τY caseand therefore neither bed plastic deformation nor pore pres- sure build-up were possible.

3. Conclusions

For some time, researchers have suggested two mechanisms to explain the generation of fluid mud under waves: progres- sive pore pressure build-up in partially consolidated deposits, and sudden shear failure in soft deposits. Both mechanisms were observed in the experiments presented here. And an explanation for each of these responses was discussed de- pending on the ratio between the bed yield stress and the shear stress profile imposed inside the bed by the action of waves. Experiments #2 and #4 are particularly relevant since they showed that a partially consolidated bed under moderate waves can suddenly get mobilized, even though the individ- ual waves were not able to mobilize the deposit. This type of fatigue failure is particularly dangerous since the usual max- imum wave hight criteria would fail to predict it.

The simultaneous measurements of the bed velocity field with the UVP and the pore-water pressure with the pres- sure transducers, made possible to clearly identify the failure mechanisms. The poro-elastic solutions for the bed deforma- tion showed that the shear stress increases down into a fi- nite thickness bed, and plastic deformations may occur in the lower layers of the deposit while only elastic deformations are possible in the top layers. If the permeability of the de- posit is low enough, these plastic deformations of the lower layers would induce the build-up of pore pressure and lead to the liquefaction of the mud bed.

Acknowledgements. We would like to thank the Agencia Nacional de Investigación e Innovación (ANII), Uruguay, for the financial support given to the first author under its scholarships program “Posgrados Nacionales” (BE_POS_2010_1_2578, 2010). Addition- ally part of the work presented here was done under the grant of PR_FMV_2009_1_1890 also from the ANII, this support is greatly appreciated. The authors would like to thank the IMFIA machine shop staff (D. Barboza and R. Zouko) for their help with the ex- perimental set-up. We would also like to thank G. Sanchez and

A. Bologna from the Instituto de Ingeniería Química of Facultad de Ingeniería, Uruguay; and Susana Vinzón and Marcos Gallo from the Area de Engenharia Costeira of the Universidad Federal de Río de Janeiro (UFRJ), Brasil for their help with the characterization of the sediment samples. The collaboration with the UFRJ was pos- sible thanks to the CAPES-UdelaR academic exchange program (026/2010) of the CAPES Foundation, Brazil, and Universidad de la República, Uruguay.

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