Depth-Dependent Seabed Properties: Geoacoustic Assessment

Lyu, Chuangxin; Park, Junghee; Carlos Santamarina, J.

doi:10.1061/(ASCE)GT.1943-5606.0002426

Open access

Technical Papers

Oct 24, 2020

Depth-Dependent Seabed Properties: Geoacoustic Assessment

Authors: Chuangxin Lyu, Junghee Park https://orcid.org/0000-0001-7033-4653 [email protected], and J. Carlos Santamarina, A.M.ASCEAuthor Affiliations

Publication: Journal of Geotechnical and Geoenvironmental Engineering

Volume 147, Issue 1

https://doi.org/10.1061/(ASCE)GT.1943-5606.0002426

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Abstract

Offshore geoengineering requires reliable sediment parameters for analysis and design. This study proposes a robust framework for effective stress-dependent geotechnical and geoacoustic properties for seabed analysis based on geophysical models, new experimental data, and extensive data sets compiled from published studies that cover a wide range of marine sediments and depths. First, effective stress-dependent porosity versus depth profiles are computed using compaction models that are valid for a wide stress range. Then, P- and S-wave velocity data are analyzed in the context of effective stress-controlled density, shear stiffness, and bulk modulus within a Hertzian-Biot-Gassmann framework. Finally, this study selects six distinct “reference sediments” that range from clean sands to high-plasticity clays and assigns self-consistent compaction and shear stiffness properties using well-known correlations reported in the literature in terms of specific surface, plasticity, and grain characteristics. Results show that robust physical models for compaction and stiffness adequately predict depth-dependent geotechnical and geoacoustic properties according to sediment type. The asymptotic void ratio at low effective stress

e_{L}

determines the sediment density

ρ_{o}

at the sediment–water boundary. New experimental studies show that the characteristic asymptotic sediment density

ρ_{o}

at very low effective stress

σ_{z}^{'} \to 0

controls the high-frequency acoustic reflection used for bathymetric imaging. The proposed analysis of geoacoustic data can be used to obtain first-order estimates of seafloor sediment properties and to produce sediment-type seafloor maps.

Introduction

Seafloor properties are critical to offshore geotechnical engineering, including foundations and anchors, piping and transmission line projects, the analysis of landslides, geological mapping and the interpretation of marine seismic data, drilling projects, marine landfills, deep-sea mining, and environmental assessment. These projects require soil models that are applicable to a wide range of effective stress.

Depth-dependent geotechnical parameters such as density

ρ

(

kg / m^{3}

), effective stress (kPa), and shear stiffness (kPa), and geoacoustic parameters such as P- and S-wave velocities

V_{P}

and

V_{S}

(

m / s

) display distinct differences among sediment types (Hamilton 1972; Hamilton and Bachman 1982; Jackson and Richardson 2007). Therefore, a geoacoustic seabed assessment can provide noninvasive information relevant to the sediment engineering properties.

Sediment characteristics at very low effective stress near the sediment–water boundary are critical for high-frequency surface reflection measurements and for the interpretation of bathymetric data to eventually produce sediment-type seafloor maps. As the effective stress increases with depth, depth-dependent geoacoustic parameters affect the analysis of layer reflections gathered with lower-frequency systems such as subbottom profilers and marine seismic towed streamer [Note: sediment depths can exceed 3,000 m; see examples in Grant and Schreiber (1990), Wunderlich et al. (2005), Schrottke et al. (2006), and Wang and Rao (2009).] Furthermore, engineered systems can induce a high effective stress, such as gas production from hydrate-bearing sediments (Moridis et al. 2011).

Seafloor acoustic assessment is particularly convenient. Contrary to previous phenomenological approaches, this study builds from the fundamental observation that sediment properties are effective stress-dependent and adopts physics-inspired models to anticipate seafloor characteristics: Terzaghi self-compaction, Hertzian-DLVO stiffness, and Biot-Gassmann bulk stiffness (from published work, including the authors’). The study benefits from an extensive database compiled from the literature (depth-dependent seafloor porosity and wave velocities

V_{S}

and

V_{P}

), and contributes new data for very low effective stress conditions where information was sparse. Finally, these data are used to address the reflection from the water–sediment interface, which controls high-frequency bathymetric studies. The parameters selected for the various models involved in this study are mutually self-consistent and satisfy well-tested published correlations.

Depth-Dependent Density and Effective Stress

Self-compaction reflects the dependency between effective stress

σ_{z}^{'}

and sediment density

ρ_{s}

. In this section, an asymptotically correct compaction model is used and the evolution of effective stress

σ_{z}^{'}

, porosity

n

, and sediment density

ρ_{s}

is investigated for a wide range of sediments in the upper 1,000 m of the sediment column.

Compaction Model: Void Ratio versus Effective Stress

Fig. 1 presents compaction trends for a wide range of soils, from high-plasticity clays to clean sands. Clearly, the sediment void ratio

e

decreases as a function of the vertical effective stress

σ_{z}^{'}

, and compressibility increases with sediment plasticity. The compaction trend is nonlinear in the conventional semi-log space, so the classical Terzaghi model

e = e_{1 kPa} - C_{c} \cdot \log (σ_{z}^{'} / 1 kPa)

fails to satisfy asymptotic conditions at very low and high effective stresses (see also Mesri and Olson 1971; Johns 1986; Burland 1990; Pestana and Whittle 1995; Gregory et al. 2006). In particular, the low effective stress asymptote void ratio

e_{L}

must be properly captured because it plays a critical role in high-frequency bathymetric data analysis.

Fig. 1. Compression curves in terms of void ratio $e$ versus effective stress $σ_{z}^{'}$ . Data points show data compiled from published studies. Lines correspond to the asymptotically correct exponential compaction model [Eq. (1)]. Table 1 lists sediment constitutive parameters for the six *reference sediments*.

Therefore, this study uses an asymptotically correct exponential compaction model in terms of void ratios

e_{L}

at low effective stress (

σ_{z}^{'} \to 0

) and

e_{H}

at very high effective stress (

σ_{z}^{'} \to \infty

); then the void ratio

e_{z}

at depth

z

is a function of the vertical effective stress

σ_{z}^{'}

(Gregory et al. 2006; Chong and Santamarina 2016):

e_{z} = e_{H} + (e_{L} - e_{H}) \exp [- {(\frac{σ_{z}^{'}}{σ_{c}^{'}})}^{η}]

(1)

where the model parameter

η

captures the void ratio sensitivity to effective stress and is often

η \approx 1 / 3

, and

σ_{c}^{'}

is the characteristic effective stress so that

(e_{z} - e_{H}) = 0.37 (e_{L} - e_{H})

when

σ_{z}^{'} = σ_{c}^{'}

.

Fig. 1 shows exponential compaction trends for six reference sediments selected to bound the experimental data. The model parameters correlate with the sediment specific surface, plasticity, and grain shape (Table 1 summarizes the model parameters for the six reference sediments). The scale used in this figure reaches

σ_{z}^{'} = 10 MPa

to test the wide stress range validity of the exponential

e_{z} - σ_{z}^{'}

model [Eq. (1)].

Table 1. Select reference sediments. Constitutive parameters for effective stress-dependent compaction model [Eq. (1): model parameter

η = 1 / 3

] and shear stiffness in terms of shear wave velocity [Eq. (5)]. Parameters are self-consistent and satisfy published correlations in terms of specific surface, plasticity, and grain shape

Reference sediment	Compaction model [Eq. (1)]			Shear wave velocity [Eq. (5)]
Reference sediment	$e_{L}$	$e_{H}$	$σ_{c}^{'}$ (kPa)	$α$ ( $m / s$ )	$β$
1	8	0.1	500	22	0.38
2	3.2	0.3	500	33	0.32
3	1.80	0.3	700	58	0.25
4	1.35	0.3	1,000	75	0.23
5	0.91	0.2	2,000	110	0.19
6	0.60	0.2	3,000	146	0.17

Source: Data from Santamarina and Cho (2004), Cha et al. (2014), Chong and Santamarina (2016).

The void ratio of sandy sediments at low effective stress

e_{L}

reflects the grain size distribution and particle shape (Youd 1973; Cho et al. 2006). At a given relative density

D_{r}

, the value of

e_{L}

can be estimated from the coefficient of uniformity

C_{u}

and particle roundness

R^{*}

as

e_{L} = (0.02 - 0.032 \cdot D_{r}) + (0.893 - 0.522 \cdot D_{r}) / C_{u} + (0.236 - 0.154 \cdot D_{r}) / R^{*}

; for example,

e_{L} = 0.89

for a sandy sediment with

C_{u} = 3

, and

R^{*} = 0.3

at

D_{r} = 30 %

.

On the other hand, mineralogy and depositional environment determine the void ratio

e_{L}

and the compressibility of clay-rich sediments (Palomino and Santamarina 2005; Wang and Siu 2006; Wang and Xu 2007). Assuming an edge-to-face fabric, the value of

e_{L}

is a function of the particle slenderness,

e_{L} = (a - 1) / 2

where the slenderness ratio

a

is equal to the particle length divided by its thickness; for example, kaolinite has

a \approx 10

and

e_{L} = 4.5

, while montmorillonite has

a \approx 100

and

e_{L} = 50

(Santamarina et al. 2001). Remolding disturbs the initial fabric and any subsequent diagenesis (Burland 1990; Leroueil 1996; Hong et al. 2012).

Depth-Dependent Density and Porosity

Consider a thin seabed layer of thickness

d z

at depth

z

. Force equilibrium combines with gravimetric-volumetric relations to predict the effective stress gradient

d σ_{z}^{'} / d z

as a function of the void ratio

e_{z}

at depth

z

(note that gravity

g = 9.81 m / s^{2}

):

\frac{d σ_{z}^{'}}{d z} = ρ_{w} [\frac{S_{G} - 1}{1 + e_{z}}] g

(2)

where the mineral-specific gravity

S_{G} = ρ_{m} / ρ_{w}

is the ratio between the mineral and water densities

ρ_{m}

and

ρ_{w}

. Eq. (1) is inserted in Eq. (2), and the differential equation is solved. The closed-form solution for

η = 1 / 3

predicts the following effective stress profile

σ_{z}^{'}

with depth

z

(for η = 1/3—See related example for methane hydrate-bearing sediments in Terzariol et al. 2020):

z = \frac{(1 + e_{H})}{(S_{G} - 1) ρ_{w} g} σ_{z}^{'} + 3 \frac{(e_{L} - e_{H})}{(S_{G} - 1) ρ_{w} g} σ_{c}^{'} {[{(\frac{σ_{z}^{'}}{σ_{c}^{'}})}^{\frac{2}{3}} + 2 {(\frac{σ_{z}^{'}}{σ_{c}^{'}})}^{\frac{1}{3}} + 2] \cdot \exp [- {(\frac{σ_{z}^{'}}{σ_{c}^{'}})}^{\frac{1}{3}}] - 2}

(3)

Fig. 2(a) shows the effective stress trends for the six reference sediments identified earlier (Fig. 1; Table 1). Effective stress gradients decrease markedly as sediments change from sands to high-plasticity clays.

Fig. 2. Soil state parameters: (a) effective stress $σ_{z}^{'}$ ; and (b) density $ρ$ profiles for different sediment types. Lines correspond to selected *reference sediments* [Eqs. (1)–(4)—constitutive parameters in Table 1].

Finally, Eq. (1) is used to compute the void ratio

e_{z}

and the sediment density

ρ_{s} (z)

as a function of depth

z

:

ρ_{s} (z) = ρ_{w} [\frac{S_{G} + e_{z}}{1 + e_{z}}]

(4)

Fig. 2(b) shows the change in sediment density

ρ_{s}

with depth

z

. At the sediment–water boundary

z = 0

, sediments experience zero effective stress and the sediment density is the asymptotic value

ρ_{o}

defined by

e_{(z = 0)} = e_{L}

[Eq. (4)]; conversely, the sediment density

ρ_{s}

increases toward the value defined by

e_{H}

as the sediment depth increases. Once again, the six trends in Fig. 2(b) correspond to the six reference sediments identified in Fig. 1 (parameters in Table 1) and show marked differences in density for sand, silts, and clays in the upper 1,000 m. While remolding by sediment transport can affect the sediment density in shallow accumulations, eventually effective stress-dependent compaction prevails as sediment burial progresses.

Fig. 3 shows the evolution of sediment compaction with depth in terms of porosity

n = e / (1 + e)

for data gathered from published references and the Ocean Drilling Program (ODP) projects. The data set involves normally consolidated sediments (i.e., no overpressure) and relatively homogeneous deposits. Once again, trends correspond to the reference sediments; the 1,000-m depth makes it possible to corroborate the wide stress range validity of the exponential

e_{z} - σ_{z}^{'}

model [Eq. (1)]. Some reported so-called sands exhibit high porosities; this may reflect grains with intraparticle porosity [e.g., carbonate sands (Goldhammer 1997)] or incorrect reporting of sandy sediments with high fines content so that fabric formation is fines-dominant. In general, computed trends for the six reference sediments selected earlier follow the field data for the different sediment types. (Note: the six reference sediment trends reflect self-compaction properties according to sediment type; these profiles are not intended to fit any particular data set.) The logarithm of depth used in Fig. 3 helps with exploring near-surface conditions in detail, but trends can be misleading: in linear scale, porosity decreases at a faster rate near the sediment–water interface.

Fig. 3. Porosity $n$ versus depth $z$ . Data points compiled from published studies. Lines show computed trends for selected reference sediments [Eqs. (1)–(3)—constitutive parameters in Table 1].

Depth-Dependent P- and S-Wave Velocities

Effective stress determines not only the sediment density

ρ_{s}

but also the stiffness of the sediment granular skeleton in the absence of cementation. In turn, stiffness and mass density define P- and S-wave velocities. This section brings together P- and S-wave velocity data compiled from the literature and new experimental data gathered in this study to overcome the scarcity of published data at very shallow depths. Then, the P- and S-wave velocity data are analyzed in the context of effective stress-dependent density, shear stiffness, and bulk modulus.

Experimental Study: P- and S-Wave Velocities at Very Low $σ_{z}^{'}$

Devices

The miniature P- and S-wave measurement probes built for this study involve split tubes to minimize the transmission of vibrations around the tube and boundary-reflected waves (dimension:

ϕ = 34 mm

in diameter and

H = 500 mm

in height). We mount the parallel-type bender elements for S-waves and the piezo disk elements for P-waves at the tip of the split tubes to reduce disturbance effects caused by probe penetration (insets in Figs. 4 and 5). Crystals are coated with silver paint and grounded to prevent electrical crosstalk [details in Lee and Santamarina (2005a)].

Fig. 4. Shear S-wave signatures versus depth: (a) fine sand; (b) silt; and (c) kaolinite. The different time scales for the three sediments.

Fig. 5. Compressional P-wave signatures versus depth: (a) fine sand; (b) silt; and (c) kaolinite. The same time scale for the three sediments.

Test Procedure

The experimental study involves sediment beds prepared with fine sand, silt, and kaolinite in large-diameter columns to minimize boundary effects during the penetration of the P- and S-wave probes (columns are 300 mm in diameter and 600 mm in height). Table 2 summarizes the sediment index properties. These seafloor analogs form by sedimentation from diluted slurries to prevent gas entrapment and layering (initial water content

ω > 2,000 %

). All sediments consolidate for 2 weeks. Then P- and S-waves are recorded every 1 or 2 cm (note that signals are stable within a few minutes after each insertion, as soon as any excess pore-water pressure dissipates).

Table 2. Tested sediments—index properties

Material	Diameter (mm)	Extreme void ratios, $e_{\max} / e_{\min}$	Mean grain size $d_{50}$ (mm)	Specific gravity, $S_{G}$	Liquid limit ( $W / B / K$ )	Specific surface ( $m^{2} / g$ )	RSCS—fines classification
Cobbles	10–20	—	15	2.65	N/A	N/A	N/A
Coarse sand	1.0–2.0	$0.82 / 0.59$	1.5	2.65	N/A	N/A	N/A
Fine sand	0.075–0.25	$0.81 / 0.45$	0.16	2.63	N/A	N/A	N/A
Silt	$< 0.075$	$1.50 / 0.73$	$1.0 \times 10^{- 2}$	2.65	N/A	N/A	N/A
Kaolinite (RP2)	$< 0.075$	N/A	$3.0 \times 10^{- 4}$	2.67	$67 / 52 / 82$	33	I-I
Bentonite	$< 0.075$	N/A	$5.0 \times 10^{- 6}$	2.65	$302 / 92 / 39$	544	H-H

P- and S-Wave Signatures

Figs. 4 and 5 present P- and S-wave signatures gathered at very shallow depths and low effective stress in the sandy, silty, and clayey sediments [field data gathered with a velocity-resistivity probe can be found in Lee et al. (2010) and Yoon and Lee (2010)]. The time to first arrival decreases with depth for S-waves, while the travel time for P-waves is almost constant with depth.

Shear Wave Velocity versus Depth

Fig. 6 plots the measured and collected shear velocity

V_{S}

data set. The shear wave velocity increases with depth for all sediments. The effective stress

σ_{z}^{'}

determines the sediment shear stiffness

G_{s}

in the absence of diagenetic cementation. In fact, the shear wave velocity

V_{s} = \sqrt{{G_{s} / ρ}_{s}}

follows a Hertzian-type power relation with effective stress (Roesler 1979):

V_{s} = α {(\frac{σ_{z}^{'}}{1 kPa})}^{β}

(5)

Fig. 6. S-wave velocity $V_{S}$ versus depth $z$ . Filled circles indicate measurements gathered in this study, and other symbols are data collected from published studies (frequency range: $\sim 2.5 Hz$ to 5 kHz). Lines represent the power trend between S-wave velocity $V_{S}$ and effective stress $σ_{z}^{'}$ for selected reference sediments [Eq. (5)—constitutive parameters in Table 1].

The

α

-factor (

m / s

) is the shear wave velocity at

σ_{z}^{'} = 1 kPa

, and the

β

-exponent represents the sensitivity of the shear wave velocity to effective stress. These

α

-factor and

β

-exponent reflect the sediment type; in general, higher-specific-surface sediments are more compressible, exhibit a lower

α

-factor, and a more pronounced increase in shear stiffness with stress, i.e., a higher

β

-exponent. Thus, there is an inverse relationship between the

α

-factor and

β

-exponent, as observed for a wide range of soils:

β = 0.7 - 0.25 \log [α / (m / s)]

[see database in Cha et al. (2014)].

The shear wave velocity for fines-controlled sediments is affected by pore fluid chemistry (Klein and Santamarina 2005; Kang et al. 2014). Furthermore, diagenesis may affect both fine- and coarse-grained sediments. In particular, synsedimentary diagenesis makes deeper and older sediments stiffer than remolded specimens at the same effective stress; in this case, the shear wave velocity increases with depth owing to the effective stress and diagenesis and the field

β

-exponent will be higher than for remolded specimens in the laboratory [see data in Ku (2012) and Ku et al. (2017)].

Table 1 lists

α

and

β

values for the six reference sediments, inferred from their compressibility (refer to Part 1). Effective stress profiles from Eq. (3) combine with Eq. (5) to predict the shear wave velocity trends shown in Fig. 6. The computed

V_{S}

profiles for the six reference sediments exhibit trends similar to those in the data and successfully bound laboratory and field measurements. Once again, the shear wave velocity increases rapidly with depth in linear-linear scale [power trend in Eq. (5)].

P-Wave Velocity versus Depth

The sediment shear modulus

G_{s} = ρ_{s} \cdot V_{S}^{2}

is a function of the shear wave velocity and the sediment mass density [Figs. 6 and 2(b)]. At small strains, the bulk modulus

B_{s k}

of the sediment granular skeleton is related to the shear modulus as

B_{s k} = G_{s} \frac{2 (1 + ν_{s k})}{3 (1 - 2 ν_{s k})}

(6)

where the small-strain Poisson’s ratio of the soil skeleton is

ν_{s k} \approx 0.15

. The bulk modulus of the water-saturated sediment

B_{s}

depends on its porosity

n

and is a function of the bulk stiffness of the skeleton

B_{s k}

, water

B_{w}

, and mineral

B_{m}

:

B_{s} = B_{s k} + {(\frac{n}{B_{w}} + \frac{1 - n}{B_{m}})}^{- 1}

(7)

On the other hand, the sediment density

ρ_{s}

(

kg / m^{3}

) is a function of the water

ρ_{w}

and mineral

ρ_{m}

densities and the sediment porosity

n

:

ρ_{s} = n ρ_{w} + (1 - n) ρ_{m}

(8)

Finally, the low-frequency Biot-Gassmann P-wave velocity

V_{P}

(

m / s

) for soft marine sediments is [from Eqs. (6)–(8)]

V_{p} = \sqrt{\frac{B_{s} + \frac{4}{3} G_{s}}{ρ_{s}}} = \sqrt{\frac{[\frac{2 (1 + ν_{s k})}{3 (1 - 2 ν_{s k})} + \frac{4}{3}] (n ρ_{w} + (1 - n) ρ_{m}) V_{s}^{2} + {(\frac{n}{B_{w}} + \frac{1 - n}{B_{m}})}^{- 1}}{n ρ_{w} + (1 - n) ρ_{m}}}

(9)

Fig. 7 shows the estimated P-wave velocity profiles versus depth for the six selected reference sediments. These trends take into consideration the depth-dependent shear wave velocity and porosity profiles computed earlier (Figs. 3 and 6). The figure includes a comprehensive data set gathered from published studies and our own experimental data (Fig. 5). Trends for the reference sediments adequately resemble the data for different sediments (not intended to fit any specific data set).

Fig. 7. P-wave velocity $V_{P}$ versus depth $z$ . Filled circles indicate measurements gathered in this study, and other symbols are data collected from published studies (frequency range: 120–400 kHz). Lines show Biot-Gassmann P-wave velocity for selected reference sediments [Eq. (9)—bulk modulus: mineral $B_{m} = 45 GPa$ , gas-free water $B_{w} = 2.37 GPa$ . Density: water $ρ_{w} = 1,024 kg / m^{3}$ , mineral $ρ_{m} = 2,680 kg / m^{3}$ ]. Small-strain Poisson’s ratio of soil skeleton $ν_{s k} = 0.15$ . Porosity $n = e_{z} / (1 + e_{z})$ from integration of Eqs. (1) and (4). [Shear wave velocity $V_{S}$ at depth $z$ from Eq. (5)—parameters in Table 1.]

The water bulk modulus

B_{w}

controls the P-wave velocity in saturated soft sediments near the seafloor (pure water

V_{P} = 1,480 m / s

; seawater

V_{P} = 1,531 m / s

), and changes in P-wave velocity are relatively minor in the upper tenths of meters in clayey deposits. In fact, the P-wave velocity may fall below that of water when the increase in mass density is faster than the increase in skeletal stiffness in plastic sediments at shallow depth. (Note: This explains the crossing of the two trends for clayey sediments in Fig. 7.)

The P-wave velocity relaxation in sediments leads to the following ratio between the Biot high-frequency P-wave velocity

V_{P \infty}

and the low-frequency P-wave velocity

V_{P o}

computed in Eq. (9) (Santamarina et al. 2001):

\frac{V_{P \infty}}{V_{P_{0}}} = \sqrt{\frac{[n ξ + n^{2} (S_{G} - 2) - n^{3} (S_{G} - 1)] [S_{G} (1 - n) + n]}{ξ n S_{G} (1 - n) + n^{2} (ξ - 1)}}

(10)

where

ξ

is a tortuosity factor. The velocity ratio is approximately

V_{P \infty} / V_{P o} \approx 1.05

[Eq. (10), porosity

n \approx 0.4

, and tortuosity factor

ξ = 2

]. Fig. 8 shows the effect of porosity

n

on P-wave velocities

V_{P o}

and

V_{P \infty}

. Data points are values measured for “undisturbed samples” recovered from the seafloor (Richardson and Briggs 1993). The low-frequency P-wave velocity

V_{P o}

[red trend—Eq. (9)] and the high-frequency

V_{P \infty}

(red line) provide lower and upper trends for most of the data shown in Fig. 8 when the skeletal stiffness is null,

V_{S} = 0 m / s

. The central trend is best predicted with Eq. (9) for a shear wave velocity

V_{S} \approx 250 m / s

, which could result from either diagenesis or suction effects when recovered specimens are tested in air (dashed line).

Fig. 8. Compressional wave velocity $V_{P}$ as a function of porosity $n$ . Data points from Richardson and Briggs (1993) include clays, silty clays, silty sands, fine sands, and coarse sands ( $frequency = 400 kHz$ ). Black and red lines show calculated low-frequency Biot-Gassmann P-wave velocity (for $V_{S} = 0$ and $250 m / s$ ); blue line is an estimate of Biot’s high-frequency P-wave velocity $V_{P \infty}$ for sediments with $V_{S} = 0$ [Eq. (9)]—bulk modulus: mineral $B_{m} = 45 GPa$ , gas-free water $B_{w} = 2.37 GPa$ . Density: water $ρ_{w} = 1,024 kg / m^{3}$ , mineral $ρ_{m} = 2,680 kg / m^{3}$ . Small-strain Poisson’s ratio of soil skeleton $ν_{s k} = 0.15$ .

Heterogeneity

Data plots in the global depth

z

-scale include changes in stratigraphy with depth [e.g., ODP holes in Leg 139–Juan de Fuca Ridge (Mottl et al. 1994)]. Compaction models make it possible to convert depth into effective stress [Eq. (3)] in order to analyze geoacoustic properties in terms of local effective stress

σ_{z}^{'}

[Eqs. (1), (4), (5), and (9)].

Discussion and Implications

In the previous two sections, a formulation and supportive database were constructed for depth-dependent geotechnical properties (density

ρ_{s}

, porosity

n

, shear stiffness

G_{s} = ρ_{s} \cdot V_{S}^{2}

) and geoacoustic properties (

V_{S}

and

V_{P}

) as functions of sediment type. The model parameters selected for the reference soils satisfy well-proven correlations with specific surface, plasticity, and grain shape. Here, the implications for bathymetric studies and seafloor sediment characterization are explored and crucial parameters that require further investigation are identified.

High-Frequency Reflection—Enhanced Bathymetric Analysis

The asymptotic conditions at the water–sediment interface

z \to 0

are of particular interest because they determine the reflectivity in high-frequency bathymetric studies. A well-controlled reflection data set was created from sediment beds formed with bentonite, kaolinite, silica flour, fine sand, coarse sands, and cobbles. Table 2 summarizes the selected sediments and their index properties. The chamber is 300 mm in diameter and 600 mm in height. All tests are repeated with two crystal pairs to measure reflections at frequencies

f_{r} = 160

and 500 kHz [see details on transducer performance in Lee and Santamarina (2005b)]. The spacing between the source and receiver crystals is 20 mm in both cases.

Fig. 9 presents P-wave signatures reflected from a submerged steel plate placed at different depths. The multiple reflection events confirm phase inversion at the air–water interface and the combined effects of geometric spreading and material attenuation. The energy in the first reflection is used as a reference.

Fig. 9. Reflection signatures. Target: steel plate at different water depths. Phase reversal occurs after every reflection at air–water interface.

Fig. 10 presents the first reflection from the steel plate in comparison to reflections from the fine sand, silt, kaolinite, and bentonite beds, all at the same water depth. Clearly, the reflection amplitude is strongly related to sediment type and the ensuing asymptotic properties at very low effective stress

σ_{z}^{'} \to 0

near the water–sediment interface

z \to 0

. The mismatch in acoustic impedance

Z = ρ \cdot V_{P}

between the water column and the reflector defines the energy

E

in the reflected signal, i.e., the reflection coefficient. Then the relative reflection coefficient

R R

between a sediment bed and the steel target is

R R = \frac{E_{s}}{E_{s t}} = {[\frac{(Z_{w} + Z_{s t}) (Z_{w} - Z_{s})}{(Z_{w} - Z_{s t}) (Z_{w} + Z_{s})}]}^{2} = 1.14 \times {(\frac{1 - \frac{Z_{s}}{Z_{w}}}{1 + \frac{Z_{s}}{Z_{w}}})}^{2}

(11)

where the subscripts

s

,

w

, and

s t

indicate sediment, water, and steel, respectively. The “1.14” factor in the last mathematical expression corresponds to the water–steel interface (steel:

ρ = 7,900 kg / m^{3}

,

V_{P} = 5,900 m / s

; water:

ρ = 1,024 kg / m^{3}

,

V_{P} = 1,531 m / s

). Fig. 11 summarizes the energy-based

R R

measured for all sediments versus their mean grain size

d_{50}

. Sandy sediments exhibit the highest reflection coefficient, while the very soft bentonite bed produces the smallest coefficient. [Note that published results corroborate the importance of sediment type on reflectivity, for example, van Walree et al. (2005, 2006) and Snellen et al. (2011); attenuation in Panda et al. (1994); spectral strength in Sternlicht and de Moustier (2003).]

Fig. 10. Reflection signatures: steel plate and various sediments tested in this study: fine sand, silt, kaolinite, and bentonite. Hanning window around reflection used for energy calculations.

Fig. 11. Energy-based relative reflection coefficient $R R$ for five different sediments versus mean grain size $d_{50}$ in logarithmic scale. Table 1 summarizes the sediment properties. The relative reflection coefficient is $R R = E_{s} / E_{s t}$ [Eq. (11)]—circles: data measured with high-damping transducer; triangles: data measured with low-damping transducer; dotted lines: theoretically computed relative reflection coefficient for six *reference sediments* at four different depths $z^{*} = 3$ , 150, 300, and 1,000 mm [Eq. (11)]. Refer to Figs. 2(b) and 7 for sediment density $ρ_{s}$ and P-wave velocity $V_{P}$ . Steel: $V_{P} = 5,900 m / s$ , $ρ = 7,900 kg / m^{3}$ ; water: $V_{P} = 1,531 m / s$ , $ρ = 1,024 kg / m^{3}$ . The lower red line is estimated in terms of void ratio $e_{L}$ for the six reference sediments.

The sediment density

ρ_{s}

and P-wave velocity profiles for the six reference sediments explored earlier make it possible to estimate the theoretically computed

R R

[Eq. (11); refer to Figs. 3(b) and 7 for the sediment

ρ_{s}

and

V_{P}

]. Fig. 11 shows the theoretical reflection coefficient computed at different sediment depths from

z^{*} = 3

to 1,000 mm. The depth

z^{*} = 3 mm

relates to the wavelength

λ

at

f_{r} = 500 kHz

, while the impedance at depth

z^{*} = 150 mm

may be more relevant for the operating frequency of subbottom profilers

f_{r} = 10 kHz

. Data trends suggest a slope of approximately

1 / 4

for the

\log (R R)

versus the

\log (d_{50})

. The theoretically computed

R R

at depth

z^{*} = 3 mm

tracks the experimental data when the mean grain size

d_{50}

is smaller than

1 / 10

of the wavelength

λ = 3 mm

. Thereafter, the reflection coefficient decreases rapidly (Brillouin zone). Field data gathered with a single-beam echosounder (Snellen et al. 2011) show good agreement with the results presented here for silts and sands where the slope between the reflectivity and grain size is about

1 / 4

in log-log scale.

Asymptotic Void Ratio

The previously discussed bathymetric study shows that the mass density

ρ_{o}

at very low effective stress

σ_{z}^{'} \to 0

is the critical parameter for high-frequency seafloor reflection studies (leveled seafloor). The

ρ_{o}

corresponds to the asymptotic void ratio

e_{L}

[Eq. (4)]:

ρ_{o} = ρ_{w} [\frac{S_{G} + e_{L}}{1 + e_{L}}] (at depth z = 0)

(12)

Furthermore, the shear stiffness vanishes at

σ_{z}^{'} = 0

and

V_{S} = 0

. Then the P-wave velocity

V_{P}

at

z = 0

becomes [Eq. (9)]

V_{p} (z = 0) = \sqrt{\frac{B_{s}}{ρ_{s}}} = \sqrt{{[(\frac{ρ_{m} + ρ_{w} e_{L}}{1 + e_{L}}) \cdot (\frac{\frac{e_{L}}{1 + e_{L}}}{B_{w}} + \frac{1 - \frac{e_{L}}{1 + e_{L}}}{B_{m}})]}^{- 1}}

(13)

Finally,

R R

is a function of the asymptotic void ratio

e_{L}

[After Eq. (11)]:

R R = 1.14 \times {[1 - 2 \cdot {(\sqrt{\frac{S_{G} + e_{L}}{\frac{B_{w}}{B_{m}} + e_{L}}} + 1)}^{- 1}]}^{2}

(14)

Eq. (14) corresponds to the line for

z^{*} = 0

in Fig. 11. The relative reflection coefficients measured with the low-frequency and low-damping transducer are lower owing to the longer wavelength. In all cases, the asymptotic void ratio

e_{L}

for the six reference sediments successfully anticipates the lower bound for

R R

.

Clearly, the asymptotic void ratio

e_{L}

emerges as an important parameter, both for self-compaction and for the stiffness evolution with depth. The asymptotic void ratio

e_{L}

is inversely proportional to the median grain size

d_{50}

in clays and silts (due to the prevalent role of interparticle electrical forces) and is affected by pore fluid chemistry [see data in Mesri and Olson (1971), Studds et al. (1998), and Stewart et al. (2003)]. On the other hand, the asymptotic void ratio

e_{L}

is geometry-controlled by granular packings in sands and gravels. In fact, data in Table 1 for the six selected reference sediments suggest

e_{L} = 0.4 \cdot [1 + {(d_{50} / mm)}^{- 0.28}

]. For comparison, this equation agrees well with the central trend in Jackson and Richardson (2007), though their data are limited to

d_{50} = 10^{- 3}

to 1 mm). Admittedly, very high-plasticity clays can form stable slurries at higher void ratios in freshwater (Liu and Santamarina 2018); however, a skeleton capable of shear wave transmission is first detected at void ratios similar to

e_{L}

values used in this paper. Overall, this analysis suggests the potential use of reflection data to estimate the asymptotic void ratio

e_{L}

and to infer the sediment type.

Sediment Classification—Nomenclature

Semiempirical seabed classification methods that rely on low-perturbation acoustic reflection measurements exhibit large variations (Bachman 1985; Leblanc 1992; Panda et al. 1994). Factors such as surface roughness, bioturbation, and variability contribute to data scatter (Jackson and Briggs 1992; Jackson et al. 1996; Clarke 1994; Lyons and Orsi 1998; Jackson and Richardson 2007). Several commercially available software packages attempt to create seafloor backscatter mosaics (e.g., Fledermaus by QPS). Analyses advanced in this study support and extend these efforts by providing mutually compatible geotechnical and geoacoustic properties.

Sediment classification requires more information than what can be extracted from acoustic data. Therefore, acoustic seafloor surveys and sediment sampling combine to provide robust spatial distributions of seafloor sediment types (Goff et al. 2004). Sediment classification for engineering purposes helps engineers anticipate the sediment properties and behavior by grouping them into similar engineering response categories (Casagrande 1948; Kulhawy and Chen 2009). Unfortunately, current marine sediment classifications use a 50% fraction to separate sand from silt or clay (Shepard 1954; Folk et al. 1970; Flemming 2000). Indeed, the 50% boundary does not capture the transition from coarse-controlled to fines-controlled sediment behavior.

The newly revised soil classification system (RSCS) overcomes this limitation and classifies sediments as sand-controlled, transitional, or fines-controlled (Park and Santamarina 2017; Park et al. 2018); in particular, the RSCS captures the critical role of the fines fraction on geoacoustic properties. This is demonstrated with sand–silt mixtures in Fig. 12, where porosity, S- and P-wave velocities, and acoustic impedance data support the transition boundaries predicted by the RSCS: geoacoustic properties are sand-controlled up to a fines fraction of

F_{F} \approx 18 %

and become clay-controlled when the fines fraction exceeds

F_{F} \approx 37 %

. Transition boundaries shift to lower fines contents

F_{F}

for higher-plasticity fines. Furthermore, sediment analyses must consider the salt concentration in pore fluid when sediments are classified with a letter F in the RSCS triangular textural chart (Jang and Santamarina 2016, 2017).

Fig. 12. Geoacoustic properties of sand–fines mixtures versus fines mass fraction $F_{F}$ . The RSCS defines the component(s) responsible for mechanical behavior and fluid flow (top). Data points for S-wave velocity $V_{S}$ at vertical effective stress $σ_{z}^{'} = 15 kPa$ and porosity from Park (2018). Saturated mass density, P-wave velocity $V_{P}$ , and impedance $Z$ are estimated from Eqs. (4) and (9). Input parameters used to compute RSCS boundaries $F_{F} |^{L}$ and $F_{F} |^{H^{*}}$ are for sand: $e_{C}^{\max} = 0.78$ and $e_{C}^{\min} = 0.53$ ; and for silt: $e_{F}^{\max} = 1.50$ and $e_{F}^{\min} = 0.73$ .

Conclusions

This study highlights the close relationship between sediment type, self-compaction, and geoacoustic properties with depth. Therefore, geoacoustic profiles and bathymetric data can be used to acquire insightful information about seafloor sediments and to anticipate their engineering properties. Important conclusions of the study are as follows:

•

The asymptotically correct exponential compaction model provides a robust fit to porosity

n

and density

ρ_{s}

depth profiles as a function of effective stress

σ_{z}^{'}

. The asymptotic void ratio at low effective stress

e_{L}

determines the sediment density

ρ_{o}

at the sediment–water boundary. The sediment specific-surface and sedimentation conditions define the value of

e_{L}

.

•

The effective stress

σ_{z}^{'}

determines the depth-dependent shear stiffness

G_{s}

, often augmented by synsedimentary or postsedimentary diagenesis. Shear stiffness vanishes as the sediment depth

z \to 0

and

σ_{z}^{'} \to 0

. The Biot-Gassmann P-wave velocity estimated for zero shear stiffness (i.e.,

V_{S} = 0

) provides a lower bound for the P-wave velocity of near-surface seafloor sediments.

•

A group of reference sediments that range from clean sands to high-plasticity clays was identified. Predicted void ratio, P-wave velocity

V_{P}

, and S-wave velocity

V_{S}

trends computed for these reference sediments capture prevalent trends observed in a large data set compiled from the literature and from a focused laboratory study conducted as part of this study.

•

The measured high-frequency reflection coefficient

R R

(relative to a steel reflector at the same depth) and the computed reflection coefficient for the selected reference sediments show distinct sediment-dependent reflectivity. In fact, the asymptotic density

ρ_{o}

at zero effective stress defines the acoustic reflection amplitude for high-frequency applications, such as bathymetric imaging.

•

Model parameters for compaction and stiffness must be congruent. Model parameters adopted for the selected reference sediments reflect correlations reported in the literature in terms of specific surface, plasticity, and grain characteristics.

•

The proposed analysis of geoacoustic data can be used to gain first-order estimates of the seafloor sediment properties and to produce sediment-type seafloor maps.

Notation

The following symbols are used in this paper:

$a$: slenderness ratio;
$B$: bulk modulus;
$C_{c}$: compression index;
$C_{u}$: coefficient of uniformity;
$D_{r}$: relative density;
$d_{50}$: median grain size;
$d z$: differential of depth;
$E$: energy;
$e$: void ratio;
$f_{r}$: operating frequency;
$G_{s}$: sediment shear stiffness;
$g$: gravity;
$n$: porosity;
$R R$: relative reflection coefficient;
$R^{*}$: roundness;
$S_{G}$: specific gravity;
$V_{p}$: P-wave velocity;
$V_{P \infty}$: high-frequency P-wave velocity;
$V_{P o}$: low frequency P-wave velocity;
$V_{s}$: S-wave velocity;
$Z$: impedance;
$z$: depth;
$α$: shear wave velocity at $σ_{z}^{'} = 1 kPa$ ;
$β$: sensitivity of shear wave velocity to effective stress;
$λ$: wavelength;
$ρ$: mass density;
$ξ$: tortuosity factor;
$ω$: water content;
$η$: compaction model parameter;
$σ_{z}^{'}$: vertical effective stress;
$σ_{c}^{'}$: characteristic effective stress; and
$ν_{s k}$: small-strain Poisson’s ratio of soil skeleton.

Data Availability Statement

All data, models, and algorithms generated or used during the study appear in the published article.

Acknowledgments

Support for this research was provided by the KAUST Endowment at King Abdullah University of Science and Technology. Gabrielle E. Abelskamp edited the manuscript.

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Journal of Geotechnical and Geoenvironmental Engineering

Volume 147 • Issue 1 • January 2021

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.

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Received: Jun 9, 2019

Accepted: Aug 13, 2020

Published online: Oct 24, 2020

Published in print: Jan 1, 2021

Discussion open until: Mar 24, 2021

Authors

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Chuangxin Lyu

Ph.D Student, Dept. of Civil and Transport Engineering, Norwegian Univ. of Science and Technology, Trondheim 7491, Norway.

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Junghee Park https://orcid.org/0000-0001-7033-4653 [email protected]

Research Scientist, Earth Science and Engineering, Bldg. 5, King Abdullah Univ. of Science and Technology, Thuwal 23955-6900, Saudi Arabia (corresponding author). ORCID: https://orcid.org/0000-0001-7033-4653. Email: [email protected]

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J. Carlos Santamarina, A.M.ASCE

Professor, Earth Science and Engineering, King Abdullah Univ. of Science and Technology, Thuwal 23955-6900, Saudi Arabia.

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Abstract

Introduction

Depth-Dependent Density and Effective Stress

Compaction Model: Void Ratio versus Effective Stress

Depth-Dependent Density and Porosity

Depth-Dependent P- and S-Wave Velocities

Experimental Study: P- and S-Wave Velocities at Very Low σz′

Devices

Test Procedure

P- and S-Wave Signatures

Shear Wave Velocity versus Depth

P-Wave Velocity versus Depth

Heterogeneity

Discussion and Implications

High-Frequency Reflection—Enhanced Bathymetric Analysis

Asymptotic Void Ratio

Sediment Classification—Nomenclature

Conclusions

Notation

Subscripts

Data Availability Statement

Acknowledgments

References

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Experimental Study: P- and S-Wave Velocities at Very Low $σ_{z}^{'}$