# Experimental Study of the Dynamic Shear Modulus Ratio and Damping Ratio of the Quaternary Sedimentary Soils in the Offshore Areas of the Yellow Sea

Authors: Yi Fang; Yuejun Lv; Dandan Xu; Yanju Peng; Xingyuan Zhou
Journal: Geofluids
 (2021)

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## Abstract

The effects of marine and continental sedimentary environments and geological ages on the dynamic shear modulus ratio and damping ratio of the Quaternary sedimentary soils in the offshore areas of the Yellow Sea were analyzed by using a resonant column device (GCTS, USA). The results show the following: (1) TheGmax of various marine soils increases with the depth and shows a typical linear relationship. (2) The marine transgression has significantly different effects on the dynamic shear modulus ratio versus the shear strain amplitude curves (i.e., G/Gmax~γa curves) and the damping ratio versus the shear strain amplitude curves (i.e., λ~γa curves) of the different soil types in the offshore areas of the Yellow Sea. The effects of marine transgression were strong on clays, moderate on silty clays, and minor on silts. (3) The geological ages have noticeable effects on the G/Gmax~γa curves of the tested marine silty clays, marine silts, and continental silty clays, but the effects of geological ages on the λ~γa curves are minimal. The fitting parameters and recommended empirical equations of the G/Gmax~γa and λ~γa curves for each type of the tested soils (silty clay, clay, and silt) were obtained mirroring the effects of sedimentary environments and geological ages.


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## Body

## 1. Introduction

The 21st century is widely considered to be the era of the ocean. All of the coastal countries have placed a higher priority on the ocean within their overall framework of national development. China has a very long coastline of more than 18,000 km, and thus, China has successively proposed marine strategic plans such as the Belt and Road and the Yellow Sea Economic Circle. In particular, the Yellow Sea and its coastal areas are experiencing intensive planning and construction of a large number of offshore traffic projects and marine projects. The Yellow Sea and its coastal areas are located in the North China Seismic Zone, which has complex seismic geological structures and is frequently subject to seismic activity, including a magnitude 6 earthquake in the Yellow Sea in 1764, a magnitude 6.5 earthquake in the Yellow Sea in 1764, and a far-field magnitude 8.5 earthquake in Tancheng in 1668. There may be Late Pleistocene faults and Holocene faults in the zone, which increase the possibility of destructive earthquakes in the future. The offshore areas of the Yellow Sea contain a thick Quaternary sedimentary sequence, which is comprised of soft soils. These soils are mainly marine plains dominated by cohesive soils and saturated sandy soils. The strong earthquakes that occur in this area may lead to a significant site amplification effect and result in the subsidence of soft soil or liquefaction of sandy soil in these areas, which poses a serious threat to the safety of major engineering structures and the performance of socioeconomic activities.The variation of the dynamic shear modulus ratioG/Gmax and the damping ratio λ against the shear strain amplitude γa directly reflects the nonlinear and hysteretic characteristics of the stress-strain relationship of soils under dynamic loads. They are not only the basic dynamic parameters to describe the nonlinear hysteretic constitutive model but also essential for accurately analyzing the seismic response of soil layers.TheG/Gmax and λ of soils are strongly region-specific since soils in different regions might be from different geological ages, exist in different sedimentary facies, and have different sedimentogenesis [1–6]. At present, a large number of studies have been carried out on marine soils. For example, Koutsoftas and Fischer explored the influence of the overconsolidation ratio OCR on the dynamic characteristics of G and λ of two kinds of marine clays through resonance column and cyclic triaxial tests [7]. Liang et al. proposed a new correlation function method for the calculation of G and λ in triaxial tests and investigated the G/Gmax–γa and λ–γa curves of saturated coral sand from the Nansha Islands, South China Sea, considering the influence of effective confining pressure and relative density [8]. Yang et al. established the empirical equations of G/Gmax–γa curves for the undisturbed soils in the Yangtze River estuary [9]. Morsy et al. evaluated the dynamic characteristics of Egyptian calcareous sand in the range of small and medium shear strains [10]. Wu et al. researched the small-strain stiffness of marine silty sand [11]. Senetakis and Payan conducted small-strain resonant column tests in torsional and flexural modes of vibration which quantified two types of damping ratios [12]. Some tests have been conducted for the dynamic characteristics of fine-grained soil, especially for high plasticity clay [13]. Based on field and laboratory tests, researchers studied the static and dynamic properties of soils in Catania [14]. Głuchowski et al. researched the laboratory characterization of a compacted-unsaturated silty sand. The results proposed that the compaction procedure caused an overconsolidation state dependent on the moisture content during compaction effort [15]. Feng et al. used the resonance column test to evaluate the influence of confining pressure, mix ratio, curing age, and cement content on the dynamic characteristics of subsea sand-silt mixtures [16]. Khosravi et al. developed a new methodology to extend an existing small-strain shear modulus Gmax model to determine Gmax of unsaturated silty soils along different paths of the soil water retention curve including the scanning loops [17].However, few tests pay attention to the influence of sedimentary environment and geological age on the dynamic properties of soil, especially if they had significant impact on dynamic shear modulus ratios and damping ratios. Furthermore, the experimental studies on theG and λ characteristics of the soils in the coastal area of the Yellow Sea have not been reported yet.To fill this knowledge gap, in this study, the dynamic shear modulus ratios and damping ratios of the soils in a typical region of the coastal areas of the Yellow Sea are tested by resonant column tests. The effects of sedimentary facies and geological ages were explored in detail. The results of this study provide a scientific and theoretical basis to analyze seismic site effects for major engineering sites.


## 2. Engineering Geological Conditions of the Study Region

The study area is located near the coast of the Yellow Sea, and most parts of the region are less than 5 m above sea level, falling in the category of a coastal marine plain. The Quaternary sediments in the region are more than 200 m thick and have experienced marine transgression five times since the late Early Pleistocene. With the formation of fluvial, lacustrine, and marine deposits alternately, broad coastal facies and alluvial facies with soft clay layers and saturated sand layers have been formed.According to the chronological order of strata, the characteristics of soil sedimentary structure are as follows:(1)
During the Holocene period, the stratum was buried at a depth of 8-25 m, mainly composed of tidal flat facies of clay, clay interbedded with silt, silt and clay interbedded, and gray clay(2)
In the Late Pleistocene, the stratum was buried at a depth of 16-21 m, mainly composed of gray clay and silt flooding facies and gray lacustrine deposits(3)
In the early Late Pleistocene, the stratum was buried at a depth of 28-42 m, mainly composed of tidal flat facies of gray clay, clay intercalated with silt sand, clay silt sand, and gray clay supertidal zone deposits(4)
In the late Middle Pleistocene, the stratum was buried 40-55 m deep and 7-20 m thick. The lower part mainly was composed of flooding facies and high tide flats, and the upper part was composed of lacustrine facies(5)
In the early mid-Pleistocene, the stratum was buried 70-106 m deep and 25-60 m thick. The lower part was composed of gray clay lagoon facies and tidal flat facies, partially with gray-green fine sand in riverbed facies and gray silt delta facies, and the upper part was composed of tidal flat facies and shallow ocean facies with gray clay and silt sandThe sedimentary environments and geological ages of the soils have a significant impact on their dynamic deformation characteristics. The soil samples were identified based on their colors and the existence of shells, calcareous nodules, and iron-manganese oxides. The identifications in conjunction with the comparison between the borehole logs and the relevant geological maps account for the classification of soil categories, sedimentary facies, and geological ages of the tested samples. The classification, summarized in Table1, reveals that there are 19 clayey soil samples in the shallow layers, within 100 m below the surface. 75% of the silt samples are mainly deposited in the Pleistocene, which is attributed to the fact that the seawater in the marine transgression carried a large amount of granular soils from the rivers, lakes, and marine facies into the flat areas where separation and sedimentation took place. The Holocene silt sand samples are mainly deposited in the marine facies. The silty clay samples from both the marine and continental facies were primarily deposited in the Holocene and Pleistocene.Table 1
Basic physical properties of undisturbed soil.
NumberLithologyDepth,h (m)Consolidation pressure,σ’ (kPa)Density,ρ (g/cm3)Moisture content,ω (%)Void ratio,eState1Silty clay51.7-52.03452.0922.770.53CL2Clay80.7-815402.1030.750.70ML3Silty clay3.7-4.0501.8534.460.91CH4Silty clay17.0-17.31151.9533.140.81CL5Silty clay21.5-21.81451.8727.030.77CL6Clay39.8-402651.9629.530.79CL7Silty clay50.1-50.33352.0223.440.63CL8Silty clay54-54.33601.9427.530.72CL9Clay79.8-80.05352.0623.400.55CL10Clay94.6-94.86352.0129.500.69CL11Silty clay3.0-3.3501.8430.790.90CH12Silty clay17.0-17.31151.8133.380.95CL13Silty clay18.7-19.01251.9629.730.79CL14Silty clay17.05-17.251152.0625.870.60CL15Clay34.05-34.252302.1324.540.52CL16Clay44.05-44.252952.0325.740.74CL17Silty clay54.05-54.253602.0322.030.57CL18Clay76.85-77.055151.9926.560.70ML19Silty clay17.2-17.41152.1124.890.58CL20Silty clay23.5-23.71601.8933.970.93CH21Clay27.6-27.81852.1423.550.50CL22Silty clay40.2-40.42701.9824.340.68CL23Clay77.3-77.55152.0325.560.64CL24Clay97.8-986552.1227.360.63ML25Silty clay33.7-342251.9540.320.92CL26Clay71.8-724802.0929.780.66ML27Clay78.7-795252.1324.910.58ML28Silty clay5.8-6501.8438.550.94CH29Silty clay12.8-13851.9133.450.88CL30Clay35-35.32351.9521.590.67CL31Silty clay40-40.32701.9426.840.72CL32Silty clay47.7-483201.9825.870.72CL33Silty clay57.7-583851.9825.510.68CL34Clay64-64.34301.9638.040.85ML35Clay79-79.35302.0126.760.68ML36Clay83-83.35551.9927.450.69ML37Clay86.4-86.75802.0325.560.66CL38Clay89.7-906002.0620.460.57ML39Clay92.7-936202.1021.760.55ML40Silty clay4-4.2501.8734.540.84CL41Silt14.8-151001.9630.560.81Medium42Silty clay30-30.22001.9722.560.66ML43Silt36.8-372452.0129.450.70Dense44Silt42.8-432851.9930.120.75Dense45Silt50.8-513402.0328.150.69Dense46Silty clay70-70.24702.1023.560.59ML47Silty clay78-78.25201.9923.450.68ML48Silt86.6-875802.0628.230.67Dense49Silty clay93-93.26202.0823.760.59ML50Silt5.5-5.7501.9331.670.81Medium51Silty clay11.5-11.7801.9624.560.70CL52Silt22-22.21501.9829.980.79Medium53Silty clay32-32.22151.9623.450.66ML54Silt54-54.23601.9929.230.76Dense55Silty clay77-77.25152.0324.870.62ML56Silt88-88.25902.0230.210.73Dense57Silty clay96-96.26402.0821.870.55ML58Silty clay7-7.2501.8632.760.89CL59Silt13-13.2901.9428.230.81Medium60Silty clay21.5-21.71451.9527.890.71CL61Silty clay35-35.22352.0423.870.63ML62Silt45.5-45.73052.0529.870.70Dense63Silty clay63.5-63.74252.0321.890.62ML64Silt80-80.25352.0226.970.72Dense65Silty clay98.5-98.76602.1120.210.56ML66Silty clay8-8.2551.9231.980.79CL67Silt18.8-191251.9832.870.80Medium68Silty clay30-30.22001.9619.870.61ML69Silt40.8-412751.9729.760.77Dense70Silt57-57.23802.0026.890.73Dense71Silt68.8-694602.0128.980.73Dense72Silt83.8-845602.0427.120.70Dense73Silty clay92-92.26152.1118.120.53ML74Silt5.8-6.0501.9833.800.81Medium75Silty clay11-11.2751.9524.210.69CL76Silt21.8-221451.9730.120.77Medium77Silty clay35-35.22351.9529.870.77Medium78Silty clay44-44.22951.9825.120.69CL79Silt52.8-533551.9928.980.74Dense80Silty clay74-74.24952.0119.210.61ML81Silty clay93-93.26202.0120.210.60ML82Silty clay9-9.2601.8931.230.85CL83Silty clay27-27.21801.9324.320.71CL84Silty clay37-37.22501.9925.210.67ML85Silty clay47-47.23151.9625.900.70CL86Silty clay58.5-58.73902.0321.230.60ML87Silty clay70-70.24702.0723.210.62ML88Silty clay83.5-83.75602.1221.320.55ML89Silty clay98-98.26552.1122.870.58ML


## 3. Soil Sampling and Testing

### 3.1. Soil Sampling

A total number of 89 undisturbed soil samples were collected from 14 boreholes in the coastal area of the Yellow Sea by using the in situ soil tube method. The depth of soil samples are from 0 to 100 m. As shown in Figure1, the borehole sites were distributed close to each other so as to reveal the dynamic characteristics of the soils in more detail. Each undisturbed soil sample was prepared into a solid cylindrical shape specimen with the diameter of 50 mm and the height of 100 mm.Figure 1
Location of the boreholes in the offshore of the Yellow Sea.


### 3.2. Resonant Column Testing

The testing was conducted using the TSH-100 high-precision fixed-free resonant column device (GCTS, USA) at the Institute of Natural Disaster Prevention and Control of the Ministry of Emergency Management (Figure2). The torque (or rotation) and the cell pressure are controlled independently by the apparatus. The consolidation pressure is provided by a pneumatic servo system, and a fully automated floating torsional drive is attached to excite at the top of the samples.Figure 2
TSH-100 resonant column testing system.First, the soil was made into a solid cylindrical sample with a diameter of 50 mm and a height of 100 mm. Isotropic consolidation was conducted after the soil specimen was installed into the test apparatus, with a membrane filmed outside it. The effective confining pressure was determined according to the depth of the soil layer. The durations of the consolidation are more than 3 hours and 12 hours for cohesionless soils and cohesive soils, respectively. After consolidation, resonant column testing was conducted by applying the multistage frequency sweeping excitation on the top of the specimen following ASTM D4105-92 to measure the shear modulusG and damping ratio λ in the shear strain range of 10-6~10-3. The schemes of the resonant column tests, specifically the index properties of the specimens and the corresponding effective confining pressures, are listed in Table 1.


## 3.1. Soil Sampling

A total number of 89 undisturbed soil samples were collected from 14 boreholes in the coastal area of the Yellow Sea by using the in situ soil tube method. The depth of soil samples are from 0 to 100 m. As shown in Figure1, the borehole sites were distributed close to each other so as to reveal the dynamic characteristics of the soils in more detail. Each undisturbed soil sample was prepared into a solid cylindrical shape specimen with the diameter of 50 mm and the height of 100 mm.Figure 1
Location of the boreholes in the offshore of the Yellow Sea.


## 3.2. Resonant Column Testing

The testing was conducted using the TSH-100 high-precision fixed-free resonant column device (GCTS, USA) at the Institute of Natural Disaster Prevention and Control of the Ministry of Emergency Management (Figure2). The torque (or rotation) and the cell pressure are controlled independently by the apparatus. The consolidation pressure is provided by a pneumatic servo system, and a fully automated floating torsional drive is attached to excite at the top of the samples.Figure 2
TSH-100 resonant column testing system.First, the soil was made into a solid cylindrical sample with a diameter of 50 mm and a height of 100 mm. Isotropic consolidation was conducted after the soil specimen was installed into the test apparatus, with a membrane filmed outside it. The effective confining pressure was determined according to the depth of the soil layer. The durations of the consolidation are more than 3 hours and 12 hours for cohesionless soils and cohesive soils, respectively. After consolidation, resonant column testing was conducted by applying the multistage frequency sweeping excitation on the top of the specimen following ASTM D4105-92 to measure the shear modulusG and damping ratio λ in the shear strain range of 10-6~10-3. The schemes of the resonant column tests, specifically the index properties of the specimens and the corresponding effective confining pressures, are listed in Table 1.


## 4. Testing Results and Analysis

Since the sedimentary environment and geological age of the soils have a significant impact on their dynamic shear modulus ratios and damping ratios, the soil samples were observed to determine their colors and whether or not they contained shells, calcareous nodules, and/or iron-manganese oxides. The observations were made in conjunction with the comparative analysis of the borehole logs and the relevant geological maps in order to categorize the soil samples based on their soil properties, sedimentary facies, and geological ages. The results (Table2) revealed that there were many clayey soils in the shallow layers within 100 m of the surface, while the silt samples were mainly deposited in the Pleistocene, which is attributed to the fact that the seawater in the marine transgression carried a large amount of gravel soils from the rivers, lakes, and marine facies into the flat areas where separation and sedimentation took place. In contrast, the silty clay samples from both the marine and continental facies were primarily deposited in the Holocene and Pleistocene. The Holocene clay samples were mainly deposited in the marine facies.Table 2
Classification and the corresponding number of the tested soil samples.
LithologySedimentary environmentGeological ageHolocenePleistoceneSilt clayMarine1115Continental619Silt sandMarine59Continental06ClayMarine09Continental010Figure3 shows the typical results of the resonant column test. The strain amplitude of the sample under different excitation frequencies is shown in Figure 3(a). The resonance frequency f1 of the sample γa at the maximum under the corresponding excitation load can be obtained. At the resonance frequency, the strain time history of the sample is shown in Figure 3(b). Under free vibration, the strain time history of the sample is shown in Figure 3(c).Figure 3
Typical results of resonant column test.


### 4.1. Change ofGmax with Depth

As an important parameter for evaluating the dynamic characteristics of soil and characterizing the maximum elastic stiffness of soil, the maximum dynamic shear modulusGmax is usually defined as G when γa≤10−6. According to the hyperbolic relationship between soil dynamic modulus and dynamic strain under small vibration proposed by Hardin and Drnevich [18], the linear relationship between 1/G and γa can be obtained as 1/G=a+bγ. And then, the hyperbolic model (γa⟶0) between 1/G and shear strain γa can be used to obtain the maximum dynamic shear modulus Gmax of marine soil.
(1)Gmax=limγ⟶01a+bγ.The TSH-100 resonant column test system developed by the GCTS company can measure the dynamic shear modulusG of the soil in the range of 10−6~10−3. Equation (1) can be used to obtain the Gmax of marine soil at different depth ranges from 15 to 140 MPa.Figure4 shows the Gmax values of various marine soils and their changes with depth. It can be seen that the Gmax of various marine soils increases with the depth and shows a typical linear relationship. The prediction relationship between Gmax and depth can be expressed as Gmax=15.37×h+1.13. The h represents the depth of the sample, and its unit is m.Figure 4
Variation relationship of the maximum dynamic shear modulusGmax with depth.


### 4.2. Effects of the Sedimentary Environment on theG/Gmax~γa and λ~γa Curves

The three-parameter Martin-Davidenkov model was adopted to investigate the variation characteristics of dynamic shear modulus ratioG/Gmax against the shear strain amplitude γa of the tested soils since it has been proven to fit experimental data well for soil samples in Jiangsu province, China [5]. The model is expressed as
(2)GGmax=1−γ/γ02B1+γ/γ02BA.Here,A, B, and γ0 are the best-fitting parameters. In particular, in the case of A=1 and B=0.5, the Martin-Davidenkov model simplifies to the H-D hyperbolic model [19], where γ0 denotes the reference shear strain and is equal to the shear strain values when G/Gmax=0.5 [20].The damping ratio versus shear strain amplitude (λ–γa) curves of each tested specimen were fitted and analyzed using the following empirical Equation (3) proposed by Chen et al. [5]:
(3)λ=λmin+λ0×1−GGmaxβ.Here,λmin is the basic damping ratio of a soil sample under a very small strain, which is related to the soil properties and consolidation state. λ0 and β are the shape coefficients of the λ–γa curve.Figure5 illustrates the effects of marine and continental sedimentary environments on the G/Gmax~γa and λ~γa curves for the various types of soils. For Holocene silty clays, the G/Gmax~γa curves of the marine silty clays are slightly lower than those of the continental silty clays, while the λ–γa curves of the marine silty clays are higher than those of the continental silty clays. This is mainly attributed to the fact that the marine silty clays were dominated by muddy silty clay deposited during the Holocene, and therefore, they exhibit stronger nonlinearity. For Pleistocene clays, the G/Gmax~γa curves of the marine clays are higher than those of the continental clays, while the λ–γa curves of the marine clays are lower than those of the continental clays, which may be due to the higher strength of the clay crust formed during the marine transgression. The differences between the marine and continental silty clays in terms of their G/Gmax~γa and λ~γa curves are smaller than the differences between the marine and continental clays. The G/Gmax~γa curves of the marine silty clays are slightly lower than those of the continental silty clays, while the marine and continental silty clays have similar λ–γa curves. For the Pleistocene silt sands, the marine G/Gmax~γa and λ~γa curves are similar to the continental G/Gmax~γa and λ~γa curves. In general, within the working range of the shear strain (10-6~10-3) of the resonant column device, the G/Gmax–γa curves of the marine soils are slightly higher than those of the continental soils, and the differences between the λ~γa curves of the two types of soils are even smaller.Figure 5
Comparison ofG/Gmax~γa curve and λ~γa fitting curves between marine deposit and continental deposit.


### 4.3. Effects of Geological Age on theG/Gmax~γa Curve and λ~γa Curves

Due to the limited number of sampling sites, the Pleistocene soils were not further classified into different Pleistocene stages. TheG/Gmax~γa and λ~γa curves of the various soil types were compared considering the two geological age categories: the Pleistocene versus the Holocene (Figure 6). The results show that in general, the geological age strongly affects the G/Gmax~γa and λ~γa curves of the marine soils (silt clays and silt sands). The G/Gmax~γa curves of the Pleistocene marine soils are higher than those of the Holocene marine soils while the λ–γa curves of the Pleistocene marine soils are lower than those of the Holocene marine soils. For continental depositional, geological age has a clear effect on the G/Gmax~γa curves of the continental silt clays. The G/Gmax~γa curves of the Pleistocene continental silt clays are significantly higher than those of the Holocene continental silt clays. However, the effect of geological age on the λ~γa curves is quite weak. Overall, geological age has less effect on the λ~γa curves of the continental soils than those of the marine soils.Figure 6
Influence of geological age onG/Gmax~γa curve and λ~γa fitting curves of different deposits.As was previously discussed, the soils formed in the Quaternary marine sedimentary environment in the offshore areas of the Yellow Sea have significantly different dynamic shear modulus ratios and damping ratios than those formed in the Quaternary continental sedimentary environment. The effect of geological age onG/Gmax is similar to its effect on λ, while the effect on G/Gmax is slightly greater than that on λ. For ease of application in practical engineering, the fitting parameters of the G/Gmax~γa curves and the λ~γa curves were obtained for each type of the classified samples (Table 3). For silty clay and silt, the newer the sedimentary age, the smaller the value of A and the bigger the value of B. The average G/Gmax and λ values at various shear strain levels calculated by the recommended parameters are presented in Table 4.Table 3
Recommended parameter values forG/Gmax–γa and λ–γa curves of Quaternary sedimentary soils in the offshore areas of the Yellow Sea.
LithologyGeological age/depositNumber of samplesFitting parametersABγ0 (10-4)λminλ0βSilt clayHolocene171.010.484.770.0340.1321.477Pleistocene341.120.406.930.0290.1361.363Silt sandHolocene51.150.392.220.0070.1271.085Pleistocene151.170.393.010.0130.1151.226ClayContinental depositional101.050.425.520.0380.1611.732Marine depositional91.090.417.320.0340.1161.376Table 4
Average values ofG/Gmax and λ at various shear strain levels for Quaternary sedimentary soils in the offshore areas of the Yellow Sea.
LithologyGeological age/depositParametersShear strain (10-4)0.050.10.51.05.01050100Silt clayHoloceneG/Gmax0.98830.97740.90040.82200.49330.33280.09580.0516λ (%)3.393.423.814.408.1910.6114.7115.54PleistoceneG/Gmax0.98840.97720.91390.85450.60430.46400.19140.1199λ (%)2.902.953.353.856.728.6913.0714.32Silt sandHoloceneG/Gmax0.96850.94370.80780.70160.38750.26680.09290.0562λ (%)1.001.262.834.138.189.7912.1512.65PleistoceneG/Gmax0.97740.95870.84990.75810.45250.32100.11660.0711λ (%)1.381.502.403.306.788.4511.1811.81ClayContinental depositionalG/Gmax0.98520.97300.89680.82560.53950.39260.14090.0835λ (%)3.813.834.124.588.0010.5816.1617.62Marine depositionalG/Gmax0.98830.97870.91810.86010.60920.46590.18750.1157λ (%)3.453.483.804.206.628.3312.1713.25


## 4.1. Change ofGmax with Depth

As an important parameter for evaluating the dynamic characteristics of soil and characterizing the maximum elastic stiffness of soil, the maximum dynamic shear modulusGmax is usually defined as G when γa≤10−6. According to the hyperbolic relationship between soil dynamic modulus and dynamic strain under small vibration proposed by Hardin and Drnevich [18], the linear relationship between 1/G and γa can be obtained as 1/G=a+bγ. And then, the hyperbolic model (γa⟶0) between 1/G and shear strain γa can be used to obtain the maximum dynamic shear modulus Gmax of marine soil.
(1)Gmax=limγ⟶01a+bγ.The TSH-100 resonant column test system developed by the GCTS company can measure the dynamic shear modulusG of the soil in the range of 10−6~10−3. Equation (1) can be used to obtain the Gmax of marine soil at different depth ranges from 15 to 140 MPa.Figure4 shows the Gmax values of various marine soils and their changes with depth. It can be seen that the Gmax of various marine soils increases with the depth and shows a typical linear relationship. The prediction relationship between Gmax and depth can be expressed as Gmax=15.37×h+1.13. The h represents the depth of the sample, and its unit is m.Figure 4
Variation relationship of the maximum dynamic shear modulusGmax with depth.


## 4.2. Effects of the Sedimentary Environment on theG/Gmax~γa and λ~γa Curves

The three-parameter Martin-Davidenkov model was adopted to investigate the variation characteristics of dynamic shear modulus ratioG/Gmax against the shear strain amplitude γa of the tested soils since it has been proven to fit experimental data well for soil samples in Jiangsu province, China [5]. The model is expressed as
(2)GGmax=1−γ/γ02B1+γ/γ02BA.Here,A, B, and γ0 are the best-fitting parameters. In particular, in the case of A=1 and B=0.5, the Martin-Davidenkov model simplifies to the H-D hyperbolic model [19], where γ0 denotes the reference shear strain and is equal to the shear strain values when G/Gmax=0.5 [20].The damping ratio versus shear strain amplitude (λ–γa) curves of each tested specimen were fitted and analyzed using the following empirical Equation (3) proposed by Chen et al. [5]:
(3)λ=λmin+λ0×1−GGmaxβ.Here,λmin is the basic damping ratio of a soil sample under a very small strain, which is related to the soil properties and consolidation state. λ0 and β are the shape coefficients of the λ–γa curve.Figure5 illustrates the effects of marine and continental sedimentary environments on the G/Gmax~γa and λ~γa curves for the various types of soils. For Holocene silty clays, the G/Gmax~γa curves of the marine silty clays are slightly lower than those of the continental silty clays, while the λ–γa curves of the marine silty clays are higher than those of the continental silty clays. This is mainly attributed to the fact that the marine silty clays were dominated by muddy silty clay deposited during the Holocene, and therefore, they exhibit stronger nonlinearity. For Pleistocene clays, the G/Gmax~γa curves of the marine clays are higher than those of the continental clays, while the λ–γa curves of the marine clays are lower than those of the continental clays, which may be due to the higher strength of the clay crust formed during the marine transgression. The differences between the marine and continental silty clays in terms of their G/Gmax~γa and λ~γa curves are smaller than the differences between the marine and continental clays. The G/Gmax~γa curves of the marine silty clays are slightly lower than those of the continental silty clays, while the marine and continental silty clays have similar λ–γa curves. For the Pleistocene silt sands, the marine G/Gmax~γa and λ~γa curves are similar to the continental G/Gmax~γa and λ~γa curves. In general, within the working range of the shear strain (10-6~10-3) of the resonant column device, the G/Gmax–γa curves of the marine soils are slightly higher than those of the continental soils, and the differences between the λ~γa curves of the two types of soils are even smaller.Figure 5
Comparison ofG/Gmax~γa curve and λ~γa fitting curves between marine deposit and continental deposit.


## 4.3. Effects of Geological Age on theG/Gmax~γa Curve and λ~γa Curves

Due to the limited number of sampling sites, the Pleistocene soils were not further classified into different Pleistocene stages. TheG/Gmax~γa and λ~γa curves of the various soil types were compared considering the two geological age categories: the Pleistocene versus the Holocene (Figure 6). The results show that in general, the geological age strongly affects the G/Gmax~γa and λ~γa curves of the marine soils (silt clays and silt sands). The G/Gmax~γa curves of the Pleistocene marine soils are higher than those of the Holocene marine soils while the λ–γa curves of the Pleistocene marine soils are lower than those of the Holocene marine soils. For continental depositional, geological age has a clear effect on the G/Gmax~γa curves of the continental silt clays. The G/Gmax~γa curves of the Pleistocene continental silt clays are significantly higher than those of the Holocene continental silt clays. However, the effect of geological age on the λ~γa curves is quite weak. Overall, geological age has less effect on the λ~γa curves of the continental soils than those of the marine soils.Figure 6
Influence of geological age onG/Gmax~γa curve and λ~γa fitting curves of different deposits.As was previously discussed, the soils formed in the Quaternary marine sedimentary environment in the offshore areas of the Yellow Sea have significantly different dynamic shear modulus ratios and damping ratios than those formed in the Quaternary continental sedimentary environment. The effect of geological age onG/Gmax is similar to its effect on λ, while the effect on G/Gmax is slightly greater than that on λ. For ease of application in practical engineering, the fitting parameters of the G/Gmax~γa curves and the λ~γa curves were obtained for each type of the classified samples (Table 3). For silty clay and silt, the newer the sedimentary age, the smaller the value of A and the bigger the value of B. The average G/Gmax and λ values at various shear strain levels calculated by the recommended parameters are presented in Table 4.Table 3
Recommended parameter values forG/Gmax–γa and λ–γa curves of Quaternary sedimentary soils in the offshore areas of the Yellow Sea.
LithologyGeological age/depositNumber of samplesFitting parametersABγ0 (10-4)λminλ0βSilt clayHolocene171.010.484.770.0340.1321.477Pleistocene341.120.406.930.0290.1361.363Silt sandHolocene51.150.392.220.0070.1271.085Pleistocene151.170.393.010.0130.1151.226ClayContinental depositional101.050.425.520.0380.1611.732Marine depositional91.090.417.320.0340.1161.376Table 4
Average values ofG/Gmax and λ at various shear strain levels for Quaternary sedimentary soils in the offshore areas of the Yellow Sea.
LithologyGeological age/depositParametersShear strain (10-4)0.050.10.51.05.01050100Silt clayHoloceneG/Gmax0.98830.97740.90040.82200.49330.33280.09580.0516λ (%)3.393.423.814.408.1910.6114.7115.54PleistoceneG/Gmax0.98840.97720.91390.85450.60430.46400.19140.1199λ (%)2.902.953.353.856.728.6913.0714.32Silt sandHoloceneG/Gmax0.96850.94370.80780.70160.38750.26680.09290.0562λ (%)1.001.262.834.138.189.7912.1512.65PleistoceneG/Gmax0.97740.95870.84990.75810.45250.32100.11660.0711λ (%)1.381.502.403.306.788.4511.1811.81ClayContinental depositionalG/Gmax0.98520.97300.89680.82560.53950.39260.14090.0835λ (%)3.813.834.124.588.0010.5816.1617.62Marine depositionalG/Gmax0.98830.97870.91810.86010.60920.46590.18750.1157λ (%)3.453.483.804.206.628.3312.1713.25


## 5. Conclusions

The sedimentary characteristics of the Quaternary soils formed during the transgression in the offshore areas of the Yellow Sea were investigated. The dynamic shear modulus ratios and the damping ratios of the soil samples were tested considering the effects of sedimentary environments, geological ages, and soil types. The main conclusions are as follows.(1)
TheGmax of various marine soils increases with the depth and shows a typical linear relationship(2)
The effects of marine transgression on theG/Gmax~γa and λ~γa curves of the Quaternary soils in the offshore areas of the Yellow Sea are significant. The effects are strong on the clays, moderate on the silty clays, and minor on the silts. The G/Gmax~γa and λ~γa curves of the Pleistocene marine clays are higher and lower than those of the continental clays, respectively, which may be due to the higher strength of the clay crust formed during the marine transgression(3)
The effects of geological ages on theG/Gmax~γa and λ~γa curves of the Quaternary soils in the offshore areas of the Yellow Sea have significant differences between soil type. The effects were strong on the marine silty clays, marine silts, and continental silty clays(4)
Compared with the sedimentary environment, geological age generally had greater effect on theG/Gmax~γa and λ~γa curves of the various types of Quaternary soils in the offshore areas of the Yellow Sea. The fitting parameters of the G/Gmax~γa and λ~γa curves were obtained for each soil type under different sedimentary environments and geological ages. Moreover, the averaged curves for each type of soil were recommended for the application in practical engineering



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