Small-strain characterization of Shanghai clays by triaxial compression tests

The mechanical properties of the upper Shanghai Layers 2-6 clays at small strain levels have been extensively investigated. Nonetheless, limited data exist on their small-strain characteristics through K 0-consolidated undrained triaxial compression tests, with even less information available for the deeper layers 8 and 10. This study employed a series of K 0-consolidated undrained TC tests on intact samples from both the upper layers 2-6 and the deeper layers 8 and 10 of Shanghai clay. We evaluated the undrained maximum secant stiffness (Eu max) and reference shear strain (γ0.7 ). An increase in over-consolidation ratio (OCR) results in a higher E u max/p’ and a more rapid decay of the G/G max with the increasing shear strain (γ). As the value of γ 0.7 increases with I p and decreases with OCR, a correlation between γ 0.7 and Ip can be established. This study observed significant correlations between the E u max, effective stress (p’), and the maximum deviatoric stress, as well as between E u max and the cone resistance obtained from field cone penetration tests. These correlations offer methods to estimate E u max and γ0.7 values based on parameters that are more readily measurable, which provide critical references for the calculations and design parameters in foundation engineering within the Shanghai region.


Introduction
Determining the small strain stiffness response of soils is crucial for both earthquake engineering and the development of design parameters in foundation engineering.Notably, ground movements resulting from foundation construction in clay are generally considered undrained.To mitigate the ground movements caused by deep excavations and minimize differential settlement of foundations, engineers need to identify the representative undrained stress-strain curve of clay.The increasing demand for deep underground spaces in Shanghai underscores the necessity of conducting laboratory tests on soils directly related to engineering constructions to elucidate the small-strain stiffness characteristics.Despite the extensive investigations undertaken to explore the mechanical properties of the upper Shanghai Layers 2-6 clays at low strain levels, the small-strain characterization of these clays through 1330 (2024) 012021 IOP Publishing doi:10.1088/1755-1315/1330/1/012021 2 K0-consolidated undrained triaxial compression (TC) tests remains scarcely documented, especially for the deeper Shanghai Layers 8 and 10.
The hardening soil model with small-strain stiffness (HSS model) necessitates two critical input parameters: the small-strain stiffness, denoted by the elastic modulus (E), and the strain-dependent stiffness, indicated by the reference threshold shear strain (0.7) [1].Additionally, 0.7 is utilized in the small-strain constitutive model based on the Shanghai soil unified model [2,3].Lo Presti [4] and Vucetic [5] introduced the concepts of linear cyclic threshold shear strains (tl) and volumetric cyclic threshold shear strain (tv), depicting the transition between the distinct categories of cyclic soil behavior.For cyclic strain levels beneath tl, soils exhibit essentially linear elastic behavior.Between tl and tv, soils exhibit marked nonlinearity without altering their microstructures.Beyond tv, soils become nonlinear and inelastic, with irreversible changes to their microstructure under cyclic loading [5].
These threshold shear strains are depicted on the normalized shear stiffness degradation curves (G/Gmax-γ), with the bands of threshold shear strains corresponding to G/Gmax values ranging from 0.65 to 0.67.Drawing on these findings, Santos and Correia [6] introduced a reference threshold shear strain (0.7), defined as the shear strain at which G/Gmax reaches 0.7 on the normalized shear modulus degradation curves.Following the analyses by Vucetic and Dobry [7] and Vucetic [5], 0.7 is posited to increase proportionately with the plasticity index (Ip).
Prior research has predominantly explored the small-strain shear stiffness of Shanghai clays, specifically those in the upper layers 2-6, employing methods such as bender elements and resonant column testing [8][9][10][11].Isotropic consolidation undrained TC tests were performed to determine the small-strain properties of these layers [12] utilizing Hall-effect local strain transducers.Furthermore, Yang et al. [13] performed undrained TC tests on clays from the upper Layers 2-6.The tests utilized a triaxial apparatus equipped with two LVDT displacement transducers to derive stiffness degradation curves from small (0.001%) to large strains (20%).Thus, a comprehensive examination of the smallstrain stiffness properties of both upper and deep Shanghai clays remains unfulfilled.
This research entailed a systematic array of K0-consolidated undrained TC tests on intact samples from both the upper (2-6) and deeper layers (8 and 10) of Shanghai clays.The deployment of two LVDT displacement transducers facilitated the measurement of small strains within the clay specimens.We meticulously assessed the small-strain stiffness characteristics, specifically the undrained maximum secant stiffness (E u max) and the reference threshold shear strain (0.7).The influence of over-consolidation ratio (OCR) and plasticity index (Ip) on E u max and 0.7, alongside the correlation between E u max and cone resistance (qc) as determined from field cone penetration test (CPT), were investigated.The findings offer invaluable insights for the determination of numerical analysis parameters for foundation engineering in Shanghai and regions with similar geotechnical context.

Geological setting
Based on the comprehensive stratigraphic chart of the Quaternary, the geotechnical engineering design codes of Shanghai [14,15] divide the soil into multiple layers.Layer 1 is composed of fill soil, upper Layers 2-6 primarily comprise clays, and the deep layers beneath Layer 6 contain alternating sandy and clayey soil strata, as listed in table 1.
Layers 7, 9, and 11 consist of sandy strata, whereas layers 8 and 10 are primarily clayey.In Shanghai, the groundwater table is typically present near ground level (G.L.), ranging from −0.3 to −1.5 m, subject to seasonal variations, with an average depth of approximately 0.5 to 0.7 m below G. L. This investigation focuses on the clays within the upper layers (2-6) and deeper layers (8 and 10).In particular, the clays in the upper layers (2-5-3) are classified as Holocene series and those in Layers 5-4-6 are classified under the Late Pleistocene series.Similarly, Layer 8 clay is categorized within the Late Pleistocene series, and Layer 10 clay is identified as belonging to the Middle Pleistocene series.As depicted in figure 1, intact samples of the upper layers of clays 2-6 were obtained using a Shelby thin-walled tube sampler for laboratory analyses at the Shanghai Traditional Chinese Medicine-Integrated Hospital (Site TCM) in the Hongkou District of Shanghai.Block samples measuring 350 mm × 350 mm × 350 mm of Layer 8 clay were collected from an excavation depth of 47.5 m at Yunling West Road (Site Y) in the Putuo District.Furthermore, undisturbed samples of the deep layers 8-10 clays were extracted with a double-tube rotary sampler at Nanchen Road (Site N) in the Baoshan District.This is the first attempt of using a high-quality sampler for deep soil specimens in Shanghai.
Field CPTs were conducted at Sites Y and TCM.At Site Y, the CPT was performed on soils from layers 2-8 using a single-component probe (measuring only tip resistance) for strata beneath layer 8. Similarly, single-component CPT (focusing solely on tip resistance) was applied to soils ranging from layers 2 to 9 at Site TCM.

Soil profile from CPT
A two-component CPT (with a 60° apex angle and a 10 cm 2 probe area) was utilized for soils from layers 2 to 8 at Site Y, enabling separate measurements of cone resistance (qc) and sleeve friction (fs).In contrast, for the soil beneath Layer 8 at Site Y and for soils from layers 2 to 9 at Site TCM, a singlecomponent CPT (with a 15 cm 2 probe) was employed.The specific penetration resistance (ps) was recorded, integrating cone-tip resistance and sleeve friction.An established relationship between qc and ps for Shanghai clays is expressed as ps = 1.1qc [16].The penetration proceeded at a rate of 20 mm/s, with continuous data capture every 5 s.
The variations in cone resistance (qc) and sleeve friction (fs) determined from the CPT are plotted in figure 2

General geotechnical properties
Figure 3 illustrates the variation of particle composition, water content (w), soil density (ρ), and initial void ratio (e0) with depth for Shanghai clays (Site Y).The silt content exceeded 50% at all depths.The natural water content (wn) ranges from 21.4% to 51.4%, exceeding the plastic limit (wp) range of 15% to 24.1%, yet remaining below the liquid limit (wL) of 28.5-46.3%.The soil density (ρ) initially decreases and thereafter gradually increases with the depth-from 1.74 to 2.17 g/cm 3 .Among the clays, Layer 4 clay exhibits the lowest soil density (ρ = 1.74).In contrast, the initial void ratio (e0) displayed an initial increase before decreasing with depth, ranging from 0.54-1.29.Among these clays, Layer 4 manifested the largest initial void ratio (e0 = 1.29).

Figure 3. Physical properties of Shanghai clays (Site Y)
The natural water content (wn) and Atterberg limits (wp and wL) for the undrained TC specimens of Shanghai clays considered in this study are listed in table 2, wherein the wn of Shanghai clays ranged from 21.3-47.8%.In Layers 3 and 4, the wn exceeded the liquid limit (wL), implying their sensitive nature.The wn of Layers 2, 5, 6, 8, and 10 clays was lower than their wL.The Ip value of Shanghai clays is relatively small, ranging from 11.5-21.9%.In the conventional oedometer test conducted, specimens were prepared with a diameter of 61.8 mm and a height of 20 mm.The loading protocol entailed doubling the applied load for each increment, with each load sustained for a 24-hour duration.The average stable groundwater level in the Shanghai area is documented at −1.5 m.The in situ vertical effective stress (σ'v0) was computed based on the depth (z) and the effective unit weight (ʹ), whereas the preconsolidation pressure (pc) was evaluated using the strain energy method proposed by Becker et al. [21].
The oedometer test results performed on the Shanghai clay specimens are presented in table 3. The maximum values of the compression index (Cc) and swelling index (Cs) were observed in the upper Layer 4 clay.The Cc/Cs ranges from 4.9-9.

Laboratory apparatus and experiment procedures 3.1 Laboratory apparatus
Undrained TC tests were conducted on clays from the upper Shanghai Layers 2-6 utilizing a highprecision small-strain triaxial apparatus, as illustrated in figure 6(a).The axial loading mechanism was equipped with a high-precision load cell capable of supporting up to 0.5 kN.Owing to the elevated in situ stresses encountered within the deep clays of layers 8 and 10, the load cell capacity and cell pressure provided by the small-strain triaxial apparatus did not meet the experimental demands.Consequently, a triaxial apparatus produced by GDS (UK) was employed, as portrayed in figure 6(b), featuring two highprecision load cells with capacities of 2 kN and 16 kN, respectively, and a maximum cell pressure of 2 MPa.
The vertical displacement of the clay specimens during the small-strain phase was monitored using two axial LVDT displacement transducers.A constant temperature, grounding, and high-accuracy DC power supply were maintained to reduce the electrical noise in the signals and ensure the accuracy of the small-strain measurements.The measurement accuracies of the LVDTs were further optimized through median filtering.
Figure 6(c) displays a clay specimen fitted with two LVDTs.The dimensions of the specimens prepared for the triaxial tests were 39.1 mm in diameter and 80 mm in height.Previous studies suggest that the gauge length of a local displacement transducer typically spans 2/3 rd of the specimen height.However, given the small dimensions of the specimens in this study, two LVDTs were strategically positioned at half the height of each specimen to diminish the impact of bedding errors [22].
(a) Small-strain triaxial apparatus (b) Triaxial apparatus manufactured using GDS (c) Specimen equipped with two LVDTs.Figure 6.Schematic of triaxial apparatus and the specimen equipped with two LVDTs The stress exerted on the specimens by the described triaxial apparatus is axisymmetric, implying that the principal stresses σ2 and σ3 are equivalent during testing.In real-world engineering contexts, such axisymmetric stress conditions are predominantly observed beneath the centerline of circular excavations.Nonetheless, for a comprehensive analysis of soil deformation, the stress-strain relationships to be established through laboratory tests extend beyond only axisymmetric cases.This represents a potential limitation of the apparatus employed in this research.

Triaxial tests procedures
The testing methodology involves four primary procedures: saturation, B-check, consolidation, and undrained shear.The saturation of specimens was accomplished through the application of backpressure, considering a specimen saturated when the pore pressure coefficient (B) reached 0.95.
For the upper Shanghai clays in Layers 2-6, a representative coefficient of earth pressure at rest (K0) value of 0.6 was adopted.These specimens were reconsolidated to their in situ stress conditions utilizing K0-consolidation with a coefficient of 0.6.In the absence of a reference K0 value for the deep Shanghai clays, a commercial software (GDSLAB) was employed to conduct the K0-consolidation tests, which utilized a radial stress ramp and volume change measurement.The volumetric strain (εv) of the specimen was determined using a back-pressure controller, ensuring that the zero radial strain (where axial strain (εa) = εv) by calculating each axial displacement (ΔH) as ΔH = H0εv, where H0 indicates the initial height of the specimen.
After attaining the target in situ stress condition, the specimens were subjected to a period of drained creep under constant stress conditions.Axial strain measurements were conducted using two LVDTs, whereas pore pressure and effective stress levels were continuously monitored.After approximately 48 h, when the excess pore pressure became negligible and the measured creep axial strain rate dropped to or below 0.001% per hour, undrained shear tests were initiated at an axial strain rate of 0.0022 mm/min.This preparatory creep period was crucial for ensuring that the initial stiffness metrics obtained during the undrained shear phase were not influenced by the ongoing deformations residual from the reconsolidation phase.

Undrained TC test results and discussion
The outcomes of the undrained TC tests on Shanghai clays are depicted in figures 7-9, showcasing the effective stress path (q-p'), the evolution of deviatoric stress (q) with axial strain (εa), and the secant stiffness decay curves.The following observations were recorded.

Effective stress paths (ESP) and stress-strain curves
The effective stress paths (ESP) of the Shanghai clays obtained from the undrained TC tests are plotted in figure 7, and the progression of deviatoric stress (q) with respect to axial strain (εa) is illustrated in figure 8.The typical mechanical behaviors of overconsolidated clay are observed in the upper layers 2, 5, 6, and the deep layer 8, which are characterized by strain hardening, as evident in the ESP.The deviatoric stress (q) increased until εa ≈ 12%, with the ESP progressing along the critical state line (CSL).Conversely, strain-softening behaviors were identified in the upper layers 3 and 4 and the deep layer 10 clays, where q decreased with the increasing εa, and the ESP exhibited a decline along the CSL.These patterns are typical of normally consolidated structured clays.Wu et al. [17] indicated that layers 3 and 4 consist of structured sensitive clays, whereas layers 2, 5, and 6 are overconsolidated.These observations align with the findings from undrained TC tests conducted in this study.

Small-strain secant shear stiffness
The decay curves of the undrained secant shear stiffness (E u sec) and normalized stiffness (E u sec/p') with the axial strain (εa) are plotted in figures 9(a) and 9(b), respectively.E u sec is defined as the ratio of Δq to Δεa.As depicted in figure 9  The study highlights that the small-strain stiffness of clay is predominantly affected by the vertical effective consolidation stress (σ'vc) or mean effective stress (p′) and the void ratio (e).A correlation was established between the undrained maximum secant shear stiffness (Eumax), void ratio, and effective stress conditions in TC tests, represented by the modified formula Eumax = AF(e)(p′/pr)n, adapted from IOP Publishing doi:10.1088/1755-1315/1330/1/01202113 an equation utilized by various researchers [24][25][26].Here, pr denotes the reference pressure of 100 kPa (equivalent to atmospheric pressure), with A and n as material constants.
The void ratio function F(e) = e − x, suggested by Jamiolkowski et al. [27], is employed to highlight the impact of soil density on stiffness.For this analysis, x = 1.3 was chosen based on the reported range of x = 1.11-1.52 for different clays [27][28][29].Figure 11 presents the relationship between the variation of Eumax/F(e) and p′/pr, mathematically expressed as E u max/e −1.3 =86.6(pʹ/pr) 0.636 (R 2 =0.91).Although normalization minimized the lithological differences within Shanghai clays, a discernible correlation persisted.The relationship between axial strain (εa), radial strain (εr), secant shear modulus (Gsec), and shear strain () is articulated as Gsec=Δq/(3Δγ), where γ is determined by the formula 2(εa − εr)/3.In isotropic elastic soils, the connection among small-strain stiffness parameters is represented by Emax=2(1+ν)Gmax.For undrained loading scenarios, Gmax is derived as Gmax=E u max/3, assuming ν u = 0.5.Thus, the analysis of undrained TC test data in this study presumes the isotropic condition Gmax = E u max/3.Figure 12 illustrates the stiffness decay curves, G/Gmax, plotted against γ for Shanghai clay specimens, juxtaposed with the curves for Ip = 0-200% [7].The stiffness decay curves (G/Gmax -) of Shanghai clays are observed within a narrow band, generally aligning between the curves of Ip = 0 and Ip = 15% [7].However, the G/Gmax-γ curve for the heavily overconsolidated clay of Layer 2 (OCR ≈ 5) closely aligns with the Ip = 0 curve proposed by Vucetic and Dobry [7], highlighting a pronounced divergence from other Shanghai clays that typically display uniformity.Previous research [30,31] reported a significant correlation between soil stiffness decay behavior and its OCR, indicating an accelerated stiffness decay in soil with increasing OCR under load.
In 1978, Hardin [32] introduced the formula G/Gmax = 1/(1+γ/γref) 2 to depict the decay of small-strain stiffness as a function of shear strain (), where ref denotes the reference threshold shear strain.Santos and Correia [6] adapted this equation to propose G/Gmax = 1/(1+a/0.7) 2 , with a = 3/7, by substituting γref with γ0.7, thus defining small-strain stiffness decay.This formula and the reference threshold shear strain (γ0.7) introduced by Santos and Correia [6] are integrated into the small-strain constitutive model for Shanghai soil [3].The G/Gmax-γ curves for Shanghai clays can be modeled using the modified formula from Santos and Correia [6], expressed as G/Gmax = 1/(1+ a/γref)² , where a = 3/7.The test data points predominantly ranged between the curves for γref = 0.03% and γref = 0.07%, as depicted in figure 12. Figure 13 illustrates the relationship between γ0.7, the plasticity index (Ip), and the OCR across different depths for Shanghai clays.The distribution of γ0.7 with depth mirrors that of Ip and is inversely related to OCR, suggesting correlations between γ0.7 and Ip, as well as between γ0.7 and OCR.Vucetic and Dobry [7] identified a linear correlation between γ0.7 and Ip, formulated as γ0.7 = 0.0021Ip -0.0055.This relationship was applied by Likitlersuang et al. [33] to estimate γ0.7 values for Bangkok clays.
For Shanghai clays, the γ0.7 values predicted by Vucetic and Dobry [7] are approximately 1.6 times greater than the values obtained through present measurements.The adjusted formula γ0.7 = 0.0011Ip provides a closer match to the measured γ0.7 values from static undrained TC tests, indicating a faster decay rate of shear stiffness in static (monotonic) trials compared to dynamic (cyclic) shear stiffness decay, which is consistent with studies by Mayne [34] and Zhang et al. [12].During the static (monotonic) shear tests, the stiffness (G) declines progressively with the increasing shear strain (), which can be attributed to the separation or slippage of particle contacts, which diminishes their contribution to the elastic stiffness of the soil.This behavior has been validated using discrete element method (DEM) simulations [35].Upon reversing the loading direction, the decay is typically reversible, as the interparticle contacts that had slid are reengaged.Nevertheless, with extended reverse loading, the elastic contacts are lost once again, resulting in reduced stiffness, representing the initial observations.
The stiffness decay rate on the reverse loading path is estimated to be about half of that seen in the initial loading curve, since elements that had previously slid need to undergo elastic recovery before deforming in the opposite direction [36].In undrained tests, stiffness reduction at moderate strain levels is further influenced by excess pore pressure buildup, reducing effective stress beyond a specific threshold shear strain, generally around 0.1% for clays [37].This phenomenon is termed as cyclic modulus degradation in clays and involves a gradual reduction in stiffness through continuous strain cycles [38].The variation in decay rates between static shear stiffness (during monotonic loading) and dynamic shear stiffness (during cyclic loading) is attributed to strain rate effects, as described by Shibuya et al. [39] and Yamashita et al. [40].In dynamic triaxial tests, the cyclic loading rate exceeds the static loading rate observed in conventional undrained TC tests, which strengthens the influence of mechanisms responsible for the observed reduced decay rate in shear stiffness.Mayne [41] advocated for the adoption of static shear stiffness decay curves as the foundational model, which could be adjusted for strain rate and other pertinent parameters to generate dynamic curves.

Relationships between small-strain stiffness and strength
Butler [42] and Hewitt [43] applied the ratio of the Young's modulus (E) to undrained shear strength (su), represented as E/su (=2E/qmax), to establish empirical relationships for estimating the settlement of structures.According to Atkinson [44], E u max/qmax ranges between approximately 400 and 4000.The E u max/qmax ratio is simultaneously influenced by both the mean effective stress (p') and the OCR [44].The value of E u max/qmax decreases with an increase in the mean effective stress (p') (for a given OCR), along with an increase OCR. Figure 15 illustrates the relationship between E u max and qmax for Shanghai clays and data up to Ushev [23], derived from K0-consolidated undrained TC tests.A robust correlation is observed between E u max and qmax for Shanghai clays, formulated as E u max = 1450 (qmax) 0.813 (R 2 = 0.93).

Figure 15.
Relationships between E u max and qmax of Shanghai clays (as well as Cowden till (Ushev [23])

5.
Correlations between E u max, qmax, and parameters from CPT In the field of foundation engineering, the logistical and financial constraints of conducting extensive laboratory tests often render such endeavors impractical.Consequently, numerous researchers [41,[45][46][47][48][49][50] have strived to establish correlation between the results of CPT and CPTu and small-strain stiffness properties.However, Long and Donohue [49] observed that while many researchers have developed models fitting their datasets, these models often underperform when applied to various contexts [51].Accordingly, this study aims to establish preliminary relationships between CPT parameters and both the small-strain stiffness (E u max) and undrained strength (qmax) derived from laboratory testing, with a focus on Shanghai clays.
Figure 16(a) demonstrates a positive relationship between E u max and the cone-tip resistance (qc) for Shanghai clays, expressed through the linear formula E u max = 110qc (R 2 = 0.97).Similarly, an increase in sleeve friction (fs) corresponds to an elevated qmax, as depicted in figure 16(b), which is expressed as qmax = 10fs (R 2 = 0.90).The data up to Ushev [22] is presented in figures 16(a) and 16(b), which further validate these linear trends.These derived correlations provide a method for estimating small-strain stiffness and undrained strength values by leveraging more accessible field-test data.

Conclusions
This investigation involved a series of K0-consolidated undrained TC tests on intact samples from the upper layers (2-6) and deep layers (8 and 10) of Shanghai clays.It specifically assessed the small-strain stiffness characteristics, including the undrained maximum secant stiffness (E u max) and the reference shear strain (γ0.7).The study yielded the following conclusions: (1) The OCR exerts a significant influence on both the normalized stiffness (E u max/p') and the decay curves of normalized stiffness (G/Gmax-γ).Specifically, an elevated OCR results in higher normalized stiffness (E u max/p'), whereas the stiffness (G/Gmax) exhibits a more rapid decay with increasing shear strain ().
(3) The stiffness decay curves (G/Gmax-γ) for Shanghai clays are distributed within a narrow band and typically reside between the curves proposed by Vucetic and Dobry (1991) for Ip = 0 and Ip = 15%.The reference shear strain (γ0.7) increases with the plasticity index (Ip) and decreases with an increase OCR.A correlation between γ0.7 and Ip is established.
(4) Relatively strong correlations were observed between the undrained maximum secant stiffness (E u max), effective stress (p'), and maximum deviatoric stress (qmax).A pronounced relationship between E u max and parameters qc obtained from field CPT was observed.

Figure 1 .
Figure 1.Locations of sampling sites , displaying a comparable qc depth profile at both sites.The clay strata were discerned by their relatively low qc and fs values.The upper layers of clays 2-6 extend to a depth of less than 40 m, with Layer 6 clay absent at Site Y. Situated below the silty sand in Layer 7, Layer 8 clay exhibits a thickness ranging from 24-30 m.Layer 9 is characterized by coarse sand extending to a depth of 98 m, whereas Layer 10 clay stretches between 98 and 110 m.

Figure 2 .
Figure 2. Variations of qc and fs with depth from the CPT (Site Y and Site TCM)

Figure 5 .
Figure 5. Activity for Shanghai clays (compared with other clays in the literature) 2 for the Shanghai clays.The OCR values for the clays in layers 2, 3, and 4 were 4.6, 1.1, and 1.0, respectively, and those for the clays in Layers 5-1, 5-2, and 6 were 1.4, 1.3, and 1.6, respectively.At Site Y, Layer 8 clay is located at a depth of 47.5 m and exhibited an OCR of 1.1, whereas at Site N, Layer 8 clay demonstrated OCR values between 2.5 and 2.7, averaging at 2.6.Layer 10 clay presented OCR values ranging from 1.0 to 1.1.These findings indicate that Layer 2 clay is significantly overconsolidated, whereas Layers 3 and 4 are characterized as normally consolidated.Layers 5 and 6 are identified as slightly overconsolidated, Layer 8 as overconsolidated, and Layer 10 as normally consolidated clay.

Figure 10 .
Figure 10.Correlation between normalized undrained maximum secant stiffness E u max/p' and OCR

Figure 11 .
Figure 11.Relationship between undrained maximum secant shear stiffness E u max (corrected by void ratio function e − x) and effective stress p (modified by atmospheric pressure pr)

Figure 13 .
Figure 13.Variation of γ0.7, Ip, and OCR with depth of Shanghai clays

14 .
(a) γ0.7-Ip(b) γ0.7-OCR Figure Relationship between γ0.7 and Ip, and between γ0.7 and OCR of Shanghai clays (as well as Cowden till Ushev [22]) The correlations between 0.7 and the plasticity index (Ip), as well as between 0.7 and the OCR for Shanghai clays, are depicted in figures 14(a) and 14(b), incorporating data up to Ushev [23].Figure 14(a) reveals that 0.7 increased with Ip, characterized by the linear equation 0.7 = 0.0011Ip (R 2 = 0.97) for Shanghai clays.In contrast, figure 14(b) demonstrates a gradual decline in 0.7 with increasing OCR, indicating that higher OCR values prompt a quicker decay in normalized stiffness (G/Gmax) with shear strain ().The fitting equation 0.7 = 0.02 (OCR) −0.34 illustrates a modest correlation between 0.7 and OCR for Shanghai clays, evidenced by a low R 2 value of 0.35, thereby necessitating further data to validate this relationship.
(a) E u max, qc (b) qmax, fs Figure 16.Relationships between E u max, qmax and the parameters obtained from CPT (as well as Cowden till (Ushev, 2018))

Table 2 .
[17]ral water content and Atterberg limits for TC specimens of Shanghai clays Figure4presents the plasticity chart for Shanghai clays, incorporating data for clays in layers 2-6 as reported by Wu et al.[17].All evaluated clays were positioned slightly above the A-line, categorizing them as low-plasticity silty clays.

Table 3 .
Oedometer test results of Shanghai clays