The effect of vertical effective overburden stress, σ 0 v0 , on the cyclic response of cohesionless soils commonly is addressed using the overburden correction factor, K σ , introduced by Seed (1983). Increases in σ 0 v0 lead to the suppression of dilation and the corresponding reduction in undrained cyclic resistance (Idriss and Boulanger 2008). Previous investigations of the effect of σ 0 v0 on the cyclic resistance of granular soils have been conducted using undrained stress-controlled cyclic laboratory tests (Seed 1983;Seed and Harder 1990;Harder and Boulanger 1997;Vaid and Thomas 1995;Vaid and Sivathayalan 1996;Hynes and Olsen 1999) to build a body of experimental data to inform trends in K σ with σ 0 v0 and adjustments to the cyclic resistance computed using penetration test-based liquefaction triggering procedures. The understanding of the effect of σ 0 v0 on the cyclic response of natural silts remains poor in comparison. Wijewickreme et al. (2005) investigated the effect of vertical effective consolidation stress, σ 0 vc , on the cyclic resistance of normally consolidated (NC) intact and reconstituted laterite tailings and copper-gold-zinc tailings classified as nonplastic and lowplasticity silt (ML) per the Unified Soil Classification System (USCS), with a plasticity index (PI) of 0, 2, and 12 for σ 0 vc ranging from 100 to 460 kPa. The laterite tailings exhibited densificationdriven dilative tendencies which outweighed the increase in contractive tendency associated with greater σ 0 vc . For the case of the copper-gold-zinc tailings, the cyclic resistance ratio (CRR) was found to be insensitive to the initial density and σ 0 vc . Sanin and Wijewickreme (2006) reported that the cyclic resistance of intact Fraser River Delta silt [classified as ML, with PI ¼ 4 and overconsolidation ratio ðOCRÞ ¼ 1] was insensitive to the variation in σ 0 vc over the range 85-200 kPa. However, the effect of damage to the natural soil fabric and the increased density resulting from increased σ 0 vc was not assessed separately. Verma and Wijewickreme (2018) noted insensitivity of the cyclic resistance to σ 0 vc for intact, low-plasticity NC Fraser River silt (classified as ML, with PI ¼ 8-9) over the range 400-1,000 kPa, whereas Soysa and Wijewickreme (2015) concluded that the cyclic resistance of intact, high-plasticity NC Fraser River silt (classified as MH; PI ¼ 34) decreased with increases in σ 0 vc due to breakdown of the natural soil fabric. Based on the results of previous studies, a systematic assessment of the sensitivity of the cyclic resistance of silts with different plasticity to σ 0 vc is needed. This study focused on assessing the effects of σ 0 vc on the cyclic response of several silts obtained from the Willamette Valley in Oregon. These silts vary from nonplastic to slightly plastic. Tests were performed on both intact and reconstituted specimens to assess the influence of soil fabric on material response.
A series of laboratory tests was performed on intact normally consolidated (NC) and overconsolidated (OC) and reconstituted NC specimens of nonplastic to high-plasticity silt deposits from Sites E and F described by Stuedlein et al. (2023b). Intact samples were retrieved in accordance with ASTM D1587 (ASTM 2015) from depths ranging from 9.4 to 10 m and from 11.4 to 12 m at Site E (denoted E-3 and E-5, respectively) (Table 1) and from 6.3 to 6.9 m at Site F (denoted F-1) (Table 1). Samples were retrieved within mud rotary boreholes using Osterberg piston samplers and specially fabricated thin-walled tubes with specifications similar to those described by Wijewickreme et al. (2019). Sample transportation, extrusion, and mounting of specimens followed the guidelines in ASTM D4220-14 (ASTM 2014), and were explained in detail by Dadashiserej et al. (2022a). Reconstituted specimens were prepared from the samples retrieved from Sites E and F using a slurry deposition method described by Wijewickreme and Sanin (2010), which attempts to replicate the soil fabric developed in fluvial environments (Krage et al. 2020).
The soils from Site E described herein were classified as low-plasticity to high-plasticity silt (ML-MH) per the Unified Soil Classification System, with an average natural water content w n ¼ 52%, 15 ≤ PI ≤ 27, and fines contents ðFCÞ ≈ 99%. Soil samples tested from Site F generally were classified as ML, with (Stuedlein et al. 2023b).
Constant-volume, cyclic direct simple shear (CDSS) tests were conducted using the SSH-100 device described by Dadashiserej et al. (2022b). The test program was performed to investigate the effect of overburden stress (i.e., σ 0 vc ) on the cyclic resistance of saturated silt soils. Intact specimens were consolidated to σ 0 vc equal to the estimated in situ σ 0 v0 to replicate the existing in situ stress state using the recompression method (Bjerrum and Landva 1966); Stuedlein et al. (2023b) presented details of and justification for the method. Additional cyclic tests were conducted on mechanically consolidated NC intact specimens (MC-NC) by exceeding the in situ preconsolidation stress, σ 0 p , and achieving σ 0 vc of 350 and 600 kPa. Reconstituted NC specimens were consolidated to σ 0 vc of 100, 350, and 600 kPa to elucidate further the effect of σ 0 vc on the cyclic resistance of silt soils. Following the completion of primary consolidation and at least one log cycle of secondary compression, specimens were subjected to uniform amplitude sinusoidal shear stress cycles, τ cyc , at selected cyclic stress ratios (CSRs), τ cyc =σ 0 vc , with a loading frequency of 0.1 Hz to a minimum single amplitude shear strain, γ, of 3.75%. The excess pore-pressure ratio, r u , for constant-volume CDSS specimens may be interpreted as r u ¼ 1 -σ 0 v =σ 0 vc (Dyvik et al. 1987), where σ 0 v is the vertical effective stress. Individual specimens are distinguished by a corresponding test designation (e.g., Table 1, Figs. 1234) which indicates the test site, sample, and test number. For example, Test E-3-15 indicates that the specimen was prepared from soils retrieved from Site E, Sample 3, and was the 15th test conducted for the specified soil sample. Reconstituted specimens are distinguished from intact specimens with the addition of the letter R to the test number in their designations.
There were significant differences in PI and corresponding void ratios, e, for the intact specimens prepared from Sample 3 of Site E and tested at σ 0 v0 (i.e., E-3-1 to E-3-4) relative to those tested at σ 0 vc > σ 0 v0 (i.e., E-3-14 to E-3-18) (Table 1). The difference in e resulted from the spatial variability within Sample 3. However, intact specimens prepared from Sample 5 of Site E and tested at σ 0 v0 (E-5-1 to E-5-6) had similar PI and e values, prior to consolidation, as Specimens E-3-14 to E-3-18. Therefore, Specimens E-5-1 to E-5-6, which are tested at σ 0 v0 , were compared with those intact specimens of Site E, Sample 3, tested at σ 0 vc > σ 0 v0 (i.e., E-3-14 to E-3-18).
Fig. 1 presents the cyclic response of intact OC and MC-NC specimens of medium to high plasticity from Site E and nonplastic to low-plasticity specimens of Site F in terms of the normalized shear stress-shear strain (CSR-γ) hysteresis and effective stress paths. The specimens all indicated the cyclic mobility-type response [Figs. 1(b,e,h,k,n,and q)], which is characterized by gradual accumulation of γ and degradation in shear stiffness [Figs. 1(a,d,g,j,m,and p)] without an abrupt loss of strength (Castro and Poulos 1977). With the exception of Specimen E-5-4 [Fig. 1(a)], the specimens exhibited sandlike behavior characterized by inverted S-shape hysteresis loops, and transient near-zero shear stiffness with the maximum cyclic shear stress-normalized minimum tangent shear modulus and cyclic shear stress difference, G tan;min =τ cyc;max and Δτ cyc =τ cyc;max (Stuedlein et al. 2023b), of approximately 2 or less and 0.55 or less, respectively, and varying degrees of dilation hardening just prior to cyclic stress reversal [Figs. 1(d,g,j,m,and p)]. Although the maximum r u ; r u;max , generally decreased with σ 0 vc for a given shear strain amplitude [Figs. 1(c,f,i,l,o,and r)], the alternate hysteretic metrics, G tan;min =τ cyc;max and Δτ cyc =τ cyc;max , proposed by Stuedlein et al. (2023b) appear to describe the observed sandlike behavior satisfactorily, the tendency for which seemed to increase with increases in σ 0 vc . Table 1 summarizes the properties of the specimens and the results of cyclic test program, including the number of loading cycles to reach γ ¼ 3% and 3.75%, N γ¼3% , N γ¼3.75% , respectively, the maximum number of loading cycles, N max , and r u;max .
The effect of increased σ 0 vc on the cyclic resistance for soils retrieved from Sites E and F was interpreted in terms of N γ¼3% for consistency with common cyclic failure models [e.g., liquefaction (Boulanger and Idriss 2015), cyclic softening (Boulanger and Idriss 2007), and cyclic failure of silts (Stuedlein et al. 2023a)]. Specimens E-5-4 and E-3-15 each resulted in N γ¼3% ¼ 1.7 [Figs. 1 (a andd)], although OC Specimen E-5-4 (OCR ¼ 2.2, e ¼ 0.96) was sheared under σ 0 v0 ¼ σ 0 vc ¼ 125 kPa and a larger CSR ¼ 0.31, compared with the denser MC-NC Specimen E-3-15 (OCR ¼ 1, e ¼ 0.83) sheared under σ 0 vc ¼ 350 kPa and CSR ¼ 0.23. The constant-volume, monotonic DSS response for Specimen E-5-M1 (OCR ¼ 2.2, PI ¼ 15) consolidated to σ 0 vc ¼ 125 kPa reported by Stuedlein et al. (2023b) indicates that the initial state for this material was contractive and that the excess pore pressure generated at failure was larger than that predicted by critical-state soil mechanics theory assuming parallel normal consolidation (NCL) and critical state (CSL) lines. Thus, a change from a dilative to a contractive tendency is not responsible for the lower cyclic resistance exhibited by Specimen E-3-15. Rather, if the CSL is steeper than the NCL in elog σ 0 v space, lower cyclic resistance results from the destruction of the natural soil fabric associated with yielding (i.e., exceedance of σ 0 p ) and a presumed increase in the state parameter relative to the less dense OC Specimen E-5-4.
The effect of OCR on the cyclic response of these silts can be removed and separated from other contributing factors by comparing the cyclic resistance of the normally consolidated (MC-NC) specimens E-3-15 (e ¼ 0.83) [Figs. 1(d ande)] and E-3-18 (e ¼ 0.65) [Figs. 1(g and h)] consolidated to σ 0 vc ¼ 350 and 600 kPa, respectively. Although Specimen E-3-15 was subjected to a larger CSR, it resulted in greater cyclic resistance (N γ¼3% ¼ 1.7) than the denser Specimen E-3-18 (N γ¼3% ¼ 0.2). This observation highlights the dominant effect of natural fabric destruction due to further increases in σ 0 vc beyond σ 0 p and a possible increase in the state parameter over any beneficial effect resulting from increasing density on cyclic resistance. The differing CSRs, which were selected in order to reliably quantify cyclic resistance under the selected strain-based cyclic failure criterion, prevent direct comparison of dilative tendencies. Similar observations about the effect of increased σ 0 vc on the cyclic resistance of intact, nonplastic to low-plasticity Site F specimens may be drawn ]. However, increased σ 0 vc resulted in a smaller reduction in cyclic resistance of the low-plasticity Site F specimens than of the high-plasticity Site E specimens, as discussed subsequently. Based on the monotonic responses reported by Stuedlein et al. (2023b) and the cyclic responses presented here, the NCL and CSL for Site E and F specimens are not parallel, they exhibit net contractive responses in their in situ state, and become increasingly contractive upon application of larger σ 0 vc as dilation is
Fig. 1. Cyclic response of intact and MC-NC specimens subjected to stress-controlled cyclic DSS tests: (a, d, and g) Site E, cyclic shear stress-shear strain hysteresis; (b, e, and h) Site E, effective stress paths; (c, f, and i) Site E, variation of excess pore pressure ratio, r u , with shear strain, γ; (j, m, and p) Site F, cyclic shear stress-shear strain hysteresis; (k, n, and q) Site F, effective stress paths; and (l, o, and r) Site F, variation of excess pore pressure ratio, r u , with shear strain, γ.
© ASCE 06023007-4 J. Geotech. Geoenviron. Eng.
Fig. 2. Cyclic response of NC reconstituted specimens subjected to stress-controlled cyclic DSS tests: (a, d, and g) Site E, cyclic shear stress-shear strain hysteresis; (b, e, and h) Site E, effective stress paths; (c, f, and i) Site E, variation of excess pore pressure ratio, r u , with shear strain, γ; (j, m, and p) Site F, cyclic shear stress-shear strain hysteresis; (k, n, and q) Site F, effective stress paths; and (l, o, and r) Site F, variation of excess pore pressure ratio, r u , with shear strain, γ.
suppressed. In summary, the intact specimens of Sites E and F demonstrate the complexity of isolating the effect of overburden stress on the cyclic resistance of naturally deposited specimens, which necessarily will exhibit varying stress histories and void ratios with depth, dictating different initial states relative to the critical state.
Owing to the inability to satisfactorily isolate and quantify the effect of intact versus destructured soil fabric with regard to OCR, state, and potential specimen-to-specimen variability on the cyclic response of natural specimens, the effect of σ 0 vc was investigated by performing CDSS tests on reconstituted specimens (Table 1). Fig. 2 presents the CSR-γ hysteresis and effective cyclic stress paths for NC reconstituted specimens prepared from the samples of Sites E and F. The reconstituted specimens exhibited cyclic mobility with gradual accumulation of γ and degradation of shear stiffness without abrupt loss of strength. There was a consistent reduction in cyclic resistance with increases in σ 0 vc . For example, Specimens E-3-R1 (σ 0 vc ¼ 100 kPa) and E-3-R5 (σ 0 vc ¼ 350 kPa), both with e ¼ 1.02 and PI ¼ 21, yielded N γ¼3% ¼ 13.2 and 8.3 for CSRs of 0.27 and 0.23, respectively [Figs. 2(a and d)]. The further reduction in cyclic resistance obtained from the denser Specimen E-3-R9 with σ 0 vc ¼ 600 kPa also is evident [Fig. 2(g)], and points solely to the suppression of dilative tendencies as a result of an increase in the contractive state, which overshadows the beneficial effect of densification of these NC specimens. The reconstituted, dense, PI ¼ 4 specimens of Site F sheared under the shared CSR of 0.18 confirm the dominant role of suppressed dilative tendencies with increased σ 0 vc [Figs. 2(j-r)], with greater shear strain amplitudes necessary to trigger dilative tendencies prior to cyclic stress reversal under higher σ 0 vc . This is more clearly evident in Fig. 3, which presents the results for additional reconstituted test specimens with similar void ratios sheared under identical CSRs. Comparison of the cyclic response of Specimens E-3-R3 and E-3-R7 (Fig. 3) indicates that although Specimen E-3-R7 was slightly denser (e ¼ 0.97, σ 0 vc ¼ 350 kPa) than Specimen E-3-R3 (e ¼ 1.03, σ 0 vc ¼ 100 kPa), it exhibited lower shear stiffness [Fig. 3(a)] and a reduced dilative tendency [Fig. 3(b)], and generated greater excess pore pressure for a given cycle of loading [Fig. 3(c)]. Comparison of the low-plasticity reconstituted NC specimens of Site F [Figs. 3(d-f), Table 1], with nearly identical e values, likewise confirms the greater net contractive tendency of such silts under large σ 0 vc .
Fig. 4 compares the cyclic resistance of the intact and reconstituted nonplastic to high-plasticity Site E and F specimens consolidated to σ 0 vc ¼ ∼100, 350, and 600 kPa in terms of their CRR -N γ¼3% relationships to demonstrate succinctly the role σ 0 vc in CRR. The average CRR of the intact, MC-NC Site E specimens was 20% smaller at σ 0 vc ¼ 600 kPa than at 350 kPa over 2 ≤ N≤ 25 [Fig. 4(a)]. Similarly, the average CRR of the intact MC-NC Site F specimens was 26% smaller at σ 0 vc ¼ 600 kPa than at 350 kPa over 1 ≤ N ≤ 21 [Fig. 4(b)]. The reductions in CRR would have been greater if the specimens had the same e. Although the reconstituted plastic Site E specimens exhibited similar reductions in CRR as σ 0 vc increased to that observed for the intact specimens, the dense reconstituted low-plasticity Site F specimens exhibited a significantly smaller reduction in CRR as σ 0 vc increased from 350 to 600 kPa. This likely was due to a greater difference in soil fabric between the intact and reconstituted low-plasticity Site F specimens than for
Fig. 3. Examples of the effect of vertical effective consolidation stress, σ 0 vc , on the cyclic response of reconstituted specimens subjected to stresscontrolled cyclic DSS tests: (a) Specimens E-3-R3 and E-3-R7, cyclic shear stress-shear strain (CSR-γ) hysteresis; (b) Specimens E-3-R3 and E-3-R7, effective stress path; (c) Specimens E-3-R3 and E-3-R7, variation of excess pore pressure ratio, r u , with number of loading cycles, N; (d) Specimens F-1-R1 and F-1-R5, cyclic shear stress-shear strain (CSR-γ) hysteresis; (e) Specimens F-1-R1 and F-1-R5, effective stress path; and (f) Specimens F-1-R1 and F-1-R5, variation of excess pore pressure ratio, r u , with number of loading cycles, N.
Site E specimens, which also can be significant for other silts (e.g., Dadashisherej et al. 2022b). Additionally, the increase in density (i.e., from e ¼ 0.54 to 0.46 as σ 0 vc increased from 350 to 600 kPa) for the well-graded Site F specimens may have resulted in a corresponding increases in CRR that offset some of the reduction in CRR due to high σ 0 vc . The reduction in cyclic resistance of the higher-plasticity Site E specimens generally agreed with findings reported by Soysa and Wijewickreme (2015) and Verma and Wijewickreme (2018) for high-plasticity intact Fraser River silt (PI ¼ 34). However, the CRR of intact NC low-plasticity (PI ¼ 4-9) Fraser River silt specimens was observed to be insensitive to σ 0 vc over a range of 75-1,000 kPa (Sanin and Wijewickreme 2006;Verma and Wijewickreme 2018). These findings differ from the responses identified from the intact Site E and F soils, perhaps pointing to the role of particle morphology, mineralogy, and/or soil fabric on overburden stress effects.
Furthermore, exponent b describing the slope of the power law CRR ¼ aN -b was sensitive to the combined effects of stress history and state (i.e., σ 0 vc and e); intact OC specimens under low σ 0 vc exhibited steeper slopes (and therefore larger b) than the denser intact MC-NC specimens sheared cyclically under high σ 0 vc . Such observations are highly relevant for thick and deep deposits of silts, such as those encountered along the banks of the Columbia River west of the Cascades mountain range (e.g., at Longview, WA and Astoria, OR), which exhibit OCRs that decrease with depth. These and similar soils will exhibit substantially differing cyclic resistances in response to near-fault, short-duration crustal (low-N) and distant, long-duration subduction zone (high-N) earthquakes. The sensitivity of b to stress history and state noted for the intact specimens reported herein differs from conclusions about the effect of OCR on b drawn by Stuedlein et al. (2023a). Stuedlein et al. (2023a) statistically analyzed 20 suites of CRR-N curves for intact specimens of nonplastic to plastic silts and determined that the OCR contribution to b was statistically insignificant; however, the majority (70%) of specimens in the database were consolidated to σ 0 v0 ¼ σ 0 vc ranging from 100 to 150 kPa, and only 12% of specimens were subjected to larger values of σ 0 vc . Thus, further research is needed to identify the effect of stress history and state on exponent b and cyclic resistance.
The effect of σ 0 vc on the cyclic response of the silts investigated in this study may be considered using the overburden correction factor, K σ (Seed 1983). For level ground, empirical reductions in CRR may be estimated using
where CRR σ 0 vc = CRR for soil consolidated under a given σ 0 vc ; and CRR σ 0 vc ¼1 = cyclic resistance ratio for the same soil consolidated under reference stress σ 0 vc ¼ 1 atm (∼100 kPa). The CRR used in Eq. ( 1) is most appropriate for soil with identical characteristics, e.g., fabric, e, OCR, and prior strain history (Montgomery et al. 2014). For reconstituted specimens, K σ was computed directly using Eq. ( 1) by normalizing CRR with respect to the CRR of specimens consolidated to σ 0 vc ¼ 100 kPa. However, because σ 0 v0 for the intact OC specimens was larger than the reference σ 0 vc ¼ 100 kPa (i.e., Site E-5: σ 0 v0 ¼ 125 kPa; and Site F: σ 0 v0 ¼ 120 kPa), K σ was computed using CRRs estimated for σ 0 vc ¼ 100 kPa through limited nonlinear interpolation of the observed variation of τ cyc with σ 0 vc for a given N using curves fitted to the available data through the origin as described by Idriss and Boulanger (2008).
Fig. 5 presents the variation of K σ with σ 0 vc and e for intact and reconstituted specimens of Sites E and F for N γ¼3% ¼ 15 and 30, illustrating the reduction in CRR with increases in σ 0 vc [Figs. 5(a andc)] and accompanying reductions in e [Figs. 5(b andd)]. Despite a 29% reduction in void ratio for the intact Site E specimens as σ 0 vc increased from ∼100 to 600 kPa, the CRR at N γ¼3% ¼ 30 decreased from 0.26 to 0.15, with a corresponding K σ ¼ 0.58. The comparison of K σ for the intact specimens of Sites E (PI ¼ 15) and F (PI ¼ 0-3), characterized by similar e and OCR, show that increases in PI lead to larger reduction in cyclic resistance and corresponding K σ , indicating the role of compressibility on K σ . This is consistent with the conclusions drawn about the effect of fines content on the compressibility of sand and its stress-dilatancy response reported by Boulanger and Idriss (2004). The K σ calculated in Fig. 5 for intact specimens may be conservative (i.e., smaller than anticipated) because it includes the coupled detrimental effects of increased σ 0 vc and the reduction in OCR associated with yielding and destruction of the soil fabric on cyclic resistance when applied to unaltered natural soil deposits (Montgomery et al. 2014). However, these K σ values are appropriate for use in assessing the CRR of such deposits in representative scenarios, for example, in the case of the construction of large structures such as dams or following preloading programs leading to the acquisition of NC states, which are common on tracts along the Columbia River. In contrast, the K σ presented in Fig. 5 for the NC reconstituted specimens may be smaller than expected, most notably for σ 0 vc > 350 kPa, because increased σ 0 vc resulted in significant reductions in e, resulting in partial compensation of the overburden stress effect. However, the effects of differing stress history and soil fabric did not contribute to K σ for these specimens.
Constant-volume, stress-controlled cyclic direct simple shear (CDSS) tests were conducted to investigate the effect of overburden stress on the cyclic resistance of nonplastic to plastic, overconsolidated (OC) and mechanically consolidated-normally consolidated (MC-NC) intact and NC reconstituted silts. The role of changes in specimen properties such as void ratio, natural soil fabric, and overconsolidation ratio resulting from the increased vertical effective stress, σ 0 vc , on the reduced cyclic resistance was identified and was found to increase the complexity of the interpretation of results on intact OC and MC-NC specimens. Reconstituted NC specimens tested to reduce the complexity of interpretation clearly identified the role of suppressed dilative tendencies to contribute to the observed reduction in cyclic resistance of the nonplastic to plastic silts evaluated. Specific conclusions of this investigation include:
• Specimens exhibited a reduction in cyclic resistance with increases in σ 0 vc , despite the accompanying increase in density (i.e., reduction in void ratio).
• The reduction in cyclic resistance of intact specimens is attributed to the dominant effects of yielding of the natural soil fabric, reduction in OCR, and suppression of dilation owing to nonparallel normal consolidation and critical state lines. These effects overshadowed the beneficial effect of increased density. • The reduction in cyclic resistance of the uniformly prepared, reconstituted NC specimens was associated solely with the suppression of dilative tendencies as σ 0 vc increased. • The overburden correction factor, K σ , depends on PI with a greater reduction with a σ 0 vc for moderately plastic silts relative to nonplastic to low-plasticity silts, highlighting the role of compressibility on the cyclic resistance of silt. • The K σ developed for reconstituted NC specimens may be unconservative due to the role of increased density (i.e., associated with increased σ 0 vc ) on cyclic resistance. • In contrast, the K σ developed in this study may be conservative for the intact specimens due to additional factors that contribute to the reduction in cyclic resistance, such as yielding of the soil fabric associated with exceedance of the preconsolidation stress. The representativeness of K σ depends on whether significant changes in σ 0 vc are anticipated following construction activity which might result in normally consolidated conditions.
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