Application of MLR Procedure for Prediction of Liquefaction-Induced Lateral Spread Displacement

For a thick liquefiable layer extending more than 1H below the channel (Fig. 7), the shear zone generated by lateral spread would form within the liquefiable layer and near the elevation of the toe of the free face and would not extend much below the bottom of the channel. That shear zone would lie well above and be nondamaging to a pipe buried 1H below the channel. The reasons for a shallow shear-zone are (1) shear zones follow paths of least resistance; in this instance, a nearly horizontal shear path that may curve slightly upward into the base of the channel would encounter less shear resistance than a deeper-seated shear zone. (2) Collapse of loose granular structures within the liquefying layer would generate upward flow of water into the shear zone, further reducing shear resistance, especially if the liquefiable layer were overlain by soil with a lower permeability. (3) If granular soil within the shear zone is slightly to moderately dilative, a common condition, dilation during cyclic shear would suck water into the zone from deeper layers, further reducing shear resistance.

For a liquefiable layer that lies deeper than 2H below ground surface or 1H below the low point of the channel (1H of nonliquefiable soil over the pipe) and channel widths less than about 4H (Fig. 8), the cover soil should have adequate strength to buttress the channel against lateral spread. In applying this criterion, however, the strength of the cover soil should be verified through penetration resistance or laboratory testing.

Alluvial and fluvial deposits with granular layers less than 0.3 m thick are seldom continuous or without undulation over a sufficient aerial extent to generate lateral spread. Predictions based on one or two boreholes with an assumption of continuous layers often lead to overpredicted displacements due to layers of discontinuities.

Accurate SPT N-values can only be assured in layers 1 m or thicker.

Accurate CPT ${\mathrm{q}}_{\mathrm{c}}$ can only be assured in layers 0.3 m or thicker.

The MLR procedure relies on SPT to define the penetration resistance of soil layers and on laboratory index testing to define grain-size properties. The only direct use of SPT $N$-values is to define the thickness parameter ${\mathrm{T}}_{15}$. (The influence of blow-count distribution within ${\mathrm{T}}_{15}$ is discussed later.) The MLR procedure is robust, in that it was regressed and verified from field measurements and laboratory index testing at sites of more than 400 measured lateral spread displacement vectors. These sites incorporate a wide variety of geotechnical properties (layer thicknesses and extents, grain sizes, and textures); geometric features (slopes and free-face ratios); and seismic factors (earthquake magnitudes and source distances).

The semiempirical procedure of Zhang et al. (2004) relies on CPT data to estimate the factor of safety against liquefaction, SBT, and lateral displacement index (LDI). These soil parameters, along with geometric parameters (slope and free-face ratio) and seismic parameters [magnitude and peak ground acceleration (PGA)], are used to predict horizontal displacement. As noted, that procedure was verified by comparing predicted displacements against measured displacements for 13 lateral spread sites underlain by layers of sand, silty sand, and sandy silt thicker than 0.6 m. With further research and development, the MLR and Zhang et al. (2004) procedures would likely gain compatibility over a broader range of soil, geometric, and seismic conditions.

One major difference between the MLR procedure and the Zhang et al. (2004) procedure is the influence of fines content on predicted displacement. In the MLR procedure, grain-size properties (${\mathrm{F}}_{15}$ and $\mathrm{D}{50}_{15}$) enter the regression as independent variables and both are statistically significant. Thus, the influences of both grain-size parameters on predicted displacement can be directly determined. For example, doubling the fines content from, say, 15 to 30%, while holding all other parameters constant, decreases predicted displacements by about a factor of 2; doubling the fines content again from 30 to 60% decreases predicted displacements by about a factor of 7. Thus, the MLR procedure is very sensitive to fines content. Fines content enters the Zhang et al. procedure indirectly through equivalent clean sand normalized CPT penetration resistance ${({\mathrm{q}}_{\mathrm{c}1\mathrm{N}})}_{\mathrm{cs}}$. However, ${({\mathrm{q}}_{\mathrm{c}1\mathrm{N}})}_{\mathrm{cs}}$ does not vary with fines content for fines content greater than 35%. ${({\mathrm{q}}_{\mathrm{c}1\mathrm{N}})}_{\mathrm{cs}}$ is used for the calculation of both the factor of safety against liquefaction and the predicted horizontal displacement. Thus, the influence of fines content on lateral displacement is hidden, but appears to have much less influence on predicted displacement than in MLR, particularly for fines content greater than 35%. For example, at the BYU test site, about 30 cm of lateral displacement was calculated to occur in sandy silt and silty sand layers below 9 m using the Zhang et al. (2004) procedure with corrections applied (Fig. 11), whereas, with the MLR procedure, zero displacement was predicted, largely because of fines content greater than 55%. As noted above, most of the CPT-based displacement came from the deformation of fine-grained layers, whereas, with the MLR procedure, fines content in the fine-grained sediments were too high to allow lateral displacement (Table 1).

For this paper, I reexamined fines contents and mean grain-size bounds for the MLR procedure and noted an error in the plot of these parameters by Youd et al. (2002), which is reproduced in Fig. 12. The error occurred in extracting data from logs from four boreholes drilled at the River Park site following the 1979 Imperial Valley earthquake ($\mathrm{M}=6.6$). Those borings (Bennett et al. 1981) were located within nearly flat pastureland and an adjacent playground area. The flat land was littered with sand boils, but where there were no visible ground fissures or other evidence of lateral ground displacement. When fines content data were extracted from those four borehole logs, the fine sand fractions (0.2 to 0.06 mm) were erroneously added to the silt and clay-size particles in determining ${\mathrm{F}}_{15}$. Those sediments were rich in fine sand, leading to incorrect fines contents that ranged from 54 to 71%, whereas the actual fines contents ranged from 19 to 30% (with the sand-silt boundary adjusted to 0.074 mm). Those four points are marked with an X, indicating an incorrect point on Fig. 12. Because those four points were characterized by zero displacement, their removal from the database has little effect on the regressed equations [Eqs. (1) and (2)], so the corrected data set was not re-regressed. I also forced the limiting curves to nearly converge at a mean grain size of 0.074 mm and a fines content of 50%, a fixed point in grain-size space. With no fines contents greater than 60% from lateral spread sites in the MLR database, extrapolation of MLR to fines contents greater than 60% is not constrained by empirical data and leads to uncertain predictions. As a side note, the three lateral spread sites in the MLR dataset (three points plotted on Fig. 12 with fines contents between 50 and 60%) are all from Alaskan lateral spread localities where liquefaction occurred during the 1964 earthquake ($\mathrm{M}=9.2$). Those sites were in glacial sediments that were rich in rock flower (blocky silt-sized particles rather than irregular lenticular particles contained in most silty sediments). Thus, for common non-glacial and non-sensitive sediments, the maximum fines content at lateral spread sites was 50%, a maximum that could be applied in screening for lateral spread susceptibility.

The influence of fines content on predicted displacements using MLR was verified, in part, by a lack of lateral spread displacements at two fine-grained, but potentially liquefiable sites [by Bray and Sancio (2006) procedure] in Adapazarı, Turkey (Youd et al. 2009). At the Ḉark Canal site, an artificial channel was incised into flat terrain, underlain by fine-grained soils. The measured fines content in the softest layer beneath the west bank was 94 and 68% for the east bank. Assuming the sediments are sandlike materials [by the Boulanger and Idriss (2006) classification] and extrapolating the MLR to fines contents greater than 60%, the predicted displacements are zero at the east bank and 0.7 m (an overprediction) at the west bank. Actual displacement at the site was too small to detect or essentially zero (Youd et al. 2009). The second site, Cumhuriyet Avenue, has 0.3% ground slope and a fines content of 73% in the softest and most liquefiable layer. Again, assuming sandlike sediment and extrapolation of the MLR procedure, a predicted displacement of 0.14 m (an overprediction) was calculated. Lateral displacements at that site were also too small to detect or essentially zero.

Criticism: The MLR model is purely empirical and is not based on soil mechanics theory.

Answer: I agree that the MLR model is empirical, but it contains some theoretical considerations. For example, the magnitude (M) versus source distance (R) relationship in the model is patterned after the M versus R relationship developed by Joyner and Boore (1993) for the attenuation of PGA. The empirical MLR model was regressed from 400 measured lateral displacement vectors with attendant measured or carefully estimated values for each independent variable in the model [Eqs. (1) and (2)]. Rigorous statistical procedures were applied in these analyses. The model was verified by the same 400 measured displacements (Fig. 5), providing verification that the model yields valid displacement predictions within the parametric limits and degree of accuracy stated with the model (Bartlett and Youd 1995; Youd et al. 2002; and this paper). Thus, MLR is based on ground truth against which other models, including theoretical models, should be tested.

Criticism: M and R are not ground motion values, such as PGA, CAV, or Arias intensity.

Answer: M is applied in MLR, similarly to its application in the simplified liquefaction evaluation procedure (Youd et al. 2001). In both instances, M is used as a rough proxy for ground shaking duration. The correlation between M and duration is not perfect and is a source for some of the scatter in the predicted versus measured displacements (Fig. 5). I also agree that R is not a ground motion parameter; however, several attenuation relationships for estimating PGA, such as Joyner and Boore (1993), are based on M and R. There is only one site in the MLR database [Wildlife (Youd and Holzer 1994)] where ground motions were measured on-site as liquefaction as ground displacement occurred; PGA for all other sites were estimated (by others) from empirical ground motion relationships, most of which were based on M and R. In formulating the MLR model, we statistically tested both PGA and R as possible independent variables. R has a higher statistical significance (produced more certain estimates of ${\mathrm{D}}_{\mathrm{H}}$) than PGA; thus, R was added as an independent variable to the MLR model.

Criticism: (a) The MLR model uses ${\mathrm{T}}_{15}$, which is not a fundamental soil property; (b) a ${\mathrm{T}}_{15}$ with, say, ${(N_1)}_{60}=3$, should yield larger displacements than a ${\mathrm{T}}_{15}$ with ${(N_1)}_{60}=14$.

Answers: (a) The thickness of the deformable layer, ${\mathrm{T}}_{15}$, is a fundamental geometrical property if not a fundamental soil property. Theoretically, ground displacement is equal to average shear strain multiplied by the thickness of the deformable layer; ${\mathrm{T}}_{15}$ is an estimate of that thickness. Thickness is an important factor in other procedures, such as the prediction of ground settlement. ${\mathrm{T}}_{15}$ has high statistical significance and hence is an independent variable in the MLR model. (b) I agree that the distribution of blow counts within ${\mathrm{T}}_{15}$ should be an important factor. However, Bartlett and Youd (1995) tested several possible independent variables as measures of the blow-count distribution, including the lowest ${({\mathrm{N}}_1)}_{60}$ in ${\mathrm{T}}_{15}$, average ${({\mathrm{N}}_1)}_{60}$ in ${\mathrm{T}}_{15}$, lowest calculated factor of safety against liquefaction in ${\mathrm{T}}_{15}$, and so on. None of those potential indices of the blow-count distribution is statistically significant and thus they are not included in the MLR model. The reason for that insignificance is not because the blow-count distribution is unimportant, but rather because there is insignificant variation of the blow-count distribution within naturally occurring liquefiable layers compiled in the MLR database. Nature has not deposited liquefiable layers with uniform blow counts of, say, 3 or 14.

Criticism: Continual modifications of MLR indicate that the procedure is unstable and should be discarded.

Answer: Empirical procedures, such as MLR, are based on compilations of real data. When new data become available or corrections to a model are needed, new data are added to the database or the corrected model and the database is re-regressed to generate an improved empirical model. Such improvements are common and are a strength of the procedure, not a weakness. For example, during the last 30 years, ground motion data have regularly been added to the ground motion database, models have been adjusted, and the data have been re-regressed to develop improved empirical ground motion prediction equations (GMPEs).

Criticism: MLR appears to have performed poorly in predicting lateral spread displacements generated by the February 22, 2011, earthquake in Christchurch, New Zealand ($\mathrm{M}=6.2$).

Answer: This criticism apparently stems from analyses and conclusions reported in a MS thesis by Deterling (2015). In that study, lateral displacements were predicted using several proposed procedures, including MLR and that of Zhang et al. (2004). Predicted displacements were then compared with measured displacements developed from analyses of satellite imagery and lidar surveys. Deterling, however, did not apply MLR in accordance with the procedures published by Youd et al. (2002); rather, several spurious modifications were introduced to facilitate computation. I note here that MLR was formulated for site-specific displacement predictions only. Correct application requires (1) an ${({\mathrm{N}}_1)}_{60}$ profile from the site in question compiled from site SPT data; (2) fines contents and mean grain sizes determined from laboratory tests on soil samples taken from the ${\mathrm{T}}_{15}$ layer; and (3) slopes and free face heights measured at the site or carefully estimated from reliable topographic maps or data. Apparently, borehole logs with SPT and grain-size information are available in the Christchurch geotechnical databases, but those data were not considered. ${\mathrm{T}}_{15}$ was calculated from Christchurch CPT logs using an unreferenced rough correlation between ${({\mathrm{N}}_1)}_{60}$ and ${\mathrm{q}}_{\mathrm{c}1\mathrm{N}}$. Fines contents (${\mathrm{F}}_{15}$) and mean grain sizes ($\mathrm{D}{50}_{15}$) were conjectured from a plot of fines contents versus mean grain sizes developed from the MLR database and published with the MLR procedure (Youd et al. 2002), revised herein in Fig. 12. Those grain-size estimates were apparently applied uniformly across the Christchurch area. Deterling apparently applied only the free-face model [Eq. (1)] to generate MLR predicted displacements, leading to statements such as, “From Fig. 5.10, it is clear that most of the points with W values less than 1% (i.e., $\mathrm{L}>100\mathrm{H}$) predict very small displacements although displacements as large as 0.9 m were observed.” Youd et al. (2002) specify that both the free-face model [Eq. (1)] and the ground-slope model [Eq. (2)] should be applied and the larger of the two predicted displacements applied for engineering design. However, for $\mathrm{W}>5\%$, the free-face model nearly always controls, predicted displacements and for $\mathrm{W}<1\%$, the ground-slope model nearly always controls. If the ground-slope model was not applied as specified, which appears to be the case, the conclusion that MLR greatly underpredicts displacement for $\mathrm{W}<1\%$ is clearly erroneous. Nearly all of Deterling’s predicted MLR displacements are much smaller than observed displacements. Consistent underprediction suggests that the R-values applied were too large. Deterling (2015) defines R as “the distance to the fault,” whereas Youd et al. (2002) define R as “the distance to the seismic energy source.” Seismic source zones for smaller magnitude earthquakes ($\mathrm{M}<6.4$) commonly do not coincide with a mapped fault. Consequently, it appears that R-values applied by Deterling were erroneously large. In summary, because Deterling (2015) did not correctly apply the MLR procedure, conclusions that MLR performed poorly and consistently underpredicted measured lateral displacements in Christchurch are without merit and must be disregarded.

Criticism: Why have some large and influential agencies, such as CalTrans, abandoned use of MLR?

Answer: Companies and agencies select lateral spread evaluation procedures that they feel best meet their needs. I obviously disagree with policies that discourage or prohibit use of MLR. When applied within stated limits, MLR is easy to apply, robust, and widely used in engineering practice, and yields valid predictions. Thus, I know of no rational reason to abandon MLR. One objection, reportedly from CalTrans, is that MLR overpredicts displacement. Perhaps that may be true for input values outside of the ranges constrained by data, for example, applying an $\mathrm{R}<0.5\mathrm{km}$, but the data plotted in Fig. 5 indicate that future lateral displacements are very likely to be within a factor of 2 of predicted displacements when the procedure is applied correctly. Also, if the predicted displacements are greater than 6 m, Youd et al. (2002) state, “predicted displacements greater than 6 m are not well constrained by case history data and only indicate that large displacements are possible.” Finally, some within CalTrans seem to have bias that favors procedures developed at the Pacific Earthquake Engineering Research Center (PEER).

Criticism: MLR appears inadequate for use with large-magnitude earthquakes ($\mathrm{M}>8$).

Answer: Youd et al. (2002) specify that MLR should not be applied for earthquakes with magnitudes greater than 8. Seismic source zones become very large for such earthquakes, particularly subduction zone earthquakes, and defining a source distance, R, becomes problematical. More research is needed to resolve this issue.

For mitigation of lateral spread hazard to buried pipelines at stream crossings, areas commonly susceptible to liquefaction and lateral spread, I recommend the following criteria for mitigation of lateral spread hazard: For incised channels in relatively flat terrain, burial of the pipe to a depth at least twice the bank height (2H) below stream banks or at least 1H beneath the low point in the channel should protect the pipe against damage from lateral spread. My reasoning for these burial depths are as follows:

The logic developed in Conclusion 1b for deep liquefiable layers could also be applied for mitigation of damage to foundations supporting bridges crossing streams; however, the adequacy of the strength of nonliquefiable soil beneath the channel must be confirmed by penetration resistance or laboratory testing. This confirmation is commonly hindered by lack of borehole or penetration data from within the channel due to access difficulties.

The thinnest documented liquefiable layers in which lateral spread has developed is 1.0 m for the Youd et al. (2002) database and 0.6 m for the case histories applied by Zhang et al. (2004) to verify their procedure. Extrapolation to thinner layers adds uncertainty to predicted displacements and a tendency to overpredict displacement.

Similarly, only nonplastic granular sediments (gravelly sands through sandy silts) are contained in liquefiable layers compiled in the MLR database and in the liquefiable layers used to confirm the Zhang et al. (2004) procedure. Inclusion of finer-grained or more plastic soils in ${\mathrm{T}}_{15}$ adds uncertainty to predictions and a tendency to overpredict.

The MLR procedure is based on regression of compiled SPT and laboratory test data, while the Zhang et al. (2004) procedure is based on CPT data. These procedures should give comparable results for granular materials (sands through sandy silts) thicker than 0.6 m. Further research could increase the range of compatibility between the two procedures.

For a project in which insufficient SPT data were available, my colleagues and I used CPT data to calculate state parameter $\psi$ profiles and then applied the criterion that, for $\psi <–0.08$, dune sands beneath the site would be sufficiently dilative to prevent development of lateral spread. We then summed the thicknesses sand layers with $\psi >–0.08$ to estimate ${\mathrm{T}}_{15}$ for use in MLR. Those predicted displacements were then applied for engineering design.