# LEAP-UCD-2017 Comparison of Centrifuge Test Results

## Abstract

This paper compares experimental results from every facility for LEAP-UCD-2017. The specified experiment consisted of a submerged medium-dense clean sand with a 5-degree slope subjected to 1 Hz ramped sine wave base motion in a rigid container. The ground motions and soil density were intentionally varied from experiment to experiment in hopes of defining the slope of the relational trend between response (e.g., displacement, pore pressure), intensity of shaking, and density or relative density. This paper is also intended to serve as a useful starting point for overview of the experimental results and to help others find specific experiments if they want to select a subset for further analysis. The results of the experiments show significant differences between each other, but the responses show a significant correlation, *R*^{2} ~ 0.7–0.8, to the known variation of the input parameters.

## Keywords

Liquefaction Lateral spreading Centrifuge model test Validation LEAP Round robin test Reproducibility## 4.1 Introduction

Twenty-four separate model tests were conducted at nine different centrifuge facilities for this LEAP exercise. The first goal of this paper is to provide an overview of all the experimental data from the 24 experiments. This overview will allow readers to quickly scan through the key time series data and various performance measures to evaluate the extent of liquefaction in the different experiments. A second goal of this paper is to demonstrate that the experiments are consistent with each other and that they define a response function or trend between key input parameters and key liquefaction response parameters. From the comparison of the results to empirical response functions, it is possible to obtain meaningful assessments of the sensitivity of the results to variations of input parameters and to assess the variability of the results in terms of their deviation from the response functions.

El Ghoraiby et al. (2017) and Para Bastidas et al. (2017) report results of laboratory testing including cyclic triaxial and DSS tests. Permeability tests using water as the pore fluid as reported by El Ghoraiby et al. (2017) were fit with a linear regression line through data over the range of *e* = 0.5–0.75:

As the pore fluid viscosity was scaled in the centrifuge tests, this measured permeability corresponds to the prototype permeability.

*L*

^{∗}=

*L*

_{model}/

*L*

_{prototype}) varied from 1/50 to 1/23, and the radii varied between 1 and 5 m. The models were all tested in a rigid model container to avoid the uncertainties associated with more complex flexible model containers. To control side boundary effects, Kutter et al. (2019) recommended 0.45 as a minimum desired width/length ratio of the model container; the actual width/length ratios are summarized in Table 4.1.

Test facilities, length scale factor, shaking direction, radius of centrifuge, and model container length/width ratio for LEAP-UCD-2017

Centrifuge facility institution |
| Shaking direction | Radius (m) | Container length/width |
---|---|---|---|---|

Cambridge University, UK | 1/40 | Tangential | 3.56 | 0.45 |

Ehime University, Japan | 1/40 | Parallel to axis | 1.184 | 0.24 |

IFSTTAR, France | 1/50 | Parallel to axis | 5.063 | 0.5 |

KAIST, Rep. of Korea | 1/40 | Parallel to axis | 5 | 0.45 |

Kyoto University, Japan | 1/44.4 | Tangential | 2.5 | 0.32 |

National Central Univ., Taiwan | 1/26 | Parallel to axis | 2.716 | 0.45 |

Rensselaer Poly. Inst., USA | 1/23 | Parallel to axis | 2.7 | 0.42 |

Univ. of California, Davis, USA | 1/43.75 | Tangential | 1.094 | 0.63 |

Zhejiang University, China | 1/30 | Parallel to axis | 4.315 | 0.59 |

## 4.2 Densities and Penetration Resistances

Each experimental facility was given suggestions regarding target densities and target input motions for the first shaking event; each site was given some latitude in deciding what input motions to apply in subsequent shaking events, if any. The details of results for all the shaking events should be described in separate papers produced by each experimental facility. The density of the sand in each model was characterized by mass and volume measurements of each model. However, it is deceptively difficult to directly measure the mass and volume to the desired level of accuracy. Small errors due to sand mounding near the container side walls during pluviation, imperfect container rectangularity, and uneven (rough) surfaces at the base and top of the sand deposit, in combination with resolution and accuracy of the load cells used to measure the weight of the sand and the empty container, contribute to the uncertainty of the mass and volume measurement. Also note that the relative density is very sensitive to density; at *D*_{r} *=* 60%, a 1% error in density results in a 6% error in relative density.

*g*

^{∗}= 1/

*L*

^{∗}) for a penetration test and then stopped for removal of the penetrometer. Then the centrifuge was spun up to the test acceleration to apply the model earthquake. Subsequent penetration tests were done at different locations in subsequent spins. Figure 4.2 shows cone penetration tests for every model test. Blank figures indicate unsuccessful penetration tests.

Since the same cone design and the same sand were used at different centrifuge facilities, the results should be comparable. However, the length scale factor in the centrifuge tests varies between 1/23 and 1/50, so the prototype diameter of the cone varies between 138 and 300 mm. At mid depth of the 4 m-thick prototype layer, the depth/diameter ratio varied between 6.7 and 14.5. Bolton et al. (1999) indicated that for dense specimens (*D*_{r}~80%) the normalized penetration distance was not sensitive to depth if depth/diameter is greater than about 10. For LEAP, we may expect minor reductions of normalized penetration resistance for cases where depth/diameter < 10. Carey et al. (2019a) observed about 5–10% greater penetration resistance for low g tests (large depth/diameter) compared to high g tests.

Bolton et al. (1999) also identified an effect of the container width on the penetration resistance. Narrow containers produced about 15–20% increase in penetration resistance. In addition to producing an increased penetration resistance for a given density, wall friction from narrow containers would also restrict liquefaction deformations for a given density; these errors are expected to counteract each other to some extent. Effects of container width on penetration resistance were not accounted for in the correlations presented later in this paper.

*ρ*

_{d}= a(

*q*

_{c}) + b, with a = 35.1 kg/m

^{3}/MPa and b = 1553 kg/m

^{3}. As indicated by the arrows in the figure, one model was reported to have a density based on mass and volume measurements of 1623 kg/m

^{3}and a

*q*

_{c}(2 m) = 2.37 MPa. At the intersection of

*q*

_{c}(2 m) = 2.37 MPa and the regression line one finds that the dry density from

*q*

_{c}is ρ

_{d}(

*q*

_{c}(2 m)) = 1636 kg/m

^{3}.

## 4.3 Base Input Motions in First Destructive Motion

_{1Hz}), the PGA of the high-frequency component, or traditional intensity measures such as the PGV, the Arias intensity (

*I*

_{a}), or cumulative absolute velocity (CAV

_{5}). For the purposes of organizing and comparing the LEAP experiments, another parameter, PGA

_{eff}, was found to be useful:

_{HF}is determined from the peak of the high-frequency component that occurs within 1 s of the peak of the PGA

_{1Hz}. (Note that the larger peak of the high-frequency component at about 17.7 s in Fig. 4.4 was not used because it was not near the PGA of the 1 Hz component.)

Table 4.2b summarizes the intensity measures for each of the first destructive motions for each experiment. It should be emphasized that many of the LEAP experiments included a total of two or three destructive motions. This paper focuses on results from the first motion only. Papers by each experiment facility explain the results from subsequent destructive motions.

Figure 4.5 shows that the base motion for test UCD2 contains several large-amplitude sharp spikes, IFSTTAR1 has more continuous high-frequency components, and CU1, CU2, and RPI2 contain significant 3 Hz components superimposed on the motion. RPI2 motion was intentionally varied to allow emulation of the high-frequency component observed in the CU experiments. The first few and last few cycles of the motion produced by the Ehime shaker are lower frequency than 1 Hz; this is a nuance of their mechanical shaker. The long period components did not much affect the PGA but did affect the cumulative absolute velocity and Arias intensity; Ehime motions were just below the median in terms of PGA_{eff}, but well above the median in terms of CAV_{5} and *I*_{a}. From the highlighting in Table 4.2b, it is apparent that in most cases the intensity measures are highly correlated to each other; two apparent exceptions include the aforementioned effect of low-frequency components for the Ehime motions and weak correlation between PGA_{HF} to the intensity measures other than PGA.

## 4.4 Acceleration Response of Soil Layers in First Destructive Motion

Three of the experiments (KyU1, ZJU3, and UCD1) show almost uniform acceleration behavior—in other words, the models behaved like a rigid body—a clear indication that liquefaction did not occur in these experiments. All of the other experiments showed significant evidence of nonlinear behavior and evidence of liquefaction. The sharp downward spikes, most significant in AH3 and AH4, we call “dilation spikes” because they are caused by the sudden increase in effective stress and hence increase in stiffness associated with negative pore water pressures produced by the tendency of the sand to dilate in response to the imposition of large shear strains. The spikes are larger in the downward direction because this corresponds to shearing in the downslope direction; strains tend to accumulate in the downslope direction.

Some aspects of the recorded data are obviously influenced by faulty instrumentation. For example, the data from AH3 and AH4 in UCD1 show almost uniform behavior, similar to the base acceleration, indicating very little deformation of the soil; therefore, it is clear that the offset seen in AH1 and to a lesser extent AH2 are anomalous and probably due to an instrumentation issue. AH1 is not reported for UCD3, and AH1 is not reported for IFSTTAR2. AH1 appears to be nonfunctional (flat) in CU1.

Based upon the response recorded by the upper accelerometers (AH3 and AH4), CU1 shows the most severe isolation of the ground surface motion associated with liquefaction; towards the end of the earthquake record, the surface motion is almost flat. Other surface records that show severe spikes or isolation are Kaist2, ZJU2, NCU1, NCU2, NCU3, CU2, IFSTTAR2, and Ehime1. Consistent with this, all of these events also produced permanent displacements larger than 250 mm (see Table 4.2c).

## 4.5 Displacement Response of the Soil Layers in First Destructive Motion

It is difficult to directly measure the potentially large multidirectional deformations of submerged slopes by conventional contact sensors. A reliable alternative approach for measuring permanent displacements is by surveying the location of the surface markers before and after liquefaction as described in the specifications for LEAP-UCD-2017 (Kutter et al. 2019). The surveys may be accomplished by direct measurement using rulers and calipers or by photography or surface scanners. High-speed photography at some sites allowed not only the determination of the residual deformations but also dynamic measurement of displacements during shaking. Dynamic displacements from photography are presented in the papers submitted by the experimenters from each site.

*v*

_{rel}is the dynamic component of the relative velocity from single integration of the difference between AH4 and the base acceleration. This function produces a reasonably shaped ramp that should be representative of the accumulation of the permanent displacements. The IPRV ramp function is then scaled to make it agree with the displacement determined from surface marker surveys. The time series labeled “combined” is obtained by adding the scaled IPRV ramp to the dynamic component of the displacement. Carey et al. (2018a, 2019b) independently determined the displacement of the surface markers as a function of time using the high-speed cameras and demonstrated that superposition of the dynamic displacements from accelerometers on the IPRV ramp produces a reasonable approximation of the displacement time series. From Fig. 4.10, the cyclic components of the displacements are negligible for tests UCD1, ZJU3, and KyU1, as would be expected considering that these models did not liquefy. The fact that KyU1 showed a permanent displacement but no cyclic displacement may be explained by the earlier observation that there may have been a systematic error in the surface marker measurement for KyU1. The cyclic displacements were the largest for test NCU1. The IPRV and the amplitude of the cyclic component of relative displacements are considered to be meaningful and reliably quantified measures of the performance of the models that would not be affected by errors in surface marker measurements; therefore, these performance measures are listed in Table 4.2c.

## 4.6 Pore Pressure Response of Soil Layers in First Destructive Motion

^{3}. The tick marks on the side of each subplot correspond to 10 kPa. The last trace in each subplot shows results from P10, a sensor in the bottom corner of the containers. It is interesting to note that, especially near the beginning of shaking, the cyclic pore pressures at P10 tend to be greater than those in the central array, possibly in response to the cyclic total stress oscillations near the wall.

Consistent with the small cyclic relative displacements in UCD1, ZJU3, and KyU1 apparent from the accelerometer arrays, these three tests showed relatively small pore pressures throughout the layer. In UCD1 and ZJU3, the pore pressure approached the overburden of 10 kPa at P4 during shaking, but only at the peaks of the cycles, and dissipation began during shaking. For all of the other models, the pore pressures appeared to reach the effective overburden stress. The extent of liquefaction could be determined by pore pressure ratios, but small errors in the depth of the sensors could make the difference between pore pressure ratios of 100% and 90%, which is significant.

*i*~

*i*

_{crit}~ 1) is 20s in prototype scale, and the permeability of the sand is 1.5 × 10

^{−4}m/s (El Ghoraiby et al. 2017), then the volume of water expelled would be (20 s) (1.5 × 10

^{−4}m/s) = 3 mm in prototype scale. After some time a break in the dissipation curve is apparent in Fig. 4.12. Such a construction was repeated for each of the first shaking events for all 24 experiments. The duration of sustained pore pressures determined by this method is summarized in Table 4.2c.

Also apparent in Figs. 4.11 and 4.12 are large spikes of negative pore pressure that appear in many traces after liquefaction develops; these negative pore pressures are attributed to dilatancy and have been observed in many laboratory element tests as well as centrifuge tests in the past. As expected, these spikes of negative pore pressure increase the effective stress and stiffen the sand and tend to be aligned with corresponding spikes of ground acceleration. The large dilatancy spikes correspond to the arresting of downslope displacements. In some sensors for some experiments, positive spikes of pore pressure are also apparent; because effective stress in sand cannot be negative, the only mechanism for which pore pressures in a soil layer could be greater than the initial total vertical stress is if the total stress is momentarily increased by dynamic vertical accelerations. Anomalous positive pore pressures might also be recorded by sensors due to local pushing or pulling on sensor cables or other soil-sensor interactions.

## 4.7 Correlations Between Displacement, *D*_{r}, and IMs

*D*

_{r}(

*q*

_{c}(2 m))) and PGA

_{eff}for 16 of the 19 tests that provided this information. All of the available data for the 24 tests used as a data source are listed in Tables 4.2a, 4.2b, and 4.2c. In addition, the data will also be available in a spreadsheet document available in the LEAP-UCD-2017 data archive in DesignSafe (https://www.designsafe-ci.org). Three of the 19 tests were excluded from the correlations because they were thought to be “outliers.” With the outliers excluded, the coefficient of correlation

*R*

^{2}= 0.846, indicating that 84.6% of the variation between these results could be explained by the two variables PGA

_{eff}and

*D*

_{r}(

*q*

_{c}(2 m)). Kutter et al. (2018a) also presented surface fits through using the same fitting function but for all 19 points without excluding outliers. Inclusion of the outliers reduced the correlation coefficient considerably to

*R*

^{2}= 0.578.

Summary of density measures for each of the models

Test ID | Dry density from mass and volume ρ(M&V) [1] |
| Pen. Resist. at 2 m depth |
a = 35.1; b = 1553 [4] |
ρ from [4] and ρ |
---|---|---|---|---|---|

kg/m | MPa | kg/m | |||

CU1 | 1656 | 0.66 | 0.81 | 1581 | 0.38 |

CU2 | 1606 | 0.47 | 0.95 | 1586 | 0.40 |

Ehime1 | 1649 | 0.63 | 3.50 | 1676 | 0.73 |

Ehime2 | 1657 | 0.66 | 3.50 | 1676 | 0.73 |

Ehime3 | 1693 | 0.79 | 4.31 | 1704 | 0.83 |

IFSTTAR1 | 1696 | 0.80 | |||

IFSTTAR2 | 1624 | 0.56 | 1.38 | 1602 | 0.46 |

KAIST1 | 1701 | 0.82 | 3.88 | 1689 | 0.77 |

KAIST2 | 1593 | 0.42 | 1.40 | 1602 | 0.46 |

KyU1 | 1683 | 0.75 | |||

KyU2 | 1659 | 0.67 | 3.74 | 1684 | 0.76 |

KyU3 | 1637 | 0.59 | 2.88 | 1654 | 0.65 |

NCU1 | 1652 | 0.64 | 3.51 | 1676 | 0.73 |

NCU2 | 1652 | 0.64 | |||

NCU3 | 1652 | 0.64 | 2.95 | 1656 | 0.66 |

RPI1 | 1650 | 0.64 | |||

RPI2 | 1659 | 0.67 | 2.18 | 1630 | 0.56 |

RPI3 | 1623 | 0.54 | 2.37 | 1636 | 0.59 |

UCD1 | 1665 | 0.69 | 3.26 | 1667 | 0.70 |

UCD2 | 1648 | 0.63 | 2.52 | 1642 | 0.61 |

UCD3 | 1658 | 0.67 | 2.19 | 1630 | 0.56 |

ZJU1 | 1651 | 0.64 | 2.85 | 1653 | 0.65 |

ZJU2 | 1599 | 0.45 | 1.00 | 1588 | 0.41 |

ZJU3 | 1703 | 0.82 | 3.90 | 1690 | 0.78 |

Summary of ground motion intensity measures for the first destructive shake

Test ID | PGA | PGA | PGA | PGA | PGV | Cumulative abs. vel. CAV | Arias intensity |
---|---|---|---|---|---|---|---|

g | g | g | g | m/s | m/s | m | |

CU1 | 0.190 | 0.186 | 0.123 | 0.125 | 0.253 | 7.75 | 1.20 |

CU2 | 0.206 | 0.195 | 0.122 | 0.146 | 0.259 | 8.04 | 1.31 |

Ehime1 | 0.169 | 0.158 | 0.135 | 0.045 | 0.202 | 8.26 | 1.07 |

Ehime2 | 0.180 | 0.158 | 0.134 | 0.048 | 0.206 | 8.25 | 1.07 |

Ehime3 | 0.168 | 0.155 | 0.136 | 0.039 | 0.200 | 8.24 | 1.07 |

IFSTTAR1 | 0.214 | 0.165 | 0.119 | 0.106 | 0.184 | 7.44 | 0.98 |

IFSTTAR2 | 0.135 | 0.129 | 0.095 | 0.069 | 0.166 | 5.68 | 0.56 |

KAIST1 | 0.178 | 0.168 | 0.119 | 0.098 | 0.209 | 7.18 | 0.85 |

KAIST2 | 0.185 | 0.166 | 0.120 | 0.092 | 0.210 | 7.30 | 0.86 |

KyU1 | 0.071 | 0.064 | 0.047 | 0.034 | 0.084 | 2.63 | 0.13 |

KyU2 | 0.119 | 0.111 | 0.098 | 0.026 | 0.155 | 5.72 | 0.50 |

KyU3 | 0.143 | 0.133 | 0.116 | 0.033 | 0.185 | 6.74 | 0.72 |

NCU1 | 0.292 | 0.237 | 0.180 | 0.114 | 0.291 | 8.93 | 1.73 |

NCU2 | 0.224 | 0.202 | 0.151 | 0.101 | 0.247 | 7.43 | 1.20 |

NCU3 | 0.217 | 0.176 | 0.125 | 0.102 | 0.205 | 5.84 | 0.83 |

RPI1 | 0.150 | 0.146 | 0.135 | 0.021 | 0.221 | 7.02 | 0.82 |

RPI2 | 0.144 | 0.148 | 0.106 | 0.085 | 0.208 | 6.67 | 0.74 |

RPI3 | 0.170 | 0.162 | 0.144 | 0.036 | 0.233 | 7.25 | 0.92 |

UCD1 | 0.165 | 0.149 | 0.119 | 0.060 | 0.197 | 6.28 | 0.64 |

UCD2 | 0.339 | 0.210 | 0.149 | 0.122 | 0.249 | 8.25 | 1.13 |

UCD3 | 0.192 | 0.183 | 0.134 | 0.099 | 0.228 | 7.31 | 0.90 |

ZJU1 | 0.167 | 0.134 | 0.094 | 0.080 | 0.151 | 5.12 | 0.49 |

ZJU2 | 0.191 | 0.148 | 0.099 | 0.098 | 0.160 | 5.33 | 0.54 |

ZJU3 | 0.135 | 0.111 | 0.078 | 0.065 | 0.126 | 4.33 | 0.33 |

Average | 0.181 | 0.158 | 0.120 | 0.077 | 0.201 | 6.791 | 0.859 |

Performance measures for each of the experiments during the first destructive motion

Test ID | Integrated pos. rel. vel. | Peak dyn. rel. disp. | depth of liq., zliq | Duration of lique-faction at P4 | Ux mean of all markers | Ux St. Dev. of all markers | Ux mean of 8 markers | Ux St. Dev. of 8 markers | Ux mean of 2 markers | Ux St. Dev. of 2 markers |
---|---|---|---|---|---|---|---|---|---|---|

m | m | m | s | mm | mm | Mm | mm | mm | mm | |

CU1 | 5.80 | 0.066 | 3 | 58 | 359 | 77 | 403 | 56 | 440 | 57 |

CU2 | 5.52 | 0.056 | 3 | 28 | 359 | 96 | 428 | 65 | 490 | 42 |

Ehime1 | 5.42 | 0.047 | 2 | 0 | -- | -- | -- | -- | -- | -- |

Ehime2 | 7.18 | 0.061 | 1 | 0 | 89 | 48 | 103 | 39 | 100 | 28 |

Ehime3 | 9.63 | 0.055 | 0 | 0 | 56 | 37 | 65 | 37 | 60 | 28 |

IFSTTAR1 | 3.22 | 0.032 | 1 | 0 | 21 | 62 | 25 | 46 | 50 | 71 |

IFSTTAR2 | 5.66 | -- | 2 | 31 | 272 | 160 | 297 | 227 | 438 | 53 |

KAIST1 | 3.05 | 0.037 | 1 | 2 | 1 | 3 | 0 | 4 | 2 | 2 |

KAIST2 | 4.58 | 0.063 | 1 | 20 | 0 | 57 | 0 | 37 | 0 | 28 |

KyU1 | 0.20 | 0.001 | 0 | 0 | 64 | 216 | 117 | 283 | 377 | 283 |

KyU2 | 4.61 | 0.040 | 3 | 20 | 108 | 44 | 141 | 43 | 150 | 61 |

KyU3 | 4.84 | 0.044 | 1 | 12 | 12 | 110 | 11 | 62 | 0 | 63 |

NCU1 | 8.73 | 0.113 | 2 | 13 | 197 | 70 | 248 | 40 | 287 | 1 |

NCU2 | 6.64 | 0.079 | 1 | 11 | 188 | 83 | 239 | 48 | 256 | 0 |

NCU3 | 4.61 | 0.054 | 2 | 14 | 233 | 79 | 270 | 59 | 279 | 56 |

RPI1 | 5.28 | 0.045 | 2 | 16 | -- | -- | 101 | 25 | 94 | 11 |

RPI2 | 5.73 | 0.061 | 2 | 14 | -- | -- | 128 | 22 | 134 | 12 |

RPI3 | 7.16 | 0.072 | 2 | 32 | -- | -- | 123 | 18 | 126 | 10 |

UCD1 | 0.63 | 0.004 | 0 | 0 | 12 | 30 | 0 | 28 | 0 | 28 |

UCD2 | 4.48 | 0.047 | 2 | 25 | 109 | 48 | 131 | 25 | 125 | 9 |

UCD3 | 5.54 | 0.051 | 2 | 19 | 116 | 80 | 134 | 35 | 160 | 3 |

ZJU1 | 4.39 | 0.035 | 1 | 18 | 133 | 56 | 150 | 53 | 135 | 21 |

ZJU2 | 5.41 | 0.046 | 1 | 25 | 221 | 86 | 283 | 33 | 263 | 53 |

ZJU3 | 0.40 | 0.002 | 0 | 0 | 29 | 42 | 26 | 16 | 30 | 21 |

_{liq}

*=*CRR/CSR is the factor of safety with respect to triggering of liquefaction and

*F*

_{α}is a function of relative density. Note that Eq. 4.4 is not applicable if FS

_{liq}is greater than 2 and would return a strain potential,

*γ*

_{max}, of zero for FS

_{liq}= 2. The curve fit equation used for displacement for this study was:

_{liq}and the b1 term corresponds to the constant, 2, in Eq. 4.4. Note that 〈

*x*〉 =

*x*if

*x*> 0; 〈

*x*〉 = 0 if

*x*< 0 . However, for the present study, coefficients b

_{1}, b

_{2}, n1, n2, n3, and n4 are determined by nonlinear regression. Inclusion of the term in Macauley brackets, with the restriction that 0.125 <

*D*

_{r}< 1, produces a smooth function and prevents this function from producing not-physically realistic uphill residual displacements. As an example, the curve fit parameters determined using a nonlinear regression algorithm in Matlab that produced the surface plotted in Fig. 4.13 are b

_{1}= 12, b

_{2}= 0.0456, n1 = 4.57, n2 = 1.157, n3 = 1, and n4 = 2.

*D*

_{r}(Mass & Vol.) in place of

*D*

_{r}(

*q*

_{c}(2 m)) in case 3 and using PGA instead of PGA

_{eff}as a shaking intensity measure in case 4. The

*R*

^{2}values summarized in Table 4.3 suggest that PGA

_{eff}is a better indicator of shaking intensity than PGA and that

*D*

_{r}(

*q*

_{c}(2 m)) is a better indicator of liquefaction resistance than is

*D*

_{r}(Mass & Vol.) for the present dataset. The mean density and shaking intensity measure (IM) of the data points analyzed are summarized in the last column of Table 4.3 along with the evaluation of the surface function at these means.

Results of nonlinear regression between displacement, relative density, and motion intensity for the first destructive motion in LEAP-UCD-2017

Case/(# pars) | Motion intensity measure (IM) (g) | Basis to determine | Data points used/excluded outliers | Correlation coef. | Sensitivity to | Sensitivity to IM at mean (mm/g) | Mean |
---|---|---|---|---|---|---|---|

1/6 | PGA |
| 16/3 | 0.846 | −708 | 1356 | 0.62, 0.165, 94 |

2/6 | PGA |
| 19/0 | 0.578 | −645 | 2125 | 0.62, 0.161, 131 |

3/6 | PGA | Mass & Vol. | 19/4 | 0.603 | −492 | 1804 | 0.65, 0.166, 131 |

4/6 | PGA |
| 19/0 | 0.485 | −829 | 611 | 0.62, 0.185, 154 |

5/6 | PGA |
| 17/3 | 0.718 | −568 | 2339 | 0.60, 0.163, 106 |

6/4 | PGA |
| 17/3 | 0.756 | −598 | 2681 | 0.60, 0.163, 106 |

Case 5 shows a later analysis done after one more data point from test IFSTTAR2 became available. IFSTTAR2 produced relatively large deformations compared to the rest of the dataset; hence the *R*^{2} value decreased from 0.846 to 0.718 by including this one point. Note however that evaluation of the curve fit at the median was not affected much by this point, and the computed sensitivities were not drastically changed by the addition of this data point. For the five cases summarized, the mean *D*_{r} varied from 0.61 to 0.65; the mean IM varied from 0.161 to 0.185 g, and the surface fit at the median point varied from 94 to 154 mm. The table also summarizes the sensitivity of the displacement to variation of the *D*_{r} and IM. The sensitivity of displacement to *D*_{r}(*q*_{c}(2 m)) varied by a factor of 1.29 (between −645 and −829 mm), and the sensitivity to PGA_{eff} varied by a factor of 1.57 (between 1356 and 2125 mm/g) for the various cases. While there is variability in the sensitivities obtained by these methods, it is believed that the sensitivities are consistent enough to claim that the results are statistically significant. The compilation of sufficient data from centrifuge tests to enable quantification of the mean, sensitivities, and correlation is unprecedented.

_{eff}vertical axis, the CSR values were divided by 1.3 for reasons explained below.

*R*

^{2}= 0.753. The result (b1 = 5.985, b2 = 1.416, n1 = 4, n3 = 0.705) is plotted in Fig. 4.15. The values of the exponents n1 and n2 were arbitrarily limited to not exceed 4.0, and the converged value of n1 = 4 was fixed by this constraint.

In statistics, the “adjusted *R*^{2}” value is meant to compensate for the tendency for *R*^{2} to decrease as additional parameters are introduced to the model. The “adjusted *R*^{2}” = 0.653 for the six-parameter model illustrated in Fig. 4.14. For the four-parameter model, the “adjusted *R*^{2}” = 0.722 is superior to that for the six-parameter model. It is interesting but certainly possible that introduction of additional parameters being fit by a nonlinear regression algorithm selected in Matlab could result in convergence to a different local minimum. Despite the simplification of the model, the resulting contours from the four-parameter model (Fig. 4.15) bear major resemblance to contours from the six-parameter model (Fig. 4.15). The results from regression to the same 17 data points for the four-parameter model are summarized as Case 6/4 in Table 4.3.

### 4.7.1 Rationale for Scaling Between PGA and CSR for Simplified Procedure

The ratio of total to buoyant densities of the soil *γ*/*γ*^{′} ≈ 2, and the depth reduction factor, *r*_{d}, is very close to 1.0 for a 4 m-deep deposit. According to Idriss and Boulanger (2008, Fig. 65), for a static stress ratio of 0.09 (which corresponds to a 5-degree slope angle), the static shear stress correction factor, *K*_{α}, may vary between about 0.8 for looser sand and 1.2 for the denser sand; for the purposes of this paper, it is assumed that *K*_{α} = 1. From a cycle counting procedure, it was determined that the prescribed ramped sine wave LEAP motion corresponds to an earthquake of magnitude *M =* 7.7 to 7.9; the corresponding magnitude scaling factor, MSF, would be approximately 0.9. The overburden stress correction factor, *K*_{σ}, would be greater than 1 because the confining pressures at mid-depth of the liquefiable soil are only on the order of 20 kPa. According to Idriss and Boulanger (2008), the correction factor depends on density as well as confining stress, and it is capped at *K*_{σ} ≤ 1.1. Assuming that the cap controls, the effect of *K*_{σ} ≈ 1.1 would effectively offset *MSF* ≈ 0.9 in Eq. 4.7. Inserting the above-described constants into Eq. 4.7 and using PGA_{eff} in place of *PGA* provides \( {\mathrm{CSR}}_{M=7.5,\kern0.5em \sigma {\prime}_{vc}=1}\approx 1.3\left({\mathrm{PGA}}_{\mathrm{eff}}\right). \)

## 4.8 Correlations Between Excess Pore Pressures, *D*_{r}, and IMs

*D*

_{r}(

*q*

_{c}(2 m)) and PGAeff in Fig. 4.16; panels (a) and (b) show two different views of the 3D plot, and (c) shows residuals between the fit and the data points. Twenty of the twenty-four centrifuge tests provided

*q*

_{c}(2 m). One of these 20 was considered to be an outlier and is excluded from Fig. 4.16. The coefficient of correlation for this regression was found to be

*R*

^{2}= 0.78, indicating that 78% of the variation can be explained by the fitting function with the variables PGA

_{eff}and

*D*

_{r}(

*q*

_{c}(2 m)). This is considered to be a clear indication that the LEAP centrifuge tests performed at different centrifuge facilities are very consistent from centrifuge to centrifuge. The thin dash-dot line in Fig. 4.16 shows the liquefaction triggering curve from Boulanger and Idriss based on the relative density at mid depth of the layer. The CRR (Cyclic Resistance Ratio) curves were scaled according to CRR = 1.3 × PGA

_{eff}as explained in Sect. 7.1. The empirical triggering curve seems to be consistent with the LEAP-UCD-2017 data.

*R*

^{2}reduced from 0.78 to 0.47 due to replacement of the density measure

*D*

_{r}(

*q*

_{c}(2 m)) by the density measure

*D*

_{r}(rho).

*D*

_{r}(rho) is determined from direct measurements of mass and volume, while

*D*

_{r}(

*q*

_{c}(2 m)) uses the density obtained by correlations with the cone penetration resistance at mid-depth. As was the case for the correlations to displacement,

*D*

_{r}(

*q*

_{c}(2 m)) produces a better correlation than relative density from mass and volume measurements. This is likely caused by cumulative errors in the direct measurement of mass and volume.

*R*

^{2}reduced slightly from 0.78 in Fig. 4.16 to 0.73 in Fig. 4.18 when CAV

_{5}is used in place of PGA

_{eff}as the IM. As was concluded by Kutter et al. (2018a), the

*R*

^{2}value is best when IM = PGA

_{eff}and when relative density is based on the cone measurements. However, the correlation of the duration of liquefaction at P4 to CAV

_{5}is also very good.

## 4.9 Correlations Between Peak Cyclic Displacements, *D*_{r}, and IMs

Another easily measurable quantity thought to be indicative of the extent of liquefaction is the magnitude of the average cyclic component of the shear strains in the soil layer. This quantity can be reliably computed as described by Kutter et al. (2017). Briefly, it is obtained by subtracting the accelerations of the base of the container (average of accelerometers AH11 and AH12) from the accelerations measured at the surface of the soil layer (accelerometer AH4) and then double integrating to determine the displacement as a function of time. A high-pass filter (about 0.3 Hz prototype scale) is used to remove the low-frequency components of the accelerations before integrating to obtain velocities and displacements. The low-frequency components, often a result of small electrical drift in the signal, become large during integration and are not reliably measured by accelerometers. Unfortunately, the filtering of the low-frequency component also removes the evidence of permanent displacements on the acceleration signal. Nevertheless, the amplitude of the cyclic component (higher than 0.3 Hz prototype scale) is also indicative of softening due to liquefaction. Figure 4.10 showed the cyclic time series of the cyclic component of displacement as a function of time. The peak of the cyclic displacement time series is summarized in Table 4.2c.

In a theoretical special case of complete liquefaction, the base might be expected to move while the ground surface was isolated from the base motion; hence, the relative cyclic displacement would equal the base cyclic displacement. The average peak of the 1 Hz component of the input base motion listed in Table 4.2b is 0.12 g. This acceleration corresponds to a cyclic displacement of ±39 mm. As is apparent in Fig. 4.19, the measured cyclic relative displacements are typically in the range of 40–80 mm—significantly greater than the base displacement. The relative displacement could be greater than the input base displacement if the surface displacements are of opposite phase to the base displacements and/or if the displacements are amplified at the ground surface.

In one case cyclic displacements were significantly greater than 80 mm; NCU1 displayed relative displacements of 113 mm (see Fig. 4.19 and/or Table 4.2c); the large relative displacement in NCU1 is at least partly explained by the fact that the 1 Hz component of the input base acceleration for NCU1 0.18 g is about 50% greater than the average 1 Hz component (0.12 g) listed in Table 4.2b. The relatively large amplitude of the low-frequency component of the base displacement for NCU1 helps explain why the cyclic displacements are the greatest for NCU1.

It should also be recalled that, due to the mechanical nature of the shaker at Ehime University, the Ehime motions contained a significant lower-frequency displacement that is very apparent for Ehime3 in Fig. 4.10.

## 4.10 Summary and Conclusions

The first goal of this paper is to provide an overview of all the experimental data from centrifuge testing for LEAP-UCD-2017. This overview will allow readers to quickly scan through the key time series data and various performance measures to evaluate the extent of liquefaction in various experiments. The second goal of this paper is to demonstrate that the experiments are consistent with each other and that they define a response function or trend between key input parameters and key liquefaction response parameters.

Time series data from input accelerations, accelerations and pore pressures in the central array and relative cyclic displacements obtained by integration of accelerations in the time domain are qualitatively compared. Residual displacements are characterized by the measured displacement from surface markers. Contour plots of lateral displacement and settlements of the surface markers are presented. Key density measures, cone penetration data, ground motion intensity measures, and response parameters are tabulated for all 24 experiments in Tables 4.2a, 4.2b, and 4.2c. All of the data in Tables 4.2a, 4.2b, and 4.2c and more data not presented here are also available in a spreadsheet document archived in the LEAP-UCD-2017 data archive in the NHERI DesignSafe (Kutter et al. 2018b). The results from Tables 4.2a, 4.2b, and 4.2c are cross plotted in 3D plots along with nonlinear regression surfaces to show the trend and to estimate the degree of correlation of the data to the response surface.

The consistency of the centrifuge experiments performed for LEAP-UCD-2017 is demonstrated by showing that responses (permanent displacement, duration of liquefaction, and the amplitude of the cyclic displacements observed in different experiments) are highly correlated to key parameters describing the resistance to liquefaction (e.g., relative density and cone penetration resistance) and the base motion shaking intensity measures (e.g., PGA, PGA_{effective}, and CAV_{5}).

The extent of liquefaction in the experiments is more highly correlated to the dry density correlated with cone penetration resistance than the dry density determined by direct measurement of mass and volume of the models, partly due to uncertainties and errors in direct density measurement. Errors in volume measurement arise due to the fact that the surfaces of the model are rough, sloped, and curved. Errors in measurement of container dimensions, sand surface location, and resolution and accuracy of load cells used to measure the weight of the container combine to produce inaccurate density measurements.

The correlation between dry density and cone penetration resistance is obtained by linear regression between dry density determined from mass and volume measurements and *q*_{c} at a depth of 2 m. Then, the densities of the models are obtained from the measured *q*_{c} and the inverse linear regression line.

The PGA of the recorded base acceleration was found to be very sensitive to high-frequency components of the base motion, which varied significantly from facility to facility. The response of the model on the other hand was more sensitive to the lower frequency components of the input motion. Thus PGA was not a good parameter to use to describe the shaking intensity.

PGA_{effective} = PGA_{1Hz} + 0.5 PGA_{HighFrequency} was arbitrarily guessed as a trial function to help researchers at different facilities decide the appropriate input motions given the unique high-frequency noise produced by their centrifuge shakers. As it turned out, PGA_{effective} is much more highly correlated to model response than is PGA. Another, less arbitrary intensity measure, cumulative absolute velocity (CAV_{5}), was also a good predictor of the duration of high excess pore pressures in the model.

Suggested measures of liquefaction response for this and future LEAP exercises are robust and easily and accurately measured and meaningful indicators of liquefaction phenomena. Until each facility can demonstrate that accurate measurements of surface markers using photographic or other scanning procedures, direct measurement of permanent displacements (especially lateral spreading and settlements) should be made using rulers, calipers, and surface markers. The displacements vary with position in the models; markers near the boundaries (end walls and side walls) are restricted by the boundaries. Displacements should be made near the boundaries and far from the boundaries to help assess boundary effects.

The duration of liquefaction of the top pore pressure sensor of a uniform soil deposit is proposed as a robust and useful indicator of the extent of liquefaction. This parameter is meaningful because the volume change of the soil deposit will be correlated to the duration of high pore pressures near the drainage boundary; the rate of volume change may be estimated using the water exit velocity from Darcy’s law, *v = ki*. The maximum pore pressure ratio, *r*_{u} = *Δu*/*σ*′_{vo}, is theoretically an important pore pressure intensity measure, but it is less robust because it is sensitive to errors in the estimation of the depth of the sensor and corresponding initial effective stress.

Until non-contact methods such as photography and stereo photogrammetry are developed for more accurate measurement of time series of boundary displacements, the cyclic component relative displacement should be used as an indicator of the magnitude of cyclic strains induced by the shaking. The cyclic relative displacements of a layer may be obtained by subtracting displacements of the top and bottom of the layer obtained by integration of acceleration records at the top and bottom of the layer. The magnitude of cyclic strains has been shown to correlate well with liquefaction because strain levels change drastically during the onset of liquefaction.

LEAP-UCD-2017 produced an unprecedented quantity of model tests of sloping ground with intentionally varying input motions and soil density. Through data analysis summarized in this paper, we have shown a repeatable response function between liquefaction response and key input parameters including shaking intensity and relative density. The repeatability of this response function proves that the results are consistent with each other within a range of uncertainty. The matrix of test results is sufficient to not only quantify the median response but also the sensitivity of response to variations in the input parameters and the centrifuge-centrifuge variability of the experimental results. The credibility of the data provided by demonstrated interlaboratory consistency allows us to move forward with meaningful use of this data for assessment of the accuracy of numerical simulation procedures. Since we have mapped out an experimental response surface with some ability to quantify experiment-experiment variability, it is recommended that the numerical procedures also be required to map out the same response surfaces.

It should be emphasized that many of the LEAP experiments included a total of two or three destructive motions. This paper focuses on results from the first motion only. Papers by each experiment facility describe the results from subsequent destructive motions.

## Notes

### Acknowledgments

The experimental work on LEAP-UCD-2017 was supported by different funds depending mainly on the location of the work. The work by the US PI’s (Manzari et al. 2017) is funded by National Science Foundation grants: CMMI 1635524, CMMI 1635307, and CMMI 1635040. The work at Ehime U. was supported by JSPS KAKENHI Grant Number 17H00846. The work at Kyoto U. was supported by JSPS KAKENHI Grant Numbers 26282103, 5420502, and 17H00846. The work at Kansai U. was supported by JSPS KAKENHI Grant Number 17H00846. The work at Zhejiang University was supported by National Natural Science Foundation of China (Nos. 51578501 and 51778573), Zhejiang Provincial Natural Science Foundation of China (LR15E080001), and National Basic Research Program of China (973 Project) (2014CB047005). The work at KAIST was part of a project titled “Development of performance-based seismic design,” funded by the Ministry of Oceans and Fisheries, Korea. The work at NCU was supported by MOST: 106-2628-E-008-004-MY3.

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