Liquefaction-induced settlements of residential buildings subjected to induced earthquakes

Soil Dynamics and Earthquake Engineering xxx (xxxx) xxx

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Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn

Liquefaction-induced settlements of residential buildings subjected to induced earthquakes Yannis K. Chaloulos a, *, Amalia Giannakou a, Vasileios Drosos a, Panagiota Tasiopoulou a, Jacob Chacko a, Sjoerd de Wit b a b

GR8-GEO Engineering Consultants1, Athens, Greece Shell Global Solutions International B.V., Rijswijk, Netherlands

A R T I C L E I N F O

A B S T R A C T

Keywords: Shallow footings Induced seismicity Liquefaction Numerical analyses

The paper evaluates the dynamic performance of existing residential houses affected by gas-extraction-induced earthquakes in an area of low tectonic seismicity where structures have not been designed against earthquake loading. The foundation consists of narrow spread footings (width, B < 0.7 m), while the seismic demand is characterized by low intensity. Nonlinear, effective stress, fully coupled, dynamic soil-structure interaction an­ alyses were performed to develop estimates of liquefaction-induced settlements for buildings on narrow spread footings, founded in a range of soil conditions, with ground motions and structural characteristics that are typically encountered in the study area. The results verify patterns observed in recent studies for slab foundations and shed light on new mechanisms. For the low magnitude earthquakes considered in this study, the total foundation settlements were found to be relatively limited, although simplified liquefaction triggering calcula­ tions would sometimes predict low factors of safety against liquefaction. A simplified equation was developed from regression of the numerical analyses results to derive estimates of liquefaction-induced settlements for residential buildings that was adopted in the latest update of the relevant seismic building code.

1. Introduction In recent years, induced seismicity has been identified as a consid­ erable hazard for structures. Induced earthquakes are in general char­ acterized by low to medium intensity, however, when they occur in areas of low natural seismicity, they might induce significant damage to structures that were not designed to resist earthquake loading. The Mw ¼ 5.8 Oklahoma earthquake in 2016, attributed to oil and gas op­ erations, is the most notable example of induced seismicity causing se­ vere damage to many buildings. In order to incorporate induced earthquake hazards in the design of structures, the United States Geological Survey (USGS) has included in its National Seismic Hazard Model earthquakes attributed to human activity [1]. Given the need to assess the performance of existing structures against induced seismicity, this paper presents the findings of a large study investigating liquefaction-induced settlements of existing resi­ dential buildings subjected to gas-extraction-induced earthquakes. The

project is in an area where tectonic seismicity is very low, thus structures have not been designed against earthquake loading. The buildings considered in the study are 1- and 2-storey residential, masonry houses supported by relatively narrow spread footings (width up to 70 cm). More importantly, the study focused on buildings resting on coarsegrained soils, identified as potentially liquefiable under the design event, thus the most critical performance aspect is the development of liquefaction-induced settlements. Three mechanisms of liquefaction-induced settlements have been identified by Bray and Dashti [2]: (a) Ejecta-induced, (b) Shear-induced and (c) Volumetric. Ejecta-induced settlements, if they occur below a foundation, would cause soil to be locally removed below it. However, they are very difficult to predict, and they cannot be analyzed with conventional continuum mechanics-based numerical schemes. Volu­ metric settlements occur as a result of drainage and re-consolidation following excess pore pressure dissipation. They mainly occur after the end of shaking, however they can in-part occur concurrently with

* Corresponding author. E-mail addresses: [email protected] (Y.K. Chaloulos), [email protected] (A. Giannakou), [email protected] (V. Drosos), [email protected] (P. Tasiopoulou), [email protected] (J. Chacko), [email protected] (S. de Wit). 1 www.gr8-geo.com. https://doi.org/10.1016/j.soildyn.2019.105880 Received 25 April 2019; Received in revised form 9 September 2019; Accepted 27 September 2019 0267-7261/© 2019 Published by Elsevier Ltd.

Please cite this article as: Yannis K. Chaloulos, Soil Dynamics and Earthquake Engineering, https://doi.org/10.1016/j.soildyn.2019.105880

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Soil Dynamics and Earthquake Engineering xxx (xxxx) xxx

the earthquake, especially if the soils are highly permeable. It is acknowledged that they can significantly contribute to the total foun­ dation settlements, however their development has not been thoroughly investigated. In practice, they are typically estimated based on simpli­ fied 1-D methodologies and SPT/CPT-based procedures [3,4] or on back-analysis of data from case histories [5]. In contrast, the accumulation of co-seismic settlements has been thoroughly investigated in the recent past. Despite specific differences, all studies agree that shallow foundations can support structures on liquefied soils provided that a Performance-Based-Design approach is applied to ensure that accumulated settlements are tolerable. This line of thought has been corroborated by observations after the occurrence of large earthquakes (e.g. Kocaeli 1999 [6]; Christchurch 2010-2011 [7]; Japan 2011 [8]) where, despite significant liquefaction, many founda­ tions suffered tolerable settlements without jeopardizing the integrity of the superstructure. The basic patterns that characterize soil response during the accu­ mulation of liquefaction-induced settlements were first identified by Liu and Dobry [9] through a series of centrifuge tests. It was observed that, although the soil at the free field was fully liquefied, excess pore pres­ sure below the foundation remained below the pre-seismic stress level, thus preventing complete liquefaction. Furthermore, as a result of sig­ nificant softening, the motion transmitted to the ground surface and below the foundation was substantially de-amplified thus reducing the inertial demand on the superstructure. Dashti et al. [10] further inves­ tigated the mechanisms governing settlement accumulation through centrifuge tests. They attributed settlement accumulation to the devel­ opment of permanent shear strains as a result of both partial bearing capacity loss as well as to SSI-(Soil-Structure-Interaction)-Induced ratcheting. The former can be induced either by soil softening below the foundation and/or by liquefaction in the free field. SSI-Induced ratch­ eting results from out-of-phase structure movement relative to the subsoil. It occurs with or without soil liquefaction, however, the magnitude of the associated settlements depends on the degradation of the foundation subsoil. Travasarou et al. [11,12] demonstrated similar phenomena for an immersed tunnel embedded in liquefiable soils, where in this case the structure moves upwards since it is lighter than the surrounding soil. Karamitros et al. [13] based on the results of nu­ merical analyses suggested that seismic settlements are associated with a Newmark-type sliding-block failure mechanism which is created under the footing due to the superposition of vertical forces i.e., the soil’s unit weight and the footing’s pressure, and horizontal inertia forces within the subsoil. For the case of harmonic excitation, this wedge-type mechanism is formed twice per loading cycle, symmetrically below each side of the footing. Thus, settlements accumulate twice per loading cycle, as also indicated by their time history whose frequency is double than that of the input ground motion. More recently, Adamidis and Madabhushi [14] performed centrifuge tests for footings on liquefiable sand of varying thickness. They observed that the mode of settlement accumulation is largely defined by the size of the stiffer nonliquefied zone below the footing. For shallow layers, settlements mainly occur due to rocking as a result of the motion transmitted to the foundation through the stiffer zone. For deep layers, however, the liquefied soil below the stiffer zone acts as a natural isolation mechanism thus de-amplifying the foundation motion. As a result, rocking-induced de­ formations are negligible, whereas settlements mainly accumulate due to the displacement of the soil surrounding the stiffer zone. The effects of the different parameters affecting the problem have been systematically studied by means of extensive parametric numerical investigation [15,16]. The analyses showed that of key importance are the properties of the liquefiable sand i.e. the relative density and the thickness, while the presence of a nonliquefiable surficial “crust” layer can be very beneficial. The geometry of the foundation and the trans­ mitted load are also of primary importance, while the inertial charac­ teristics of the superstructure appear to have a secondary effect. The settlement magnitude is directly related to the intensity of the input

motion, and typical intensity measures like Arias Intensity (Ia) and Cu­ mulative Absolute Velocity (CAV) can reasonably capture the effects. The above observations have led to the development of simplified methodologies for the estimation of liquefaction-induced settlements. Karamitros et al. [17,18] and Dimitriadi et al. [19] evaluated data from 2D and 3D numerical analyses and proposed a sliding-block type equation for the evaluation of settlements for the common case of footings on liquefiable soils overlaid by a nonliquefiable crust. More recently, a new generation of methodologies have been developed which are based on the results of a very large number of numerical analyses and subsequent regression analysis. These include the procedures developed by Bray and Macedo [20] and Bullock et al. [5] which correlate seismic settlements with the most critical soil, foundation, structure and excitation motion factors. It should be noted, however, that the above studies and methodol­ ogies focus on buildings resting on continuous rigid slab foundations (i. e. minimum footing widths of about 5 m) subjected to relatively large earthquake events (i.e. corresponding to magnitudes larger than Mw ¼ 6), typically associated with several cycles of significant loading. As a result, their findings could not be readily applied to the buildings of the present study, which involves (a) narrow spread footings which might experience different deformation patterns compared to the wide rigid slabs and (b) earthquakes of medium intensity (Mw � 5.0) typically associated with few cycles of significant loading. Furthermore, under these conditions, the contribution of post-seismic volumetric settlements as a fraction of the total settlements might be more important, thus a more detailed study to estimate the magnitude of post-seismic volu­ metric settlements is also required. This paper presents the results of an extensive parametric study on the assessment of liquefaction-induced settlement accumulation (both co-seismic and post-seismic) of narrow spread footings supporting existing residential buildings subjected to moderate shaking levels and proposes a simplified equation for their estimation. First, the idealized inputs used in the parametric study that bracket the conditions in the study area in terms of soil profile and properties, building characteristics and ground motions are discussed. Then, the major assumptions of the numerical methodology adopted to analyze the problem are described and are validated against a centrifuge test and a case history. Subse­ quently, results of an extensive numerical study of more than 500 ana­ lyses considering critical soil, structure, foundation and input motion parameters are presented and the mechanisms that affect settlements are discussed. The results of the parametric study are regressed, and a simplified equation is developed that can be used directly to derive es­ timates of liquefaction-induced shear and volumetric settlements. This equation has been adopted in the update of the applicable building code for the area. 2. Development of input parameters for numerical study 2.1. Idealized soil stratigraphy and properties The geological setting of the project area involves an approximately 840 m thick layer of Paleogene, Neogene, Pleistocene and Holocene deposits with a notable degree of heterogeneity. These deposits are underlain by limestones of the Cretaceous period which constitute the reference bedrock horizon. The Paleogene formations consist of marine grey sands, sandstones and clays overlaid by clayey marine formations, while the Neogene formations consist of marine clays, sands and loam. The Pleistocene deposits consist of fluvial, glacial and marine sediments. A key characteristic of the geological setting of the area is the formation of “tunnel valleys” produced by subsequent glacial periods. These “valleys” are filled with sand, clay and younger sediments including glacial till and eolian sand transferred through the cold wind. Finally, the Holocene deposits contain alternations of shallow marine deposits and peat. Idealized profiles and properties for use in the numerical parametric 2

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study, were developed from 40 Cone Penetration Tests (CPT). Overall, large variability in soil conditions was encountered in the upper 10–15 m. More specifically, spatial variability analysis of the data indicated that even between adjacent CPTs (located approximately 10–15 m apart) substantial nonuniformity in the subsoil conditions may exist i.e., soil conditions may differ even below the same building. The Ishihara Liquefaction Potential Index (LPIish, [21]) was estimated to range between LPIish ¼ 6–14 for the design earthquake with Mw ¼ 5 and 2475-year return period peak ground acceleration (PGA) of 0.25 g. Fig. 1 presents two CPT logs in terms of tip resistance qc, friction resistance ratio Rf, factor of safety against liquefaction FSL, soil behavior type index Ic and soil classification per Robertson [22]. FSL values were estimated based on an area-specific liquefaction triggering methodology [23], for the design earthquake. As shown on the figure, the site con­ ditions consist of Holocene deposits of loose to medium dense sands and soft to firm clays, underlain by Pleistocene deposits of dense sands and hard clays. Layered deposits comprising alternating thin laminations of coarse-grained (yellow) and fine-grained (green and red) materials are present in the upper 10–15 m of the soil profile. As discussed in Tasio­ poulou et al. [24], CPT-based liquefaction assessment of sand layers in such deposits may not be representative due to the effect of the clay layers on the CPT tip resistance measured within the thin “sandwiched” sand layers. Experimental and numerical data on similar deposits pre­ sented in Tasiopoulou et al. [24] have shown that they exhibit higher liquefaction triggering resistance compared to homogeneous sands. Nevertheless, the signature of the CPT data (which is essentially showing an averaged response of multiple layers) is often similar to that of a loose silty sand or a sandy silt, with values of Ic between 2.05 and 2.6. In the present study it was decided to conservatively neglect the effects of clay laminations within the sand deposits and to treat the laminated layers as homogeneous sand layers with low tip resistance. The CPT data also indicate that a surficial clay crust may or may not be present. The bot­ tom of the Holocene sequence typically includes a firm clay layer un­ derlain by a layer of dense Pleistocene sand. The idealized stratigraphy used in the parametric evaluations included in descending sequence (Fig. 2a):

Fig. 2. (a) Idealized soil profile based on several CPT data (b) shear wave velocity and static shear strength values interpreted from CPT data together with the idealized profiles for Hcr ¼ 0.0 and Hliq ¼ 10.0 m

� Liquefiable layer of varying thickness, Hliq. � Holocene clay layer extending down to El. 15.0 m. � Pleistocene Sand extending from El. 15.0 m to El. 25.0 m. The cumulative frequency distribution of the relative density of the potentially liquefiable sands (i.e. with Ic values less than 2.6) within 5 m below the foundation depth (i.e. within 5–10 footing widths) was esti­ mated using the Boulanger and Idriss [25] procedure and all available CPT data, and is shown on Fig. 3. As shown on this figure the median relative density value is about 50% while sands with relative densities of about 40% correspond to the 3rd percentile of the distribution. The shear wave velocity of the different layers was estimated as the average of published correlations with CPT data [26–29]. Static un­ drained shear strength estimates for the Holocene clay layer were esti­ mated from tip resistance using an Nk factor of 15, while a 20% increase was applied to account for strain rate effects during dynamic loading. For the Pleistocene dense sand, a friction angle of 40� was assumed. The hydraulic conductivity of the liquefiable sand layers was considered anisotropic and equal to 10 6 m/s and 5 � 10 7 m/s for horizontal and

� Top soil consisting of non-saturated sand extending from ground surface at El. �0.0 m to foundation level (varies between El. 0.5 m and El. 0.9 m). � Non-liquefiable crust layer of varying thickness, Hcr.

Fig. 1. Typical CPT logs showing tip resistance, friction resistance ratio, factor of safety against liquefaction FSL and Ic factor, and soil classification per Rob­ ertson [22]. 3

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Fig. 3. Cumulative Frequency Distribution of relative density of liquefiable sands (Ic < 2.6).

vertical drainage respectively based on empirical correlations [30–33]. Fig. 2b presents plots of shear wave velocity and static shear strength values interpreted from CPT data together with the idealized values used for an example profile with Hliq ¼ 10 m and Hcr ¼ 0 m. 2.2. Structural characteristics Two structures, representative of the residential building stock in the project area, were considered in the analyses: i) a 1-storey detached house with an attic and ii) a 2-storey terraced house. The 1-storey structure is 7.8 m by 10.7 m in the transverse and lon­ gitudinal directions respectively. It is made of masonry [i.e., no Rein­ forced Concrete (RC) beams present] and its foundation system consists of strip footings, mainly along the perimeter of the building. The 3D structure was incorporated in the analysis by introducing an equivalent 2D frame model, along the transverse direction of the building, with properties provided by the structural engineers. Recent studies [34] suggest that this approach is adequate to capture superstructure inertial effects in terms of liquefaction-induced settlements, as long as the equivalent model accurately represents the inertial characteristics of the structure (i.e., mass, stiffness, fundamental period). The equivalent model is shown in Fig. 4a. As shown on the figure, a concentrated mass, representing the mass of the building that participates into the inertial load due to the earthquake, was also assigned. It is noted that this mass provides solely inertial load and does not contribute to the vertical loading of the footing. The latter were assigned directly onto the footings as vertical distributed forces and were varied in the parametric evalu­ ations. The estimated inertial mass was 30 Mgr and the fixed-base period of the frame was 0.11 s. Typical ranges of foundation dimension and bearing pressure were obtained from data on buildings in the project area. The frame is considered to rest on two strip foundations which are 0.45 m tall and their width varies from 0.25 to 0.70 m. The footing bearing pressure varies between 20 and 120 kPa. In order to transform the 3-dimensional building geometry into 2 dimensions, loads and stiffnesses were scaled by the tributary out-of-plane length of the equivalent frame (i.e. 10.7/2 ¼ 5.35 m in the transverse direction). An equivalent model was also developed for the longitudinal direction, however sensitivity analyses showed negligible differences in settlement accumulation, thus it was not included in the parametric investigation. The equivalent 2-D frame model for the 2-storey building is shown on Fig. 4b. The building is 7.8 m wide and has a tributary out-of-plane length of 6.3 m. The effective masses assigned to the first and second floor level are 61 and 36 Mgr respectively. For the case of the 2-storey building parametric analyses were performed for two values of the fixed-base period i.e. 0.10 and 0.22 s, by properly adjusting the stiffness

Fig. 4. Numerical for the simulation of the (a) 1-storey and (b) 2-sto­ rey building.

of the beam elements simulating the structure. Note that the crawling space between the foundations is empty for the 1-storey house and filled with 30 cm of soil for the 2-storey house. 2.3. Ground motions Input acceleration time histories were developed and applied as outcrop motions at the base of the numerical model (El 25 m). Eleven acceleration time histories were selected and spectrally matched, using the computer code RSPMATCH [35], to the target spectra at reference bedrock horizon (i.e. at about El. 800 m with Vs30 ¼ 1400 m/s). 1D site response analyses were subsequently performed to propagate the mo­ tions to the elevation corresponding to the base of the numerical model. The seed motion selection was based on site-specific parameters such as magnitude, site-to-source distance, frequency content (i.e., spectral shape), peak intensity measures, and ground motion duration (D5-75). Fault rupture mechanism, and site class were also taken into consider­ ation. The key characteristics of the eleven selected earthquake ground motions are presented in Table 1. Equivalent linear site response analyses were performed using the computer code STRATA [36] to obtain the outcrop motions at the base of the numerical model (EL. 25.0 m). Namely, two types of analyses were performed, one by “cutting” the profile at EL. 25.0 m and one by propagating the motion to the ground surface (at EL. 0.0 m) and extracting outcrop motions at 25.0 m. The two procedures showed minor differences. The 1D profile used in the convolution analysis was developed based on subsoil explorations performed by the local au­ thorities. Scale factors of 1.15 and 0.75 were applied on the ground motions to capture the range of amplitudes that are representative of the ground motion variation at the ground surface in the project region. Fig. 5 presents the developed response spectra at the ground surface for scale factors of 0.75 and 1.15. Various intensity measures can be used to describe the ground motions, and Table 2 presents the characteristics of the motions in terms of PGA, Arias Intensity Ia, Cumulative Absolute 4

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Table 1 Earthquake ground motions used in the numerical analyses (NGA# is from NGA-West2 Database). ID

NGA#

Earthquake

Year

Station

Mw

Mechanism

Rrup (km)

Vs30 (m/sec)

1 2 3 4 5 6 7 8 9 10 11

419 1312 2021 2426 4284 4312 4369 4520 6093 6434 8775

Coalinga-07 Ano Liosia - Greece Kalamata - Greece (aftershock) Chi-Chi –Taiwan - 02 Basso Tirreno - Italy Umbria-03 - Italy Umbria Marche - Italy (aftershock 1) L’Aquila - Italy (aftershock 1) Kozani - Greece (aftershock) Izmit - Turkey (aftershock) 14383980

1983 1999 1986 1999 1978 1984 1997 2009 1995 1999 2008

Sulphur Baths (temp) Athens 2 (Chalandri District) Kalamata OTE Building TCU137 Naso Gubbio Nocera Umbra Salmata Sulmona Karpero Town Hall LDEO Station No. C1058 BV Chilao Flat Rngr Sta

5.2 6.0 4.1 5.9 6.0 5.6 5.5 5.6 5.2 4.9 5.4

Reverse Normal Normal Reverse Strike Slip Normal Normal Normal Oblique Normal Thrust Reverse Oblique

12 9 8 23 19 16 12 42 16 (epic.) 26 (epic.) 50

617 411 399 635 620 922 694 612 665 502 927

induced settlements (i.e. settlement analyses) and ii) Assess whether the footing has lost its bearing capacity (i.e. stability analyses). To perform these analyses, knowledge of the monotonic post-liquefaction response of the soil is required i.e. the stress-strain relationship and the residual shear strength. In estimating volumetric settlements, the stress-strain curve is important, which for the case of a simplified elastic-perfectly plastic law reduces to the elastic moduli. In evaluating foundation sta­ bility, the residual shear strength of the soil is important. The procedures adopted to perform these analyses are addressed separately in the following paragraphs. Post-earthquake reconsolidation settlements occur as excess pore water pressures dissipate and the soil’s effective stress increases. In practice, this type of settlement is estimated from empirical free-field reconsolidation methods (e.g., [3]). However, as shown later in the paper, this approach may lead to highly conservative estimates. Numerically, simulation of the process is a rather tedious task. This is because constitutive models like PM4Sand, typically used in liquefaction analyses, are based on the decomposition of strains into an elastic and a plastic component, with the latter responding only to changes of the stress-ratio. As a result, for the case of 1-D volumetric strains, which occur under constant stress-ratio, only the elastic strains develop, thus substantially underestimating the predicted settlements by up to an order of magnitude [38]. For the purpose of this study, the liquefied soil was modeled with a Mohr-Coulomb model, with the elastic moduli calibrated using the Ishihara and Yoshimine [3] empirical correlation between shear and volumetric strains. More specifically, the procedure consisted of the following steps:

Fig. 5. Developed response spectra at the ground surface for 0.75 and 1.15 amplification factor.

Velocity CAV, Standardized Cumulative Velocity CAVdp and Significant Duration D5-75 for the 1.15 and 0.75 PGA scale factor. 3. Modeling approach 3.1. Overview Two-dimensional, dynamic, effective stress analyses were performed with the finite difference code FLAC v8.0 (Itasca 2016). A typical finite difference mesh showing the stratigraphy and the basic input parame­ ters for the case of 1-storey structures is shown on Fig. 6, while a detail of the model close to the structure area has already been presented on Fig. 4 for both 1- and 2-storey structures. The seismic performance of the foundation was evaluated for two stages: a) during seismic shaking (i.e. co-seismic); and b) after the end of seismic shaking (i.e. post-seismic). The first stage (co-seismic) involves performing dynamic, nonlinear, effective stress analyses to estimate the liquefied zones and the deformations that occur during strong shaking (primarily shear-induced settlements). For the first stage sand layers are modeled using the PM4Sand constitutive model [37]. For the second stage (post-seismic), two types of analyses were performed with the following objectives: i) Estimate the post-seismic volumetric-strain Table 2 Range of Intensity Measures for the selected ground motions (El.

PGA Scale factor: 1.15 PGA Scale factor: 0.75

a) Monitoring of the maximum shear strain developed in the liquefiable zones during shaking; b) Updating the constitutive model to Mohr-Coulomb in zones where the maximum excess pore pressure ratio during shaking exceeded a specified threshold, indicative of significant pore pressure generation (e.g., ru > 0.7 [39]). Assigning a constrained modulus corresponding to consolidation strains estimated from the maximum shear strains that developed during the earthquake using the chart suggested by Ishihara and Yoshimine [3] and a Poisson’s ratio of 0.3; and c) Performing a static analysis under gravity loads with the revised constitutive model and stiffness parameters. The above procedure was implemented in the analysis via a custom subroutine written in FLAC’s programming language FISH. This pro­ cedure was applied to model the Port Island Case Study [38,40] and

25.0 m).

Peak Ground Acceleration PGA (g)

Arias Intensity Ia (m/s)

Cumulative Absolute Velocity CAV (g-sec)

Standardized Cumulative Velocity CAVdp (g-sec)

Significant Duration D5-75 (sec)

0.10–0.17 0.06–0.11

0.11–0.35 0.05–0.15

0.18–0.60 0.12–0.39

0.0–0.5 0.0–0.3

2.3–8.6 2.3–8.6

5

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Fig. 6. Typical finite difference mesh for 1-story structure and basic input parameters.

predicted reconsolidation settlements on the order of 30 cm which are within the range of the reported reconsolidation settlements 20–50 cm. Alternatively, volumetric settlements were also estimated using the empirical scheme employed in PM4Sand which reduces the elastic shear modulus. A comparison between the post-earthquake reconsolidation settlements estimated using PM4Sand’s scheme and the procedure described above indicated that the latter predicts somewhat larger reconsolidation settlements for the range of conditions relevant to this study. Thus, it was decided to conservatively adopt it. Post-earthquake stability may be critical even if stability is ensured during shaking as has been demonstrated in documented case histories (e.g. Lower San Fernando dam case history). As described in Naesgaard & Byrne [39], proper simulation of critical macroscale mechanisms that affect the residual shear strength, like void redistribution, soil mixing and strain localization below impermeable layers, is difficult using conventional continuum mechanics analyses. For this purpose, the present study adopts the procedure proposed by Naesgaard & Byrne [39] which is based on the use of a Mohr-Coulomb model for the liq­ uefied soil which is assigned the residual strength as estimated from empirical relationships (e.g. [41,42]). The latter are based on interpre­ tation of case studies, thus capture the above mechanisms. More spe­ cifically, post-earthquake stability analyses included the following procedure:

liquefaction triggering curves for no-bias (α ¼ 0) and with-bias (α ¼ 0.1 and 0.2) with the calibrated PM4Sand model (black lines) and the target liquefaction triggering curve (red line) for relative densities of 40% (Figs. 7a) and 50% (Fig. 7b). Non-Liquefiable soils were modeled with the Itasca S3 hysteretic model [44] in combination with a Mohr–Coulomb failure criterion. The model parameters were calibrated to capture the shear modulus reduction curves proposed by Darendeli [45] for PI ¼ 0 and 40% for Pleistocene sand and Holocene clay, respectively.

a) Monitoring the maximum excess pore water pressure developed in the liquefiable zones during shaking; b) For areas where the maximum excess pore pressure ratio during shaking exceeded a specified threshold indicative of liquefaction (e. g., ru > 0.7 [39]) updating the constitutive model to Mohr-Coulomb and assigning residual strength (using the empirical relationship for residual strength as a function of qc1Ncs given by Idriss and Boulanger [42]); and c) Conducting static analyses under gravity loads with the revised constitutive model and properties until equilibrium is reached. 3.2. Soil constitutive models and model calibration The response of liquefiable sands during shaking was simulated with the PM4Sand constitutive model [37]. The model was calibrated to capture liquefaction triggering and shear strain accumulation behavior for both level (no-bias) and sloping ground (bias) conditions [43]. In particular, calibration against liquefaction triggering at low number of cycles corresponding to Mw ¼ 5 earthquakes was based on empirical liquefaction resistance curves by Green et al. (2018) for level ground conditions (no-bias). For sloping ground conditions (bias) the correc­ tions for the level of static horizontal shear stress (α ¼ τst/σ0 v) recom­ mended by Idriss and Boulanger [42] were adopted. Fig. 7 presents the

Fig. 7. Site-specific liquefaction curves and PM4Sand calibration with (α ¼ 0.0) and without bias (α ¼ 0.1 and 0.2). 6

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3.3. Modeling of structures and foundations The structural members were simulated with linear elastic beam elements described in terms of mass density, ρ; Young’s modulus, E; cross-section area, A; and moment of inertia, I. The footings were simulated as elastic solid elements. Interface elements following an elastic-perfectly plastic constitutive law were placed both at the base and along the vertical sides of each footing (Fig. 4). For the elastic stiffness an adequately large value (to avoid interface deformation) was selected. For the plastic parameters a value of 35� (approximately equal to the friction angle of the sand) was assigned, based on the results of sensitivity analyses which indicated minor effects of interface properties on settlement accumulation. 3.4. Boundary conditions The model was subjected to one-directional horizontal dynamic loading using outcrop time histories developed from 1D site response analyses as described above. A compliant base was used at the bottom of the model to simulate the half space. Dynamic excitation was specified using the compliant-base procedure proposed by Mejia and Dawson [46] and implemented in FLAC v8.0 [44]. In this procedure a shear stress time history compatible with the half space stiffness is applied to the base of the model. This is derived by multiplying the outcrop velocity time history by the half-space shear wave velocity and density. Regarding side boundaries, the corresponding nodes at the same elevation were tied together to simulate shear-box type boundary conditions. 4. Validation of numerical approach A centrifuge experiment and a case history with modeling conditions as similar as possible to the ones at hand were selected as validation cases. The validation cases thus comprised: (1) a centrifuge test of a frame structure on spread foundations resting on liquefiable sand [47]; and (2) a case history of a 2-storey residential building on spread foundations at Kaiapoi, New Zealand subjected to the 2010-2011 Can­ terbury earthquake sequence.

Fig. 8. (a) Layout of the centrifuge test and applied input motion (b) Calibra­ tion of PM4Sand against experimental data on Fraser sand for static bias α ¼ 0.0, 0.05, 0.11 and 0.20.

4.1. Centrifuge test of building on spread footings on liquefiable sand A series of centrifuge tests of a frame structure resting on two spread foundations overlying Fraser River sand was performed at C-CORE’s geotechnical centrifuge facility [47]. One of these tests simulated a 16-m-thick homogenous Fraser River sand with Dr ¼ 55% relative den­ sity, overlying a 4-m-thick dense sand (Dr ¼ 75%) as shown on Fig. 8a. This test (described in prototype dimensions) was selected for the vali­ dation of the numerical approach described above. A rigid box was used in the experiment and 3.8 m-thick Duxseal layers were placed at each end wall of the box to create absorbing boundaries. The structure is 6.0 m tall and 4.9 m wide with a fixed-based period of Tstr ¼ 0.476 s, while the two strip footings are 1.8 m wide and transmit to the soil a bearing pressure of Q ¼ 110 kPa. The input ground motion (Fig. 8a) was based on a synthetic time history with many cycles corresponding to a 2475-year design event for the Vancouver area (NBCC 2005, [48]). The synthetic time history was amplified by 1.46 to obtain a peak ground acceleration of 0.25 g in the centrifuge tests and applied as the hori­ zontal input at the base of the box. The specific test was selected for the validation since it was the only one, to the authors’ knowledge at least, that employed a structure and a foundation scheme similar to the ones subsequently analyzed in the parametric investigation. This parameter was of critical importance since a validation of the methodology for conditions far different from the ones eventually analyzed can be misleading and unavailing. While the use of a rigid box implies different boundary conditions than in the field case, the fundamental phenomena related to the narrow shallow foundation problem on liquefiable soil are

captured in the test. The test was numerically simulated using the approach described in the previous section, with the PM4Sand model calibrated to match Cy­ clic Simple Shear test results under level and sloping ground conditions on samples of Fraser River Sand [49,50]. The calibrated PM4Sand model is compared with the lab results on Fig. 8b (black and red lines respec­ tively) in the form of CSR versus number of cycles to liquefaction, for initial static bias α ¼ 0.0, 0.05, 0.11 and 0.20. Experimental data were on samples prepared at a relative density of Dr ¼ 59%, while the nu­ merical simulations were performed for Dr ¼ 55%, the actual relative density reported in the centrifuge test. The Duxseal placed along the sidewalls of the box was modeled as elastic with a Young’s Modulus of 8 MPa and a Poisson’s ratio 0.46 [51]. Fig. 9a presents numerical analyses results in the form of maximum excess pore water pressure ratio and deformed shape at the end of shaking. Fig. 9b compares excess pore water pressure ratio measure­ ments (black lines) with numerical predictions (red lines) at Points A (free field) and B (under the foundation) shown on Fig. 9a. As shown on these figures, the numerical model captures both the liquefaction in the free field and the complex response below the foundation, where the increased confinement and the interaction with the foundation impedes the development of large excess pore pressure ratios, in line with ob­ servations from various experimental tests [9,10,52]. Finally, Fig. 9c presents comparisons of foundation settlements for the left and the right 7

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footing. The numerical analysis results obtained using the methodology described above agree well with the experimental measurements. 4.2. Case history of residential building at Kaiapoi, New Zealand The second validation case considered was that of a residential building with fundamentally similar structural and foundation charac­ teristics to the residential buildings considered in this study which experienced liquefaction-induced settlements during the 2010-2011 Canterbury earthquake sequence. Information about the building char­ acteristics, observed settlements and geotechnical conditions were gathered by BICL [53]. The 2010-2011 Canterbury earthquake sequence includes the 4th September 2010 Mw ¼ 7.1 Darfield earthquake and the 22nd February 2011 Mw ¼ 6.2 Christchurch earthquake among other events. Wide­ spread liquefaction in Christchurch and the surrounding areas were reported after these events. The residential building analyzed is a 2-sto­ rey unreinforced masonry and timber framed construction founded on perimeter strip footings. It is located at Kaiapoi, approximately 16 km north of the Christchurch Central Business District. According to BICL [53], the building suffered differential settlement during the Mw ¼ 7.1 Darfield earthquake event (September 2010) with the Eastern corner of the building reported to have experienced differential settlement of about 5–10 cm relative to the Northern corner. Little to no further dif­ ferential settlement was attributed to the subsequent Mw ¼ 6.2 Christ­ church earthquake event (February 2011). Available geotechnical data from CPTs located close to the corners of the building, revealed differential ground conditions between the eastern and northern corner of the building, with thicker liquefiable deposits present near the eastern corner of the building. Based on the CPT data and the observed settlements at the site, the Northeastern side of the building was selected for numerical analysis. Idealized soil pro­ files were developed based on the CPT data at the northern and eastern corners of the building that were advanced to depths of 10 m and 7 m below the ground surface, respectively. The values of relative density, Dr, assumed for the soil profiles at each corner were based on the Bou­ langer and Idriss [25] correlation with CPT data. Markham et al. [54]

Fig. 9. Comparison between experimental and numerical results: (a) Deformed shape at the end of shaking and maximum excess pore pressure ratio during shaking (b) Excess pore pressure ratio time histories (c) Settlement time histories.

Fig. 10. Numerical model, idealized soil profile and input motions for the simulation of the Christchurch case study.

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suggest that the Riccarton Gravel formation, which is encountered at depths less than 40 m from the ground surface in the wider area sur­ rounding Christchurch, can be considered stiff enough to be selected as engineering bedrock. Below the CPT termination depths and down to 18.5 m (i.e. top of Riccarton gravel and the base of the numerical model), the soil profile at the Kaiapoi North School (KPOC) station [55, 56], situated about 700 m north of the building, was used. Fig. 10 presents the model mesh together with the idealized stra­ tigraphy and relative density values assigned to the sand layers. The liquefaction triggering curve for the critical surficial layer with the lowest relative density of 40–45% was based on laboratory tests on Christchurch fluvial silty sand [57], shown on Fig. 11. Ratios from empirical liquefaction triggering correlations on generic sands [25] and judgment were used to scale up the target resistance to liquefaction triggering of the layers with higher relative density (also shown on Fig. 11). Relative to the baseline Dr ¼ 40–45% curve, the corresponding scaling factors were in the order of 1.2–1.8 for Dr ¼ 50–65%. Numerical modeling of the structure involved the development of an equivalent frame model based on input from the structural engineers. The equivalent frame is shown on Fig. 10 and has a fundamental period of 0.08 s. The load exerted on the soil is estimated to be 56 kPa approximately with a foundation width of 0.8 m. In the absence of downhole data or rock/stiff soil recordings in the building vicinity, an alternative approach was required to obtain input motions at the top of the Riccarton Gravel formation (base of numerical model) for the numerical analyses. The deconvolved Riccarton outcrop ground motions (fault-normal and fault parallel components) developed by Markham et al. [54] from the Canterbury Aero Club Station (CACS) recording were used as input motions for the numerical analyses applied at 18.5 m depth. Furthermore, Markham et al. [54] estimated scaling factors for the deconvolved motions to be applied at other locations to account for differences in Vs and site-to-source distance between the site being studied and the CACS site. To check this approach, 1-D site response analyses were performed using the KPOC profile (the one closest to the building analyzed), and it was observed that the proposed scaling factor SF ¼ 0.47 proposed by Markham et al. [54] for the Darfield event resulted in an unsatisfactory agreement between the recorded and the estimated response spectrum at the ground surface. The comparison is shown on Fig. 12a in terms of response spectra (black and green line respectively) and in Fig. 12b in terms of residual values (green line). To improve the prediction, a higher scaling factor equal to SF ¼ 1.0 was used and the estimated acceleration response spectrum at the surface indicated a better agreement with the acceleration spectrum of the recorded motion and smaller residuals (red line on Fig. 12a and b respectively). For the Christchurch event, analyses

Fig. 12. Ground surface response spectra at the KPOC station and corre­ sponding residual error for the fault-normal component of the Darfield event.

were performed using a factor of 0.73 as suggested by Markham et al. [54] and the resulting surface spectra were in good agreement with the spectra of the recorded motion at KPOC. The deconcolved Riccarton ground motions were rotated to the building coordinates and the component parallel to the northeastern side was selected for analyses (Fig. 10). Fig. 13 presents numerical analyses results in the form of maximum excess pore pressure ratio and settlement contours for the Darfield and Christchurch events. For the Darfield event, the contours of maximum excess pore pressure ratio, indicate that liquefaction occurs in the Dr ¼ 40–45% layer below the footing at the eastern corner of the building and in the free field at the eastern side. The denser underlying layers do not liquefy. The settlement contours show that the right (eastern) footing settles 31 cm (26 cm during shaking and 5 cm during reconsolidation) and the left (northern) one settles only 8 cm (with negligible reconsolidation settlements) resulting in a differential settle­ ment of about 23 cm (as compared to 5–10 cm reported). By contrast, the maximum excess pore pressure ratio that develops during the Christchurch event is limited to less than 50%, with significantly lower differential settlements on the order of 1.3 cm (as compared to no noticeable additional settlement reported). Although the numerical analyses somewhat overpredict the reported differential settlements, the comparison of field observation during the different earthquake events with numerical model predictions is considered satisfactory considering the uncertainties and subsequent simplifications involved (ground mo­ tions, site conditions, structural characteristics etc). In particular, the ability of the simulations to capture the different behaviors experienced in the two earthquakes is considered encouraging. It should also be

Fig. 11. Calibration of PM4Sand for the simulation of the Christchurch case study. 9

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Fig. 13. Contours of maximum excess pore pressure ratio and total (co-seismic and reconsolidation) settlement for the Sept. 2010 Darfield and the Feb. 2011 Christchurch event.

noted that these results are unrestrained differential settlements and the presence of a continuous perimeter foundation under the footing in some cases reduces the observed differential displacements from those predicted using 2D plane strain analyses.

seismic volumetric-induced settlements is discussed later. 5.1. Mechanisms affecting settlement accumulation Fig. 14a shows contours of maximum excess pore pressure ratio during shaking superimposed with displacement vectors at the end of shaking for the case of a 1-storey building (Tstr ¼ 0.11 s), Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m and Q ¼ 36 kPa and ground motion 4312. Only the area close to the structure is plotted, however, the pore pressures at the two ends of the plot are representa­ tive of the free field response. For the same case, Fig. 14b presents, from top to bottom, time histories of left and right foundation settlements (black and red line respectively) as well as time history of CAV (blue line), excess pore pressure ratio in the free field and below the footing (black and red line respectively) and acceleration at the base of the model and directly below the footing (black and red line respectively). Excess pore pressure ratio time histories correspond to a depth of 2.0–2.5 m below the footing, i.e. the depth where maximum ru occurs. As shown on Fig. 14a, the soil does not fully liquefy, a result of the medium intensity of the input motion. Large excess pore pressure ratios (ru > 0.9) and soil liquefaction only develop in a narrow zone, approx­ imately 0.5–1.0 m thick, close to the base of the layer. This reduces the magnitude of strength degradation and subsequent deformations. Another benefit from this type of response stems from the fact that the footing analyzed is narrow, with a small stress bulb, interacting mostly with the nonliquefied soil at shallow depths and not with the deeper liquefied soil. Moreover, as the direction of the displacement vectors suggests, the weight of the soil at the outer edges of the footings, in combination with the softening of the underlying sand, creates a spiral deformation mechanism, which pushes the soil below the crawl space upwards. For these reasons, the calculated settlements are rather small, on the order of 3.0 cm. Fig. 14b shows that the majority of the settlements (60–70%) develop during strong shaking (between 2 and 7 s), and especially after large excess pore pressures have developed (after 5–5.5 s). Also, as shown on the figure, the settlement accumulation is similar to the evo­ lution of CAV at the ground surface (the effectiveness of various In­ tensity Measures will be further discussed later). It is also noteworthy that, as a result of relatively low excess pore pressure build-up, the motion transmitted to the foundation is not significantly de-amplified. While a natural isolation mechanism has been systematically observed in other studies [13,15], those studies focused on strong input motions

5. Parametric Numerical Evaluation of spread foundation performance under induced earthquakes More than 500 analyses were performed to investigate the effects of most important soil, foundation and structure properties for the range of values shown in Table 3. Foundation parameters considered include the width B, the load Q and the embedment depth D. Structure parameters considered include the building typology (1-storey and 2-storey) as well as the fixed-base period, Tstr. Soil parameters considered include the thickness Hliq and the relative density Dr of the liquefiable sand layer as well as the thickness Hcr and the undrained strength su of the crust. The latter is normalized with foundation pressure as su(πþ2)/Q. This normalization corresponds to the static factor of safety against bearing capacity for an equivalent uniform clay layer. It should be noted, that this is not the static factor of safety of the foundation, since this also depends on the strength of the underlying sand layer. The selected range of soil properties corresponds to a range of LPIish ¼ 1 to 22, i.e. it covers the variability in the area of the project where the estimated LPIish range was 6 to 14 (see Section 2.1). The following paragraphs present key trends regarding accumulation of settlements, as they were identified in the numerical analyses. These analyses and observations focus on set­ tlements that accumulate during shaking, while the contribution of postTable 3 Range of values considered in the parametric study. Parameter

Description

Range

Hliq (m) Dr (%) Hcr (m) su(πþ2)/Q

Liquefiable layer thickness Liquefiable layer relative density Non-liquefiable crust thickness Undrained shear strength of crust as a function of the foundation pressure Q Foundation width Foundation Embedment Depth Foundation pressure Structure typology

0.5–10.0 30–50 0.5–1.0 1.0–10.0

Fixed-base Structural Period Scale factor applied to input motion

0.10–0.22 0.75–1.15

B (m) D (m) Q (kPa) Number of Storeys Tstr (s)

0.25–0.70 0.0–0.9 20–120 1–2

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Fig. 14. (a) Maximum excess pore pressure ratio during shaking and displacement vectors at the end of shaking (b) Time histories of acceleration at the base of the model and below the footing, footing settlement and CAV (at ground surface), and excess pore pressure ratio at the free field and below the footing (1-storey, Tstr ¼ 0.11 s, Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, Ground Motion 4312).

and extensive soil liquefaction. Finally, as shown on the figures, and as observed in all other cases analyzed, differential settlements were negligible (less than 0.5%), thus in the following sections, the average of the left and right footing settlements will be presented.

foundation continuously de-amplifies, thus reducing settlement accu­ mulation). However, as shown on Fig. 14b, this mechanism does not apply herein. The observed response can be more realistically explained through the mechanisms discussed in the previous section i.e., moderate liquefaction, a small zone of influence for the footing and footing embedment. For the thicker sand deposits, the influence of these factors is more pronounced, firstly because liquefaction/softening occurs deeper, where there is no interaction with the footing, and secondly because for thicker layers, a larger volume of soil with the tendency to move upward beneath the structure is mobilized.

5.2. Density and thickness of sand Fig. 15 presents the variation of footing settlements with sand thickness for relative density Dr ¼ 40 and 50% (black and red line respectively). These results are for a 1-storey building with Tstr ¼ 0.11 s, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa subjected to ground motion 4312. For Dr ¼ 50% the estimated settlements remain below 1 cm for all cases, as a result of minor excess pore pressure build-up. The results for Dr ¼ 40%, show a more complex response. Initially, settlements increase with Hliq, however, beyond a certain point, the settlements plateau and eventually decrease for thicker sand layers. Similar responses were observed in recent studies [15] and were attributed to the natural base isolation mechanism discussed previously. (As the thickness of the sand increases, the motion transmitted to the

5.3. Presence and properties of nonliquefiable crust The influence of a nonliquefiable crust is demonstrated on Fig. 16 in terms of settlements vs. crust thickness for different values of the normalized undrained shear strength for a 1-storey building (Tstr ¼ 0.11s), Dr ¼ 40%, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa and ground motion 4312. The crust thickness was increased by equally reducing the sand thickness, so that the total thickness of the crust and the sand

Fig. 15. Effect of liquefiable sand properties (relative density and thickness) on settlement accumulation (1-storey, Tstr ¼ 0.11 s, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, Ground Motion 4312).

Fig. 16. Effect of nonliquefiable crust properties (thickness and strength) on settlement accumulation (1-storey, Tstr ¼ 0.11 s, Dr ¼ 40%, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, Ground Motion 4312). 11

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remained constant. The data presented on Fig. 16 correspond to a total crust plus sand thickness of 3.0 m. Focusing first on the case of a stiff crust (black line), it is observed that its presence can substantially reduce foundation settlements. The results show that for a crust thickness of 1.0 m, i.e. less than 1.5 times the footing width, settlements decrease by more than 80% (from 3.0 cm to less than 0.5 cm), while, even for the case of a thinner crust (0.5 m) the decrease is still significant and reaches approximately 50%. The benefit of the crust is less pronounced as the strength of the crust decreases and shear-induced deformations also accumulate in a deformable crust. 5.4. Foundation and structure properties The influence of foundation load as well as the typology and the fundamental period of the building on settlements are presented on Fig. 17. More specifically, the figure shows settlement vs. foundation load curves for the 1-storey building (black line) and the 2-storey building with fundamental period Tstr ¼ 0.10 and 0.22 s (red and green lines respectively). These analyses are for Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, and ground motion 4312. Note that variation of Tstr was achieved by only modifying the lateral stiffness of the structure, while keeping the inertial mass, the geometry and the foundation load constant. As shown on Fig. 17, the estimated settle­ ments tend to increase with foundation load albeit with a progressively decreasing rate. Similar results have been reported previously [13,15, 16] and were related to factors such as the increase in confinement and the shear-induced dilative response of the soil below the footing as settlements accumulate. The predicted settlements for the 1-storey buildings were greater than for the 2-storey buildings, however this is related to the fact that, for the 2-storey buildings, a crawl space was not included. This was verified by comparative analyses with and without crawl spaces, which showed that the presence of soil under the building (between the footings) can reduce settlements. For the ranges consid­ ered, and in accordance with previous studies [15], Tstr appears to have an overall minor effect on settlements. However, it should be noted that the present study considered short and rather stiff structures, whereas the effects might be more pronounced for the case of tall and more flexible buildings which are more sensitive to rocking-induced de­ formations (but would likely require different foundation types for the soil types considered here). The influence of the footing width is presented on Fig. 18a for a 1-sto­ rey building (Tstr ¼ 0.11s) Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, Q ¼ 36 kPa, and ground motion 4312. The results suggest an approxi­ mately linear increase in settlements as the width of the footing

Fig. 18. Effect of foundation properties on settlement accumulation: (a) Footing width and (b) Embedment Depth and crawl space (1-storey, Tstr ¼ 0.11 s, Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, Q ¼ 36 kPa, Ground Mo­ tion 4312).

increases. However, it should be noted that, while the influence appears to be relatively small, the range of values analyzed is not very broad (B ¼ 0.25–0.7m). The influence of foundation embedment and crawl space is demonstrated on Fig. 18b. For the case without a crawl space (red line), the benefit from embedment can be appreciated by considering the D ¼ 0.0 m case, which shows a large increase in foundation settlements (by 3–4 times) compared to footings with D/B > 0.65. As discussed previously, the presence of a crawl space (black line) creates a defor­ mation mechanism which pushes the soil below the foundation up­ wards, thus reducing settlements. 5.5. Ground motion characteristics The influence of different ground motion intensity measures (IM) on foundation settlements is demonstrated on Fig. 19. Fig. 19a–Fig, 19f illustrate, respectively, the effect of significant duration (D5-75), Arias Intensity (Ia), Cumulative Absolute Velocity (CAV), Standardized Cu­ mulative Velocity (CAVdp), Peak Ground Acceleration (PGA) and spec­ tral acceleration at T ¼ 0.7 s (SaT¼0.7s). All parameters have been evaluated at the ground surface from a parallel total stress analysis. Each set of symbols and colors on the figure correspond to a different scenario regarding soil, foundation and structure properties which was analyzed for all eleven ground motions listed in Table 1. The specifics of each scenario are presented in the legend of the figure, while all results correspond to Dr ¼ 40 % and su (πþ2) / Q ¼ 1.5 (for the scenarios where

Fig. 17. Effect of structure properties (Number of storeys and Fixed-base period) on settlements (Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, Ground Motion 4312). 12

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Fig. 19. Effect of surface ground motion characteristics on liquefaction-induced settlements: (a) PGA, (b) D5-75, (c) Ia, (d) CAV, (e) CAVdp and (f) SaT¼0.7s (Dr ¼ 40%, D ¼ 0.9 m, B ¼ 0.70 m).

a crust is present). As shown on these figures, foundation settlements increase system­ atically with ground motion characteristics such as Ia, D5-75, CAV, CAVdp, with the last two showing the best correlations. The foundation settlements do not correlate well with PGA since the high-frequency components do not meaningfully affect liquefaction related phenom­ ena. In contrast, and in line with previous studies [20], a better corre­ lation is observed with spectral accelerations at longer spectral periods (i.e. 0.7 s), which is closer to the soil and to the structure fundamental periods (taking into account Soil-Structure-Interaction). 6. Volumetric settlements The results presented in the previous section were focused on set­ tlements accumulated during shaking, as a result of shear-induced soil deformation. This section focuses on volumetric settlements that accu­ mulate post-shaking, as a result of excess pore pressure dissipation and reconsolidation. Fig. 20 presents the estimated settlements in terms of sand thickness. The black line shows the co-seismic settlements and the red the corresponding volumetric settlements, calculated using the nu­ merical procedure described in section 3.1. A second set of volumetric settlement estimates, shown in green, was obtained using the Ishihara and Yoshimine [3] empirical chart after performing a liquefaction triggering analysis with the assumptions described in section 2.1. The results shown are for a 1-storey building (Tstr ¼ 0.11s), Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, and ground motion 4312. The numerical estimates using the procedure described in Section 3.1, show that the accumulation of volumetric settlements follows the same trend as the co-seismic settlements, i.e. they initially increase with Hliq until they reach a plateau, and eventually reduce for much thicker layers. However, this does not necessarily imply that volumetric set­ tlements depend on the corresponding shear-induced settlements. In general, volumetric settlements are the direct result of excess pore

Fig. 20. Contribution of co-seismic, shear-induced and post-seismic, volu­ metric-induced settlements on the total settlements of the foundation (1-storey, Tstr ¼ 0.11 s, Hliq ¼ 3.0 m, Dr ¼ 40%, Hcr ¼ 0.0 m, D ¼ 0.9 m, B ¼ 0.70 m, Q ¼ 36 kPa, Ground Motion 4312).

pressure build-up, while shear-induced settlements are the result of much more complex mechanisms. For instance, for the case of a footing resting on a thick nonliquefiable crust underlain by a thick liquefiable layer, the shear-induced settlements would be minor (due to the pres­ ence of the crust), however, excess pore pressure build-up within the sand would yield large volumetric settlements. Thus, it was decided not to correlate the post-seismic and the co-seismic settlements. Note that for the specific case shown on the figure, the excess pore pressures developed for the Hliq ¼ 10 m case were low (presumably due to differing soil inertial characteristics), thus leading to smaller volumetric settlements. Quantitatively, for the case shown on the figure as well as 13

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for most of the cases analyzed in the study, it is shown that the postseismic reconsolidation settlements are on the same order of magni­ tude as the co-seismic settlements. The numerical estimates of reconsolidation settlements are generally much lower than those estimated using the simplified 1-D analytical procedure. This is primarily because the simplified methodology over­ estimated the extent of liquefaction and thus excess pore pressure development, while, as described previously (e.g. Fig. 14a) liquefaction occurred only locally within the sand. Secondarily, the numerical ana­ lyses showed that, as a result of the non-uniform excess pore pressure distribution and the presence of the structure, both horizontal and ver­ tical displacement components were observed indicating that reconso­ lidation is not explicitly a 1-D phenomenon. In general, this comparison suggests that for cases of moderate liquefaction, 1-D simplified ap­ proaches can potentially lead to over-conservative estimates of volu­ metric settlements.

In order to select the most suitable IMs for the regression model, several regression analyses were performed using the equation pre­ sented above and considering different intensity measure parameters or combinations of them. It was observed that Arias intensity of the input ground motion provided the best fit to the data while PGA appeared to be the least reliable predictor. Although Arias intensity (Ia) and cumu­ lative absolute velocity (CAV / CAVdp) showed better correlation with settlement, it was decided to use ground motion parameters that were readily available to the practitioners in the study area. For this reason, significant duration at the ground surface, D5-75 [s], and 5%-damped spectral acceleration at 0.7sec period at the ground surface, SaT¼0.7s [g], were selected for the regression model. In light of the above, the final form of the regression equation becomes: �� � lnðsÞ ¼ a0 þ a1 ln Q þ a2 B þ a3 Hcr þ a4 ln tanh Hliq þ a5 Dr þ a6 lnðD5 75 Þ þ a7 lnðSaT¼0:7s Þ þ ε (2)

7. Regression analysis

The regression resulted in the following model coefficients:

α0 ¼ 2.570, α1 ¼ 0.200, α2 ¼ 0.742, α3 ¼ 0.454, α4 ¼ 1.924, α5 ¼ 0.031, α6 ¼ 0.588, α7 ¼ 1.900, and ε is an error term defined as a

The results of the parametric study were regressed to develop a design equation that could be used to estimate liquefaction-induced settlements for typical residential buildings in the study area. Based on the trends identified between liquefaction-induced settle­ ments and the various parameters analyzed, and following the Bray and Macedo [20] approach, several functional forms were investigated to represent the total footing settlement due to liquefaction (i.e. including both co-seismic shear-induced and post-seismic reconsolidation settle­ ments). The functional form that was selected based on the quality of fit to the available numerical results is given by the following equation: �� � lnðsÞ ¼ a0 þ a1 ln Q þ a2 B þ a3 Hcr þ a4 ln tanh Hliq þ a5 Dr þ a6 lnðIM1 Þ

normal random variable with a mean of zero and a standard deviation of 0.458 in natural log units. The accuracy of the proposed equation is evaluated on Fig. 21. Fig. 21a compares the settlements estimated using the equation with the settlements calculated from the numerical ana­ lyses. The concentration of the data points close to the diagonal supports the selection of a linear form to predict the logarithm of settlement. Furthermore, as shown on Fig. 21b, the residuals of the regression analysis are not biased. This is further confirmed on Fig. 21c where the histogram of the residuals is reasonably approximated with a normal distribution function. The error term ε of the predicted total settlement was estimated from the variance of the residuals calculated from the regression analysis.

þ a7 lnðIM2 Þ þ ε (1)

8. Conclusions

where s is the total (co-seismic plus post-seismic) liquefaction-induced settlement of the footing [cm], Q is the footing contact pressure (load) [kPa], B is the width of the footing [m], Hcr is the thickness of the nonliquefiable soil below the footing [m], Hliq is the thickness of the liq­ uefiable soil layer [m], Dr is the relative density of the liquefiable soil [%], IM1 and IM2 are ground motion intensity meaures, α0 to α7 are the regression coefficients, and ε is the error term in natural log units.

The paper presents the outcome of a large study investigating the accumulation of liquefaction-induced settlements of existing residential houses in areas of medium seismicity due to induced activities. Compared to previous relevant studies, this study addresses new chal­ lenges as it: a) involves earthquakes of medium intensity that do not

Fig. 21. Evaluation of proposed equation for the prediction of liquefaction-induced settlements: (a) one-to-one comparison of estimated and measured values, (b) histogram of residuals (c) residuals vs estimated values. 14

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cause complete soil liquefaction, and b) concerns narrow spread footings in lieu of rigid slab foundations. Analyses were performed with an advanced numerical methodology validated against both a welldocumented centrifuge test as well as a case history. A set of more than 500 parametric analyses were performed investigating the effect of all critical, soil, foundation and structure parameters and 11 earthquake motions with a range of characteristics. Analyses showed that the accumulation of settlements is limited as a result of different mechanisms that occur concurrently. Due to the me­ dium intensity of the design earthquake, soil liquefaction occurs only within a narrow zone, approximately 0.5–1.0 m thick. Furthermore, the narrow spread footings employed in the investigation, have a relatively small zone of influence and are not sensitive to liquefaction at depth they mostly interact with the soil close to the footing, which is only partially liquefied. Regarding the various parameters that affect liquefaction-induced soil settlements, the investigation confirmed trends already identified in other studies. The properties of the liquefiable sand are of critical importance, while the presence of a nonliquefiable crust can have a substantial beneficial effect. Settlements are also affected by the foun­ dation pressure and width, while they are rather insensitive to the range of typologies considered and the inertial characteristics of the super­ structure. The ground motion effects can be adequately captured using one of the various intensity measures and the spectral acceleration at a longer period (e.g. SaT¼0.7s). Finally, the contribution of volumetric settlements can represent a significant fraction of the total, although the use of simplified 1-D procedures may produce highly conservative estimates.

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[19]

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Acknowledgements

[23]

The authors would like to acknowledge Rob Jury and the structural team from BICL for providing the structural details of typical residential houses in the study area and input for the modeling of the superstructure in the numerical analyses as well as for collecting field data and obser­ vations for the New Zealand Kaiapoi case history. We would also like to thank Professor Jonathan Bray for providing the Markham et al. [54] input time histories on Riccarton Gravel formation for the New Zealand Kaiapoi case history.

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