FoRDy: Rocking Shallow Foundation Performance in Dynamic Experiments

By Bruce L Kutter, Andreas Gerasimos Gavras, Ioannis Anastasopoulos, Lijun Deng, Sivapalan Gajan, Angelos Tsatsis, Keshab Sharma, Tetsuya Kouno, Manouchehr (Manny) Hakhamaneshi, George Gazetas, Krishnan Athipotta Variam

Version 1.0






Published on

Oct 07, 2019


In recent years, numerous centrifuge (e.g., Rosebrook 2001, Ugalde et al. 2007, Gajan and Kutter 2008, Deng et al. 2012, Hakhamaneshi et al. 2012, Liu et al. 2013, Allmond and Kutter 2014, Loli et al. 2014) and 1g  shake-table (e.g., Shirato et al. 2008, Drosos et al. 2012, Antonellis et al. 2015, Tsatsis and Anastasopoulos 2015) experiments have become available, demonstrating that rocking shallow foundations can be designed to provide recentering and energy dissipation with little permanent damage. Each test series studies specific response aspects by varying soil profiles, structural properties, and ground motions, while still contributing to the larger goal of understanding and predicting dynamic rocking shallow foundation performance. As a result of this cumulative body of research, the concept of intentional mobilization of controlled soil inelasticity and foundation uplift as a rational seismic protection strategy for new and retrofitted structures has been gaining acceptance (e.g., Mergos and Kawashima 2005, Kutter et al. 2006, Anastasopoulos et al. 2010, Pecker et al. 2013, Kutter et al. 2016).

The FoRDy database (Foundation Rocking - Dynamic) contains data from a large subset of these recent dynamic experiments, whereas a separate database compiles data from pseudo-static monotonic and slow-cyclic tests (FoRCy database). Currently, the database compiles results of single-degree-of-freedom-like structures on rocking shallow foundations from five centrifuge and three 1g  shake-table test series. It includes 13 different structures, 18 different soil profiles, over 50 different ground excitations, and a total of 200 event model case histories.

Concept of Rocking Foundations

Figure 1 shows the schematics of two simplified hypothetical structures supported on rocking (as opposed to sliding) shallow foundations under planar ground excitation. Each footing has a length of L  and width of B, parallel and normal to the horizontal ground excitation, respectively, and plan area of A = B∙L. Inertial forces developed at the structures due to ground shaking result in dynamic moment (Mfy), shear load (Vfx), and axial load (Pf) demands at the base centroid of the footings (point O'). These loads can, in turn, cause the base centroid of the footings to rotate (θfy), and slide (ufrx) and settle (sfr = sft - sss) relative to the surrounding soil (ussx and sss in Figure 1 represent the horizontal displacement and settlement of the free-field soil surface).

For non-rigid soil, as the footing rocks, it does not bear on a sharp corner of the footing. Instead, a minimum contact area (Ac) is required to support the axial and shear loads, where Ac = B∙Lc in the case of Figure 1. The moving of the contact area under cyclic rocking results in a curved soil surface below the footing, with localized bearing failure apparent near the edges of the footing (Wiessing 1979), and (typically) progressive footing settlement. However, if Lc < 0.5L  that is typical of rocking foundations that are not heavily loaded statically, the base centroid of the footing will uplift and create a transient gap with the underlying soil. Once the ground excitation ceases, the static axial load causes gap closure and thus provides a natural recentering mechanism.

Figure 1: Dynamic equilibrium schematics of (a) a flexible column superstructure and (b) a stiff wall superstructure on rocking shallow foundations, including nomenclature and sign convention used in the database.

Database Organization


The data is organized and presented in a tabular format in two different Dataviews. The first one is the default DataHub Dataview  (available from the View Data  link of the Resource  page), whereas the second one is customized specifically for the FoRDy database and is available from the FoRDy Parameters  links in the Parameters  column of the first Dataview.

Each row in the Dataviews  describes a single event representing the dynamic response of a specific soil-structure model to a single ground motion. For example, if a test series includes two test days and has five structure stations in the container (Figure 2) that are subjected to a sequence of four input motions per test day, that test series can produce up to 40 single events. The corresponding free-field soil response is integrated within the information of each single soil-structure-motion event and it is not assigned a separate row. It is noted that typical excitation protocols also include small-amplitude input motions (e.g., step waves, sweep waves, white-noise motions) that are used to check sensors and/or evaluate the evolution of the specimen’s fundamental period with shaking progression. These motions result in essentially elastic foundation response and are not included in the database. Dataview Rows Organization table indicates the location of each soil-structure model in the database and provides a high-level description of the soil, footing, structure, and rocking system properties, whereas Database Critical Plots document provides a summary of the critical excitation, foundation, and structure response plots for each database event.

Figure 2: Elevation view of hypothetical model container showing typical examples of structures and nomenclature used in the database (overall drawing not to scale).

The columns of the Dataviews  provide the supplemental information for each event; for the customized Dataview, they are categorized by Test Series Info, Event Info, Soil Profile Properties, Structural Properties, Rocking System Properties, Ground Motion Properties, Performance Results, Miscellaneous, Report(s), Data, Photos, Videos, etc., and Drawings/DiagramsDataview Column Definitions table defines the individual columns of the customized Dataview. Each of these columns is also categorized by the entered data format as either Text, Integer, Floating, Date, or File(s).

Data Files

In addition to the information summarized in the spreadsheets, each event in the database is accompanied by three tab-delimited text files, which are as follows:

  • Critical Data files containing the time series data of selected critical excitation and response parameters;
  • Baseline Corrected Motions files containing the pad-stripped, baseline-corrected time series of the soil base and surface motions; and
  • Response Spectra files containing the 5%-damped linear response spectra of the soil base and surface motions.

Data Files Column Definitions tables provide the default structure and column definitions of the above-described text files. Note that for best viewing of the data files, the Notepad++ text editor is recommended.

Supplemental Information and Illustration of Selected Parameters

Coordinate System

The database uses a common right-handed coordinate system across all tests to define sign-dependent quantities such as generalized accelerations, displacements, and forces. In this coordinate system, x-axis is parallel to the (primary) horizontal ground excitation direction and positive z-axis extends vertically upwards, as shown in Figures 1 and 2. Exceptions to this coordinate system are made in the z-direction: settlement is defined positive as the downward movement of the footing and free-field soil, whereas footing axial load is defined positive as the compressive vertical load at the soil-footing interface.

Use of Abbreviations

When appropriate, the abbreviations N/A, N/M, and N/R  for data of text format, or 7777, 8888, and 9999  for data of numerical format, respectively, are used as follows:

  • Not applicable (N/A  or 7777 ) - when the considered parameter is not applicable to a specific event (e.g., the undrained shear strength for a sand layer);
  • Not measured (N/M  or 8888 ) - when the considered parameter was either not measured in the test, or it has been concluded that measurement is poor/unreliable and should be neglected; and
  • Not reported (N/R  or 9999 ) - when the considered parameter is currently unavailable but there is the possibility that sufficient good quality data has been collected for it to be determined in the future.

Soil Properties

Critical soil profile properties (i.e., layer thickness, relative density or undrained shear strength, total density, and water content) are summarized in the Soil Profile Properties  columns of the customized Dataview. Those interested in the index properties of the soil materials used to construct each layer are referred to the data report and other references relevant to each test series. Index properties for soils used in other experiments at the Center of Geotechnical Modeling facility at the University of California, Davis can be found at FLIQ: Soil Properties (Allmond et al. 2015) and LEAP Soil Properties and element test data (Carey et al. 2017). Please note that the index properties (e.g., emax and emin used for relative density calculations) of Nevada sand, in particular, were observed to vary depending on the sand batch delivery date as noted by Carey et al. (2017).

Footing Shape Parameters

The database includes parameters to describe the shape of footings that are non-rectangular and non-circular, as well as footings with their primary axes rotated with respect to the horizontal ground excitation axes. These parameters are described in the Dataview Column Definitions  table and are also illustrated in the Footing Shape Parameters figure.

Performance Results

Selected response metrics of the rocking systems are provided in the Performance Results  columns of the customized Dataview; these metrics can be grouped as follows:

  • Deformation demands - include the peak, incremental peak, residual, and incremental residual values of the structure drift ratio, and footing rotation and sliding, as well as the residual and incremental residual values of the footing and free-field soil (total) settlement. An example calculation of the above values for a hypothetical footing rotation time series across two shakes is shown in PkResRot Illustration figure. Cumulative footing rotation demand (Deng et al. 2012), conceptually the sum of all the local peaks of the rotation series that exceed an arbitrary threshold rotation, is also included; an example showing the identification of peaks is depicted in cRot Illustration figure.
  • Force demands - include the footing maximum and minimum axial load, maximum absolute shear load and moment, and minimum absolute moment capacity due to reduced transient axial load. An example calculation of the above parameters for two different-intensity motions is shown in MaxMinForces Illustration figure.
  • System softening - assessed by the comparison of the fundamental period of the rocking system before and after the specific event. Note that these metrics are available only if appropriate small-amplitude motions (i.e., step waves, sweep waves, white-noise motions) were included in the motion protocol.

Data Curation

All of the data uploaded to the database has been checked, primarily by the first author, to make sure it is reasonable and consistent. Some of the most important specific checks are listed in the Data Curation Checklist document. It is also important to note the following:

  • The analytical/empirical methods used to calculate the rocking system properties (i.e., FSva, A/Aca0, A/Aca, Mfca, Cr, and T1a) can vary across test series and data contributors. These methods can be conceptually similar but have different details. Since they are based on available literature and their assumptions are consistent with data reported in the database, these differences were considered acceptable and were not part of the data curation process. The details of each method are outlined in the System Properties Calculation Sources  documents located in the Report(s)  column of the Dataview.
  • Sliding displacements of rocking foundations in dynamic experiments are relatively difficult to be determined accurately. The sensors used to determine sliding are usually placed at some distance above the footing base, and therefore, the sensor data is affected by –and need to be corrected against– footing rotation. Furthermore, if the high-frequency transient footing sliding is obtained from footing accelerometers, then this data also needs to be corrected against the transient free-field horizontal displacement, which may vary across the container. While in absolute terms the uncertainty of the sliding displacements is comparable to the uncertainty of other displacements (e.g., footing rotation, deck drift ratio), sliding is typically more uncertain in percentage terms because actual sliding for rocking-dominated footings tends to be small. Thus, it is common that the footing shear load-sliding hysteretic response for many events in the database is less well-defined compared to other hysteretic responses.
  • Pending data curation checks and identified data quality issues at the time of initial publication of the database are summarized in the Comments  documents located in the Report(s)  column of the Dataview.
  • As a result of the data curation process, some modifications to the original data have been made with the consent of the data contributors. These changes are not documented within the database. Whenever discrepancies between the information in the database and provided references are identified, the database should be considered as the more accurate and up-to-date one.

Adding to the Database

We strongly encourage other researchers to submit any existing or new experimental data that can be added to the database. Please contact one of the people listed at the end of this page to determine logistics.  Most likely, one of them will help guide you through the process, and could also provide you with templates and sample MATLAB/Mathcad  routines. To prepare your data for upload, please follow the Data Curation Checklist  described above.

How to Cite this Work

If your work heavily relies upon a small subset of the experimental data (i.e., data from one or two test series), it is strongly recommended that, in addition to citing the FoRDy database, you also cite the researchers that produced this data using the citation(s) provided in the database.


Allmond, J. D. and Kutter, B. L. (2014). “Fluid effects on rocking foundations in difficult soil.” In Proceedings, 10th National Conference on Earthquake Engineering: Frontiers of Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK.

Allmond, J. D., Kutter, B. L., Bray, J., and Hayden, C. (2015). “FLIQ: Foundation and ground performance in liquefaction experiments.”, DOI:10.4231/D3M61BQ73.

Anastasopoulos, I., Gazetas, G., Loli, M., Apostolou, M., and Gerolymos, N. (2010). “Soil failure can be used for seismic protection of structures.” Bulletin of Earthquake Engineering, 8(2), 309-326.

Antonellis, G., Gavras, A. G., Panagiotou, M., Kutter, B. L., Guerrini, G., Sander, A. C., and Fox, P. J. (2015). "Shake table test of large-scale bridge columns supported on rocking shallow foundations." Journal of Geotechnical and Geoenvironmental Engineering, 141(5), 04015009.

Carey, T. J., Kutter, B. L., Manzari, M. T., and Zeghal, M. (2017). "LEAP Soil properties and element test data.", DOI: 10.17603/DS2WC7W.

Deng, L., Kutter, B. L., and Kunnath, S. K. (2012). “Centrifuge modeling of bridge systems designed for rocking foundations.” Journal of Geotechnical and Geoenvironmental Engineering, 138(3), 335-344.

Drosos, V., Georgarakos, T., Loli, M., Anastasopoulos, I., Zarzouras, O., and Gazetas, G. (2012). “Soil- foundation-structure interaction with mobilization of bearing capacity: experimental study on sand.” Journal of Geotechnical and Geoenvironmental Engineering, 138(11), 1369-1386.

Gajan, S. and Kutter, B. L. (2008). “Capacity, settlement, and energy dissipation of shallow footings subjected to rocking.” Journal of Geotechnical and Geoenvironmental Engineering, 134(8), 1129-1141.

Hakhamaneshi, M., Kutter, B. L., Deng, L., Hutchinson, T. C., and Liu, W. (2012). "New findings from centrifuge modeling of rocking shallow foundations in clayey ground." In Proceedings, GeoCongress 2012: State of the Art and Practice in Geotechnical Engineering, Oakland, CA, 195-204.

Hakhamaneshi, M. and Kutter, B. L. (2016) “Effect of footing shape and embedment on the settlement, recentering, and energy dissipation of shallow footings subjected to rocking.” Journal of Geotechnical and Geoenvironmental Engineering, 142(12), 04016070.

Kutter, B. L., Martin, G. R., Hutchinson, T. C., Harden, C., Gajan, S., and Phalen, J. D. (2006). “Workshop on modeling of nonlinear cyclic load-deformation behavior of shallow foundations.” PEER Report No. 2005/14, Pacific Earthquake Engineering Research Center, Berkeley, CA.

Kutter, B. L., Moore, M., Hakhamaneshi, M., and Champion, C. (2016). “Rationale for shallow foundation rocking provisions in ASCE 41-13.” Earthquake Spectra, 32(2), 1097-1119.

Liu, W., Hutchinson, T. C., Kutter, B. L., Hakhamaneshi, M., Aschheim, M. A., and Kunnath, S. K. (2013). “Demonstration of compatible yielding between soil-foundation and superstructure components.” Journal of Structural Engineering, 139(8), 1408-1420.

Loli, M., Knappett, J. A., Brown, M. J., Anastasopoulos, I., and Gazetas, G. (2014). “Centrifuge modeling of rocking-isolated inelastic RC bridge piers.” Earthquake Engineering & Structural Dynamics, 43(15), 2341-2359.

Mergos, P. E. and Kawashima, K. (2005). “Rocking isolation of a typical bridge pier on spread foundation.” Journal of Earthquake Engineering, 9(Sup 2), 395-414.

Pecker, A., Paolucci, R., Chatzigogos, C., Correia, A. A., and Figini, R. (2014). “The role of non-linear dynamic soil-foundation interaction on the seismic response of structures.” Bulletin of Earthquake Engineering, 12(3), 1157-1176.

Rosebrook, K. (2001). “Moment loading on shallow foundations: centrifuge test data archives.” M.S. Thesis, Department of Civil and Environmental Engineering, University of California, Davis, Davis, CA.

Shirato, M., Kouno, T., Asai, R., Nakatani, S., Fukui, J., and Paolucci, R. (2008). “Large-scale experiments on nonlinear behavior of shallow foundations subjected to strong earthquakes.” Soils and Foundations, 48(5), 673-692.

Tsatsis, A. and Anastasopoulos, I. (2015). “Performance of rocking systems on shallow improved sand: shaking table testing.” Frontiers in Built Environment, 1, 9.

Ugalde, J. A., Kutter, B. L., Jeremić, B., and Gajan, S. (2007). “Centrifuge modeling of rocking behavior of bridges on shallow foundations.” In Proceedings, 4th International Conference on Earthquake Geotechnical Engineering, Thessaloniki, Greece, Paper No. 1484.

Wiessing, P. R. (1979). “Foundation rocking on sand.” M.E. Thesis, Report No. 203, School of Engineering, University of Auckland, Auckland, New Zealand.

Please submit questions regarding this database by using the Questions  tab, or by email to Andreas Gavras (This email address is being protected from spambots. You need JavaScript enabled to view it.), Bruce Kutter (This email address is being protected from spambots. You need JavaScript enabled to view it.), or Manouchehr Hakhamaneshi (This email address is being protected from spambots. You need JavaScript enabled to view it.).

Cite this work

  • Bruce L Kutter, Andreas Gerasimos Gavras, Ioannis Anastasopoulos, Lijun Deng, Sivapalan Gajan, Angelos Tsatsis, Keshab Sharma, Tetsuya Kouno, Manouchehr (Manny) Hakhamaneshi, George Gazetas, Krishnan Athipotta Variam (2019), "FoRDy: Rocking Shallow Foundation Performance in Dynamic Experiments,"


Shear Walls, Dynamic Response, shallow foundations, Physical modeling, Centrifuge modeling, Shaking table testing, Bridge piers, Nonlinear soil-structure interaction, Seismic testing, Foundation rocking