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Copyright, Mxico, 2010 Sociedad Mexicana de Ingeniera Geotcnica, A.C. Valle de Bravo No. 19 Col. Vergel de Coyoacan, 14340 Mxico, D.F., MXICO Tel. +(52)(55)5677-37-30, Fax+(52)(55)5679-36-76 Pgina web: www.smig.org.mx Correo electrnico: [email protected] ISBN 978-607-95506-1-5 Prohibida la reproduccin parcial o total de esta publicacin, por cualquier medio, sin la previa Autorizacin escrita de la Sociedad Mexicana de Ingeniera Geotcnica, A.C. Total or partial reproduction of this book by any medium requires prior written consent of the Sociedad Mexicana de Ingeniera Geotcnica, A.C. Las opiniones expresadas en este volumen son responsabilidad exclusiva de los autores. Opinions expressed in this volume are the sole responsibility of their authors. Edicin: Norma Patricia Lpez Acosta. Revisin de formato: Jos Luis Lezama Campos y Cupertino Garca Flores.
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SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
CONSEJO DE HONOR Leonardo Zeevaert Wiechers
Ral J. Marsal Crdoba Alfonso Rico Rodrguez Enrique Tamez Gonzlez
Guillermo Springall Caram Edmundo Moreno Gmez
Carlos Jess Orozco y Orozco Luis Vieitez Utesa
Gabriel Moreno Pecero Ral Lpez Roldn
Ral Flores Berrones Luis Miguel Aguirre Menchaca
Gabriel Auvinet Guichard Luis Bernardo Rodrguez Gonzlez
Ral Vicente Orozco Santoyo
CONSEJO CONSULTIVO Mario Jorge Orozco Cruz
Juan Jacobo Schmitter Martn del Campo Hctor M. Valverde Landeros
Jos Francisco Fernndez Romero Rigoberto Rivera Constantino
MESA DIRECTIVA
Walter Ivn Paniagua Zavala Presidente
Alberto Cuevas Rivas Vicepresidente
Felipe F. Cancino Lpez Secretario
Juan de Dios Alemn Velsquez Tesorero
Margarita Puebla Cadena Ricardo E. Ortz Hermosillo
Ricardo R. Padilla Velzquez Carmelino Zea Constantino
Vocales
COMIT ORGANIZADOR XXV RNMS e IG Ricardo Enrique Ortz Hermosillo
Norma Patricia Lpez Acosta Alexandra Ossa Lpez
Juan Pauln Aguirre Juan Flix Rodrguez Rebolledo
Oscar Jess Luna Gonzlez Juan Jacobo Schmitter Martn del Campo
Luis Bernardo Rodrguez Gonzlez Walter Ivn Paniagua Zavala
Juan de Dios Alemn Velsquez
COMIT ORGANIZADOR XVI RNPMS e IG
Ricardo R. Padilla Velzquez Margarita Puebla Cadena
Carmelino Zea Constantino Rosemberg Reyes Ramrez
Paul Garnica Anguas
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2010
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XXV Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica
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Prlogo En el barco de la Sociedad Mexicana de Ingeniera Geotcnica no hay pasajeros; todos somos tripulacin.
Como cada dos aos la Mesa Directiva de la Sociedad Mexicana de Ingeniera Geotcnica (SMIG) en turno organiza con entusiasmo su Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica (RNMSeIG).
En esta ocasin, el Comit Organizador de la XXV RNMSeIG decidi programar quince Sesiones Tcnicas y dos Conferencias Plenarias. Cabe decir que es la primera vez que en una reunin nacional se presentan las Sesiones de Presas de Jales, Instrumentacin, Mecnica de Rocas, y Normatividad y Prctica Profesional. Por otro lado, en cada una de las Sesiones Tcnicas se incluy una Conferencia Magistral; para las que fueron invitadas reconocidas personalidades de la Ingeniera Civil Nacional e Internacional. Con respecto a las Conferencias Plenarias estuvieron como invitados el Ing. Federico Mooser y el Prof. Jean-Louis Briaud. En estas memorias se incluyen dichas participaciones, adems de las Conferencias Magistrales y de los ms de cien artculos de distinguidos ingenieros geotecnistas de todo el pas, todos ellos con alta calidad tcnica.
Por otro lado, es importante reconocer que este evento representa la culminacin de un esfuerzo realizado en equipo. En particular, se agradece la participacin activa de las siguientes personas: Alexandra Ossa Lpez, Coordinadora de las Sesiones de Presas, Cimentaciones y Mecnica de Rocas; Juan Paulin Aguirre, Coordinador de las Sesiones de Mejoramiento de Suelos, Geoambiental, Ingeniera Ssmica, Geotecnia y Estructuras, y Normatividad y Prctica Profesional; Juan Flix Rodrguez Rebolledo, Coordinador de las Sesiones de Modelado Numrico y Obras Subterrneas; y Ricardo E. Ortiz Hermosillo, Coordinador de las Sesiones de Caracterizacin de Suelos, Geotecnia Marina y Obras Portuarias, y Presas de Jales.
De igual manera, se agradece a las siguientes personas por sus valiosas opiniones durante los desayunos de trabajo que se llevaron a cabo para la organizacin de este importante evento: Juan Jacobo Schmitter Martn del Campo, Oscar Jess Luna Gonzlez, Juan de Dios Alemn Velsquez y Luis Bernardo Rodrguez Gonzlez. Tambin se agradece a los panelistas invitados por sus contribuciones, as como a los Presidentes de Sesin por su colaboracin desinteresada antes y durante la XXV RNMSeIG.
Finalmente, se da un especial reconocimiento y agradecimiento a la Dra. Norma Patricia Lpez Acosta y a su equipo de trabajo por su importante apoyo en la revisin de formato de todos los artculos que se presentan en estas memorias, as como por su paciencia y dedicacin en la edicin de las mismas.
Walter Ivn Paniagua Zavala
Presidente SMIG Mesa Directiva 2009-2010
Ricardo Enrique Ortiz Hermosillo Presidente Comit Organizador XXV RNMSeIG Mesa Directiva 2009-2010
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CONFERENCIAS PLENARIAS........... 1
Estructura geolgica del granito de Acapulco y sus alrededores M. Cruz-Almanza y F. Mooser-Hawtree..................... 3
Excavation support using deep mixing technology J. L. Briaud y C. J. Rutherford 7
SESIN 1. OBRAS SUBTERRNEAS.. 31 Conferencia Magistral Anlisis, diseo, construccin y comportamiento de obras subterrneas en suelos
G. Auvinet y J. F. Rodrguez... 33 Aportaciones Diseo geotcnico-estructural de dovelas para tneles en suelos blandos
A. S. Menache.. 43
Construccin de un tnel para Metro con escudo EPB en la zona de Lago de la ciudad de Mxico
I. Benamar y D. A. Zaldvar 51
Mtodo analtico para el clculo de presiones laterales y elementos mecnicos en recubrimientos de lumbreras
D. H. Palencia, B. C. Mndez, E. Botero y M. P. Romo. 59
Confiabilidad de lumbreras realizadas por el mtodo de flotacin V. D. Orduo y G. Auvinet.. 67
Estabilidad, por formacin de cuas, para un tnel en roca J. Rodrguez y G. Franco 75
Influencia de las variaciones de la presin de poro en el comportamiento del revestimiento primario de tneles construidos en suelos blandos
J. L. Rangel-Nez, E. Ibarra-Razo y R. Domnguez-Pea 83
Prueba de carga en un modelo a escala real de un tnel de dovelas con revestimiento secundario
O. S. Aguilar, L. R. Mendoza, E. A. Tavera, Y. Alberto y J. Morelos. 87
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Comentarios sobre las cargas que actan sobre el tnel de dovelas en el tramo Atlalilco Mexicaltizingo, Lnea-12
L. B. Rodrguez y B. Soria... 97
SESIN 2. MEJORAMIENTO DE SUELOS.. 103 Conferencia Magistral Mejoramiento de suelo con Jet Grouting, para tneles de interconexin
R. Monroy-Salgado, R. Gonzlez-Parilli, J. Morey y J. Pauln-Aguirre 105 Aportaciones Mejoramiento de las condiciones mecnicas del suelo para evitar la falla por extrusin
L. E Gutirrez.......... 111
Inyeccin de compactacin como mitigacin del potencial de licuacin. Mtodo de diseo I. Henrquez-Pantalen, C. Oteo-Mazo y G. Armijo-Palacio. 117
Evaluacin del potencial de licuacin de los suelos y su mejoramiento donde se construye la Terminal de Gas Natural Licuado cerca de la Ciudad de Manzanillo, Colima
R. Martnez-Rojas... 127
Construccin de pantalla perimetral impermeabilizante, previa a la excavacin de muros Miln, para una lumbrera
J. D. Valencia y J. J. Schmitter... 139
Ground improvement of tunnels by means of fiberglass anchors A. Corba.. 147
Tratamiento de arcillas expansivas mediante estabilizacin y aplicacin de carga T. Lpez-Lara, J. B. Hernndez-Zaragoza, J. Horta-Rangel, J. A. Zepeda-Garrido, J.C. Rodrguez-Uribe y V. M. Castao-Meneses 153
Estudio de la eficiencia de algunos materiales utilizados para sustituir arcillas expansivas T. Lpez-Lara, J.B. Hernndez-Zaragoza, J. Horta-Rangel, J.A. Zepeda-Garrido H. Hernndez-Villares 159
SESIN 3. MECNICA DE ROCAS.. 167 Aportaciones Corte carretero realizado en una formacin rocosa de precaria estabilidad
S. Herrera, J. J. Schmitter, J. Colonia, V. H. Macedo y E. A. Reynoso. 169
Anlisis geolgico geotcnico para el desplante de la cimentacin del muro de reposicin del plinto del P.H. La Yesca
E. Montiel y V. Pez 177
Anlisis geotcnico preventivo en la estabilidad de taludes de la estructura de control del P.H. La Yesca
E. Montiel 187
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Derrumbe de grandes dimensiones en el portal de tnel carretero, problemtica geolgica y soluciones implementadas
V. H. Macedo, P. L y A. Castro. 195
Soluciones geotcnicas de proteccin para evitar daos por cados de roca al pie de una ladera natural
A. Rbago-Martn... 203
The unvirgin theoretical equation of compressibility applied to grainstone rockfill E. Jurez-Badillo 213
SESIN 4. CARACTERIZACIN DE SUELOS... 215 Conferencia Magistral Some geotechnical properties to characterize Mexico City Clay
E. Ovando-Shelley... 217 Aportaciones Actualizacin de la zonificacin geotcnica del valle de Toluca, en el Estado de Mxico
G. Garca-Rocha, R. Rodrguez-Gonzlez, F. Garca-Cruz, M. Martnez-Govea y B. Silva-Zrate. 229
Estudios preliminares de microzonificacin ssmica para la ciudad de Coatzacoalcos, Ver. J. A. Guzmn, F. de J. Trejo, F. Williams, G. Riquer, R. Leyva y J. Lermo................... 241
Propuesta de zonificacin geotcnica de la zona urbana de la ciudad de Coatzacoalcos, Ver.
L. Astudillo, J. A. Guzmn, F. de J. Trejo, F. Williams, G. Riquer y R. Leyva.. 247
Una investigacin sobre los mdulos de deformabilidad y compresibilidad de los fenmenos de expansin y recompresin en suelos finos saturados
C. Zea, R. Rivera y G. Lpez, J. L. Umaa y E. Elizalde 253
Suelos expansivos A. Jaime y R. J. Ballinas. 259
Comparacin entre los valores tericos y reales de los asentamientos de un terrapln desplantado en suelos arcillosos muy blandos, y observado a lo largo de tres aos
H. Moreno y A. Smano.. 269
Propagacin de ondas dinmicas en muestras de suelos en una cmara triaxial M. Flores-Guzmn, E. Ovando-Shelley y C. Valle-Molina 277
Prueba de campo para control del mdulo de deformacin de un relleno granular con una fraccin arcillosa significativa
H. Moreno y A. M. Lpez 283
Caracterizacin del material denominado Tepetate T. Lpez-Lara, J. B. Hernndez-Zaragoza, J. Horta-Rangel, M. L. Prez-Rea, D. Rosales-Hurtado y V. M. Castao-Meneses.. 289
Caracterizacin de las arcillas expansivas de San Francisco Totimehuacan, Puebla O. Linares, O. Flores, A. Hernndez y A. Aguilar.. 295
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Caracterizacin geotcnica del subsuelo en el Circuito Interior E. Mndez, G. Auvinet, M. Jurez y U. Matus 303
Caracterizacin de anomalas geotcnicas en las zonas lacustre y de transicin de la ciudad de Mxico
E. Mndez, U. Matus, G. Auvinet y M. Jurez 311
Caracterizacin de las arcillas blandas de la zona oriente del Valle de Mxico A. Vzquez, O. Flores y M. P. Romo... 323
Contribucin a la caracterizacin geotcnica de la zona norte de la cuenca de Mxico M. Jurez, G. Auvinet, F. Hernndez y E. Mndez. 333
Contribucin a la caracterizacin geoestadstica del subsuelo del sur del valle de Mxico M. Jurez, G. Auvinet, A. Barranco y E. Mndez... 345
Prediccin de deformaciones a largo plazo en arcillas sensitivas A. Demneghi.. 353
Determinacin experimental de la reologa fraccional en suelos A. Hermosillo, R. Magaa, O. Flores y M. P. Romo..
363
Presente y futuro de los estudios geotcnicos en Mxico aplicables a proyectos de lneas de transmisin y parques elicos
A. Lpez-Contreras. 371
Sobre la conveniencia de crear un campo de pruebas geotcnicas en un sitio del ex Lago de Texcoco
M. J. Mendoza-Lpez.. 387
Basic stress strain equation for clays E. Jurez-Badillo 393
Identificacin de suelos expansivos y colapsables R. V. Orozco y I. Y. Orozco. 407
Dispersin de ondas superficiales aplicadas a la caracterizacin dinmica del suelo y estructuras
E. Martnez, E. Snchez, S. Fernndez, M. Dvila y A. Uribe... 411
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SESIN 5. GEOAMBIENTAL...... 417 Aportaciones Recomendaciones geotcnicas en la planeacin de muestreos ambientales de sitios contaminados por hidrocarburos
J. J. Torres-Garca y M. L. Prez-Rea 419
Aspectos geotcnicos en el diseo, construccin, operacin y clausura de rellenos sanitarios en Mxico
N. Parra-Piedrahita, E. Ovando-Shelley, M. Trigo-Lara y R. Contreras-Galvn. 427
Capacidad de absorcin de agua del poliestireno expandido EPS, bajo diferentes condiciones de esfuerzo
A. Ossa y M. Romo.. 437
Pantalla flexo-impermeable para remediacin de suelos contaminados en la Refinera 18 de Marzo, en la ciudad de Mxico
W. Paniagua, J. A. Valle y A. Elvira... 445
SESIN 6. CIMENTACIONES................................................................................ 451 Conferencia Magistral Anlisis y diseo de cimentaciones: una comparacin de prcticas
A. Jaime y S. E. Jurez 453 Aportaciones Mejoramiento de suelos a base de pilas de agregado compactado para la cimentacin del Centro de Distribucin Herdez, en el Estado de Mxico
P. Prez, H. M. Valverde y A. M. Gutirrez... 463
Interaccin ssmica suelo-estructura en pilotes y pilas de cimentacin; caso III J. Medina......... 471
Nuevo procedimiento de re-nivelacin de edificios A. S. Menache y J. J. Alonso... 481
Modelacin de cimentaciones superficiales sobre suelos potencialmente expansivos J. F. Romero-Zepeda, A. Prez-Garca, A. Zepeda-Garrido, T. Lpez-Lara, D. Hurtado-Maldonado y J. Horta-Rangel.
489
Validacin de ndices de esfuerzo para tres tipos de suelo bajo cimentaciones rectangulares uniformemente cargadas
D. Miramontes 501
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Cimentaciones de estructuras sobrecompensadas y excntricas: casos prcticos E. B. Valle, J. A. Segovia y R. Alans.. 511
Tcnicas de subexcavacin J. Hernndez-Chias, E. Ovando-Shelley y E. Santoyo............................. 521
Aplicaciones de la pantalla de precorte V. Hernndez, E. Santoyo y J. Segovia... 531
Uso de inclusiones rgidas en suelos blandos de origen lacustre E. Holgun, L. Vega, E. Santoyo y R. Contreras. 541
Casos prcticos de taludes permanentes J. A. Segovia, E. Len y R. Contreras. 549
Pruebas de carga axial y lateral para control y aseguramiento de calidad en pilas de la Terminal de Gas Licuado en Manzanillo, Colima
W. Paniagua, A. Elvira y E. Ibarra. 555
Diseo y construccin de foso con muro Miln para silo de almacenamiento de grano W. Paniagua, E. Ibarra y A. Elvira. 563
Discontinuidades e irregularidades en pilas, detectadas con pruebas de integridad W. Paniagua, A. Elvira, E. Ibarra, J. L. Gonzlez y J. L. Rangel.. 569
Estudio experimental sobre la influencia de la rugosidad en la capacidad de carga por fuste de pilas coladas in situ en medios granulares
E. Ibarra y M. J. Mendoza.. 577
Capacidad de carga axial de un modelo de pilote instrumentado: una revisin de los mtodos Alfa y Beta
M. Rufiar, M. J. Mendoza y E. Ibarra......................................................... 585
Pruebas de carga axial a compresin y extraccin en pilas de cimentacin instrumentadas del Viaducto Bicentenario, Estado de Mxico
M. J. Mendoza, E. Ibarra, M. P. Romo, M. Rufiar, J. M. Mayoral, W. Paniagua y E. Garcs. 595
SESIN 7. INSTRUMENTACIN.......................................................................... 605 Aportaciones Resultados del sistema de instrumentacin geotcnica de la zona inestable en la margen izquierda de la presa La Yesca
E. Torres y G. Prez 607
Variacin de la relacin k0 en un subsuelo arcilloso, durante el paso de un escudo presurizado
L. E. Gutirrez y J. J. Schmitter.. 613
Instrumentacin de los bordos del ro de La Compaa y anlisis de las mediciones, del km 0+000 al km 10+360
R. Gmez, E. Gutirrez y R. Hernndez.. 619
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Aspectos relevantes para la instalacin y medicin de inclinmetros J. F. Gonzlez-Valencia.. 629
El impacto de las mediciones en los procesos de anlisis, diseo y toma de decisiones M. T. Santaella 635
Instrumentacin del deslizamiento en el Canal Juan del Grijalva, Chiapas A. Vargas. 641
Programa de cmputo para la prueba de consolidacin en equipo instrumentado E. Vsquez, A. Muoz, F. Olivera, C. Cabrera y C. Dumas... 649
Instrumentacin geotcnica en lumbreras de gran dimetro R. Contreras, I. Rivera y M. Trigo.. 657
Instalacin de piezmetros mltiples con inyeccin de grout en el Valle de Mxico R. Contreras, P. Choquet y I. Rivera.. 667
Instrumentacin y monitoreo de la ladera de un puente en la autopista Cuernavaca Acapulco
O. Lpez, G. Servn y E. Santoyo 677
Automatizacin de un consolidmetro neumtico O. Flores, E. Gmez, S. Hernndez y D. Carren.................. 683
Diseo y construccin de un mdulo de adquisicin porttil E. Gmez, G. Velasco, O. Flores y S. Hernndez................... 691
Instrumentacin y automatizacin de una celda Rowe O. Flores, E. Gmez, M. P. Romo y A. Vzquez. 699
SESIN 8. INGENIERA SSMICA..................................................................... 707 Conferencia Magistral Aspectos geotcnicos que controlan la respuesta ssmica en estructuras diseadas conforme a reglamento
J. Avils... 709 Aportaciones Efectos de la variabilidad de los movimientos del terreno en la respuesta ssmica de un paso vehicular elevado
J. M. Mayoral, J. Z. Ramrez y F. A. Flores... 717
Evaluacin de los movimientos ssmicos incoherentes en estructuras lineales E. Botero, B. C. Mndez y M. P. Romo... 727
Mesa vibradora hidrulica para ensayes geossmicos B. C. Mndez, E. Botero y M. P. Romo... 733
Comportamiento dinmico de una estructura metlica miniatura por cambios en la estratigrafa
S. Hernndez, A. E. Posada y C. Balmaceda.. 743
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Estudio de vibracin ambiental en arreglos instrumentales en la ciudad de Monterrey, Nuevo Len
R. Vzquez, J. Aguirre, H. Mijares y J. C. Montalvo.. 751
Efectos geotcnicos y estructurales observados en el valle y ciudad de Mexicali, provocados por el sismo El mayor-Cucupah del 4 de abril del 2010
J. L. Rangel-Nez, A. Tena-Colunga y A. Gmez-Bernal. 765
Aspectos geotcnicos en los daos en Concepcin, Chile, debidos al terremoto (Mw 8.8) del 27 de febrero de 2010
M. J. Mendoza-Lpez, E. Ovando-Shelley, F. A. Villalobos-Jara, M. Rodrguez-Gonzlez y P. Orstegui.
781
Movimientos efectivos debidos a la interaccin cinemtica L. E. Prez-Rocha y J. Avils-Lpez... 793
SESIN 9. PRESAS..................................................................................................... 805 Aportaciones Evaluacin de la estabilidad de taludes en las presas del S.H. de Necaxa
N. Melchor, R. Ruedas y O. Nava........................................................... 807
Efecto de la zonificacin de los materiales en la respuesta ssmica de presas de enrocamiento con cara de concreto
N. Sarmiento y M. P. Romo. 817
Esfuerzos de compresin en la cara de concreto en presas de enrocamiento de gran altura N. Sarmiento y M. P. Romo. 825
Diseo de los tratamientos de impermeabilizacin-consolidacin en la cimentacin y empotramientos del P.H. La Yesca
J. A. Lpez-Molina, J. A. Valencia y J. A. Espinosa... 831
Fuerzas de filtracin y efectos de sumersin en taludes granulares de presas y bordos X. Li-Liu.. 841
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SESIN 10. GEOTECNIA Y ESTRUCTURAS.................................................. 849 Contribucin especial Developments in elastic settlement estimation procedures for shallow foundations on granular soil
Braja M. Das... 851 Aportaciones Esfuerzo horizontal producido por una carga rectangular horizontal uniforme aplicada en el interior de un slido
J. Medina..... 871 Estudio preliminar sobre la caracterizacin de morteros para la inyeccin de minas localizadas en el Municipio de Atizapn, Estado de Mxico
R. Ortz y J. Chvez. 877 Diagnostico de agrietamiento de casas habitacin en Guadalupe Nuevo Len
A. Trejo 889 Base de datos de deslizamientos inducidos por sismo y lluvia en Mxico para calibrar un modelo de anlisis de talud infinito
M. A. Jaimes, M. Nio, E. Reinoso y R. Carlos.. 895 Desplazamiento horizontal de una casona catalogada en la ciudad de Mxico
E. B. Valle, J. A. Segovia y E. Santoyo... 903 Estabilidad de laderas y taludes
A. Jaime, A. Coliente y V. H. Medrano-Rivera............................................... 911 Estudio geolgico - geotcnico para la ampliacin de la Central Hidroelctrica El Infiernillo (CHI), ro Balsas, Michoacn Guerrero
J. Snchez y O. Ortz... 921
SESIN 11. MODELADO NUMRICO........................... 929 Conferencia Magistral Recent developments on modelling time-dependent behaviour of soft natural clays
M. Karstunen, M. Rezania, N. Sivasithamparam, M. Leoni y Zhen-Yu Yin.................... 931 Aportaciones Calibracin de modelos de elemento finito para el anlisis de interaccin suelo-pila
J. M. Mayoral y J. Z. Ramrez. 939
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Evaluacin del riesgo aceptable por deslizamientos de taludes en regiones tropicales montaosas: Caso Medelln
P. A. Isaza-Restrepo y H. E. Martnez-Carvajal. 949 Anlisis con MEF de secuencias de excavacin en lumbreras
J. G. Clavellina, J. Pauln, . J. Luna, A. Pantoja y A. G. Lira..... 959 Modelacin con elementos finitos de la prueba de integridad en una pila de cimentacin
J. F. De la Mora y J. L. Gonzlez... 965 Anlisis numrico de los movimientos del suelo generados por la construccin de tneles en arcillas muy blandas
J. M. Mayoral y F. A. Flores... 969 Efecto de la flexibilidad del muro y del apoyo en la respuesta ssmica de lumbreras
L. E. Prez-Rocha y J. Avils-Lpez... 979 Efectos de las filtraciones en condiciones de flujo establecido en lumbreras de gran profundidad
N. P. Lpez-Acosta, M. A. Prez y G. Auvinet 989 Importancia de las condiciones de frontera en el anlisis numrico de taludes
B. C. Mndez, E. Botero y M. P. Romo... 999 Capacidad de carga de celdas estructuradas: Un mtodo de anlisis simplificado
S. A. Martnez-Galvn y M. P. Romo.. 1005 Correlacin de imgenes digitales y su aplicacin a la geomecnica
M. Orozco-Caldern, S. A. Hall, T. Lam-Nguyen y L. N. Equihua-Anguiano... 1015 Modelado numrico del comportamiento de un pilote sometido a friccin negativa y cargas accidentales
J. F. Rodrguez y G. Auvinet... 1023 rbol de regresin para determinar el potencial de licuacin: ARELI
S. R. Garca, M. P. Romo y E. Ovando... 1031 Capacidad de carga de celdas estructuradas sujetas a momento de volteo: Un mtodo de anlisis simplificado
S. A. Martnez-Galvn y M. P. Romo.. 1041 Puntos a considerar en los modelos para anlisis geotcnico empleando el programa de elemento finito Plaxis 3D Tunnel
. J. Luna, A. G. Lira, J. M. Reyes, S. F. Zaldvar y J. C. Vzquez... 1053
SESIN 12. PRESAS DE JALES.............................................................................. 1059 Conferencia Magistral La ingeniera geotcnica en las presas de jales mexicanas
R. V. Orozco
1061 Aportaciones Anlisis de estabilidad para la ampliacin y elevacin de una presa de jales en Zacatecas
C. Dumas..................... 1069
Pgina
XXV Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica ndice Volumen 3
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C. xix
La normatividad ambiental en materia de presas de jales
O. Briseo-Senosiain.. 1075 Consideraciones sobre la normatividad mexicana para presas de jales
J. F Fernndez-Romero.. 1083 La importancia de incorporar temas relacionados con las presas de jales en los planes de estudio de las carreras de Ingeniera de Minas y Metalurgia
Santos J. J. E., Guzmn H. V. y Chacn W. L. 1087 Diseo geotcnico de una presa de jales en el estado de Hidalgo
O. Flores, H. R. Aguilar, L. Reyes y R. V. Orozco.. 1095
SESIN 13. NORMATIVIDAD Y PRCTICA PROFESIONAL............... 1107 Aportaciones Desplome de un conjunto de edificios. El calvario de un propietario
E. Rojas, D. Hurtado, A. Zepeda y M. L. Prez-Rea.. 1109 Certificacin profesional de los ingenieros civiles
E. Castilla... 1121 La interaccin suelo-estructura no es un mito
A. Vzquez... 1125 Campo de actividad profesional del Ingeniero Civil, Geotecnista (ICG)
J. J. Schmitter...... 1129
SESIN 14. GEOTECNIA MARINA Y OBRAS PORTUARIAS................ 1133 Conferencia Magistral CPT for soft sediments and deepwater soil investigations
P. K. Robertson... 1135 Aportaciones Factores indispensables para el diseo geotcnico y geofsico de proyectos costa afuera
L. N. Equihua-Anguiano..... 1147 Alternativa de cimentacin para la construccin de tetrpodos en el patio de la terminal martima de Cobos en Tuxpan, Veracruz
D. J. Albarrn......... 1153 Modelos de interaccin suelo-ducto para aguas profundas
M. Orozco-Caldern y P. Foray............. 1159 Visualizacin del mecanismo de ruptura del penetrmetro mini T-bar
M. Orozco-Caldern, A. Puech y P. Foray..................... 1165 Prediccin de la velocidad de onda cortante de depsitos marinos arcillosos
V. M. Taboada, Xingnian Chen, C. Cardona, K. C. Gan, D. Cruz, P. Barrera, E. Espinosa, C. Gonzlez y D. Carrasco............................................................. 1175
Pgina
ndice XXV Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica Volumen 3
xx SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Mejores prcticas para la definicin de proyectos, caso PEMEX-PEP y UNAM
F. Fuentes-Nucamendi, J. A. Ruz-Garca y M. Orozco-Caldern. 1185
SESIN 15. VAS TERRESTRES............................................................................ 1193 Conferencia Magistral Sobre los cambios esperados en el mdulo de resiliencia de un suelo compactado y sus implicaciones en diseo de pavimentos
P. Garnica-Anguas.. 1195 Aportaciones Estimacin de mdulos elsticos en pavimentos usando redes neuronales artificiales
G. Beltrn y M. P. Romo. 1201 Evaluacin de la relacin mdulo de resiliencia-succin para suelos finos compactados
N. Prez-Garca, P. Garnica-Anguas y H. Nute-Vargas 1209 Evaluacin de la curva caracterstica en trayectoria de secado y su aplicacin en el modelo climtico integrado de la gua de diseo AASHTO emprico-mecanicista
N. Prez-Garca y P. Garnica-Anguas........... 1215 The principle of natural proportionality applied to the creep of compacted recycled asphalt pavement
E. Jurez-Badillo............ 1221 Variacin del mdulo de resiliencia en tezontle sometido a cambios de humedad relativa
C. Chvez-Negrete, J. Alarcn-Ibarra, E. Arreygue-Rocha, T. Domnguez-Tllez, F. J. Jernimo-Rodrguez y T. A Hurtado-Solrzano..... 1227
Estabilizacin fsico-qumica de suelos arcillosos con aditivos elaborados con precursores nano-mtricos (Parte I: Evaluacin mecnica)
C. Chvez-Negrete, J. C. Rubio-Avalos, J. Alarcn-Ibarra, E. Arreygue-Rocha y E. O. Cervantes-Gutirrez....................................... 1235
Modernizacin del laboratorio de vas terrestres del Instituto de Ingeniera, UNAM A. H. Noguera, E. Ovando-Shelley y F. A. Rangel-Ordez.. 1241
Tneles carreteros A. Jaime P. y B. R Cuenca.. 1245
Falla sbita de un terrapln apoyado sobre suelo arcilloso, que al fallar se comport como un lquido
J. J. Schmitter, R. V. Orozco, S. Vzquez y L. Reyes.................................................. 1255 Aplicacin del Phicmetro en el anlisis de la estabilidad de taludes
O. Lpez-Velzquez, F. Sosa y E. Santoyo............................................. 1261 Rehabilitacin y reforzamiento de un corte en la autopista Cuernavaca-Acapulco
O. Lpez-Velzquez, J. Cosme y E. Santoyo... 1269
Pgina
Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica
Sesin 10:
Geotecnia y estructuras
XXV
XXV Reunin Nacional de Mecnica de Suelos e Ingeniera Geotcnica
Acapulco, Gro., del 11 al 13 de noviembre de 2010
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
1 INTRODUCTION
The estimation of settlement of shallow foundations is an important topic in the design and construction of buildings and other related structures. In general, settlement of a foundation consists of two major componentselastic settlement (Se) and consolidation settlement (Sc). In turn, the consolidation settlement of a submerged clay layer has two parts; that is, the contribution of primary consolidation settlement (Sp) and that due to secondary consolidation (Ss). For a foundation supported by granular soil within the zone of influence of stress distribution, the elastic settlement is the only component that needs consideration. This paper is a general overview of various aspects of the elastic settlement of shallow foundations supported by granular soil deposits. During the last fifty years or so, a number of procedures have been developed to predict elastic settlement; however, there is a lack of a reliable standardized procedure.
2 ELASTIC SETTLEMENT CALCULATION PROCEDURESGENERAL
Various methods to calculate the elastic settlement available at the present time can be divided into two general categories. They are as follows:
a) Methods Based on Observed Settlement of Structures and Full Scale Prototypes. These methods are empirical or semi-empirical in nature and are correlated with the results of the standard in situ tests such as the standard penetration test (SPT), the cone penetration test (CPT), the flat dilatometer test, and the pressurementer test (PMT). The procedures usually referred to in practice now are those developed by Terzaghi and Peck (1948, 1967), Meyerhof (1956, 1965), DeBeer and Martens (1957), Hough (1969), Peck and Bazaraa (1969),
Schmertmann (1970), Schmertmann et al. (1978), Burland and Burbidge (1985), Briaud (2007), and Lee et al. (2008).
b) Methods Based on Theoretical Relationships Derived from the Theory of Elasticity. The relationships for settlement calculation available in this category contain the term modulus of elasticity (Es).
The general outline for some of these methods is given in the following sections.
3 TERZAGHI AND PECKS METHOD
Terzaghi and Peck (1948) proposed the following empirical relationship between the settlement (Se) of a prototype foundation measuring BB in plan and the settlement of a test plate [Se (1)] measuring B1B1 loaded to the same intensity
+
=2
1)1( 1
4
BBS
Se
e
(1)
Although a full-sized footing can be used for a load test, the normal practice is to employ a plate of the order of 0.3 m to 1 m. Bjerrum and Eggestad (1963) provided the results of 14 sets of load settlement tests. This is shown in Figure 1 along with the plot of Eq. (1). For these tests, B1 was 0.35 m for circular plates and 0.32 m for square plates. It is obvious from Figure 1 that, although the general trend is correct, Eq. (1) represents approximately the lower limit of the field test results. Bazaraa (1967) also provided several field test results. Figure 2 shows the plot of Se/Se (1) versus B/B1 for all tests results provide by Bjerrum and Eggestad (1963) and Bazaraa (1967) as compiled by DAppolonia et al. (1970).
Developments in elastic settlement estimation procedures for shallow foundations on granular soil
Braja M. Das, Dean Emeritus, California State University, Sacramento Henderson, Nevada, U.S.A
ABSTRACT: Developments in major procedures available in the literature relating to elastic settlement of shallow foundations supported by granular soil are presented and compared. The discrepancies between the observed and the predicted settlement are primarily due to the inability to estimate the modulus of elasticity of soil using the results of the standard penetration tests and/or cone penetration tests. Based on the procedures available at this time, recommendations have been made for the best estimation of settlement of foundations
852 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
The overall results with the expanded data base are similar to those in Figure1 as they relate to Eq. (1).
Figure 1. Variation of Se/Se (1) versus B/B1 from the load settlement results of Bjerrum and Eggestad (1963) (Note: B1 = 0.36 m for circular plates and 0.32 m for square plates).
Figure 2. Variation of Se/Se(1) versus B/B1 based on the data of Bjerrum and Eggestad (1963) and Bazaraa (1967) (adapted from DAppolonia et al., 1970).
Terzaghi and Peck (1948, 1967) proposed a correlation
for the allowable bearing capacity, standard penetration number (N60), and the width of the foundation (B) corresponding to a 25 -mm settlement based on the observation given by Eq. (1). This correlation is shown in Figure 3. The curves shown in Figure 3 can be approximated by the relation
2
60 303(mm)
+= .BB
NqSe
(2)
Where q = bearing pressure in kN/m2; and B = width of foundation (m)
If corrections for ground water table location and depth
of embedment are included, then Eq. (2) takes the form 2
60 303
+= .BB
NqCCS DWe
(3)
Where CW = ground water table correction; CD = correction for depth of embedment = 1 (Df /4B); and Df= depth of embedment
Figure 3. Terzaghi and Pecks (1948, 1967) recommendation for allowable bearing capacity for 25-mm settlement variation with B and N60.
Jayapalan and Boehm (1986) and Papadopoulos (1992)
summarized the case histories of 79 foundations. Sivakugan et al (1998) used those case histories to compare with the settlement predicted by the Terzaghi and Peck method. This comparison is shown in Figure 4. It can be seen from this figure that, in general, the predicted settlements were significantly higher than those observed. The average value of Se (predicted)/Se (observed) 2.18.
Similar observations were also made by Bazaraa (1967). With B1 = 0.3 m, Eq. (1) can be rewritten as
2
)1( 304
+= .BB
SSe
e
or
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SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
=
+ )1(2
41
30 ee
SS
.BB
(4)
Combining Eqs. (2) and (4)
=
)1(60 413
e
ee S
SN
qS
or
75060
)1( .N
Sqe
= (5)
Figure 4. Sivakugan et al.s (1998) comparison of predicted with observed settlement for 79 foundationspredicted settlement based on Terzaghi and Peck method (1948, 1967).
Figure 5. Bazaraas plate load test resultsplot of q/Se (1) versus N60.
Bazaraa (1967) plotted a large number of plate load test results (B1 = 0.3 m) in the form of q/Se (1) versus N60 as shown in Figure 5. It can be seen that the relationship given by Eq. (5) is very conservative. In fact, q/Se (1) versus N60/0.5 will more closely represent the lower limiting condition.
4 MEYERHOFS METHOD
In 1956, Meyerhof proposed relationships for the elastic settlement of foundations on granular soil similar to Eq. (2). In 1965 he compared the predicted (by the relationships proposed in 1956) and observed settlements of eight structures and suggested that the allowable pressure (q) for a desired magnitude of Se can be increased by 50% compared to what he recommended in 1956. The revised relationships including the correction factors for water table location (CW) and depth of embedment (CD) can be expressed as
m) 1.22(for 251
60
= BN
q.CCS DWe (6)
and
m) 1.22(for 30
2 2
60
>
+= B.BB
NqCCS DWe
(7)
0.1=WC (8) and
BD
.C fD 401 =
(9)
If these equations are used to predict the settlement of the 79 foundations shown in Figure 4, then we will obtain Se (predicted)/Se (observed) 1.46. Hence, the predicted settlements will overestimate the observed values by about 50% on the average.
Table 1 shows the comparison of the maximum observed settlements of mat foundations considered by Meyerhof (1965) and the settlements predicted by Eq. (7). The ratios of the predicted to observed settlements are generally in the range of 0.8 to 2. This is also what Meyerhof concluded in his 1965 paper.
854 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Table 1. Comparison of observed maximum settlements provided by Meyerhof (1965) for eight mat foundations with those predicted by Eq. (7)
Structure B (m) Average N60
q (kN/m2)
Maximum Se(observed) (mm)
Se(predicted) by Eq. (7) (mm) )observed(
predicted)(
e
e
SS
T. Edison, Sao Paulo Banco do Brasil, Sao Paulo Iparanga, Sao Paulo C.B.I. Esplanada, Sao Paulo Riscala, Sao Paulo Thyssen, Dusseldorf Ministry, Dusseldorf Chimney, Cologne
18.3 22.9 9.15 14.6 3.96 22.6 15.9 20.4
15 18 9 22 20 25 20 10
229.8 239.4 220.2 383.0 229.8 239.4 220.4 172.4
15.24 27.94 35.56 27.94 12.70 24.13 21.59 10.16
29.66 25.74 45.88 33.43 19.86 18.65 21.23 33.49
1.95 0.99 1.29 1.20 1.56 0.77 0.98 3.30
Average 1.5
5 DE BEER AND MARTENS METHOD
DeBeer and Martens (1957) and DeBeer (1965) proposed the following relationship to estimate the elastic settlement of a foundation
H
C.S
o
oe
+= 10log32
(10)
Where C = a constant of proportionality; o= effective overburden pressure at the depth considered; = increase in pressure at that depth due to foundation loading; H = thickness of the layer considered
The value of C can be approximated as
o
c
q.C 51 (11)
Where qc = cone penetration resistance. Equation (10) is essentially in the form of the
relationship for estimating the consolidation settlement of normally consolidated clay. We can rewrite Eq. (10) as
+
+= oo
o
ce
He
CS 10log1 (12)
=+ c
o
o
c
q
eC 5.1
1 (13) Where Cc = compression index; eo = in situ void ratio. For the field cases considered by DeBeer and Martens
(1957), the average ratio of predicted to observed settlement was about 1.9. DeBeer (1965) further observed that the above stated method only applies to normally consolidated sands. For overconsolidated sand, a reduction factor needs to be applied which can be obtained from cyclic loading tests carried out in an oedometer. Hough (1969) expressed Cc in Eq. (12) as
)( beaC oc = (14) Approximate values of a and b are given in Table 2.
Table 2. Values of a and b from Eq. (14) (based on Hough, 1969)
Type of soil Value of constanta b*
Uniform cohesionless material (uniformity coefficient Cu 2) Clean gravel Coarse sand Medium sand Fine sand Inorganic silt
0.05 0.06 0.07 0.08 0.10
0.50 0.50 0.50 0.50 0.50
Well-graded cohesionless soil Silty sand and gravel Clean, coarse to fine sand Coarse to fine silty sand Sandy silt (inorganic)
0.09 0.12 0.15 0.18
0.20 0.35 0.25 0.25
* The value of the constant b should be taken as emin whenever the latter is known or can conveniently be determined. Otherwise, use tablulated values as a rough approximation.
Braja M. Das 855
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
6 THE METHOD OF PECK AND BAZARAA
Peck and Bazaraa (1969) recognized that the original Terzaghi and Peck method in Section 3 was overly conservative and revised Eq. (3) to the following form
2
601 30)(2
+= .BB
NqCCS DWe
(15)
Where Se is in mm, q is in kN/m2, and B is in m;
(N1)60= corrected standard penetration number
foundation theof bottom below the 0.5at foundation theof bottom below the 0.5at
BBC
o
oW = (16)
o = total overburden pressure o = effective overburden pressure
50
4001.
fD q
D..C
=
(17)
= unit weight of soil
The relationships for (N1)60 are as follow:
)kN/m 75(for 0401
4)( 260601 += oo
.NN
(18)
and
)kN/m 75(for 010253
4)( 260601 >+= oo
..NN
(19)
Where o is the effective overburden pressure (kN/m2) DAppolonia et al. (1970) compared the observed
settlement of several shallow foundations from several structures in Indiana (USA) with those estimated using the Peck and Bazaraa method, and this is shown in Figure 6. It can be seen from this figure that the calculated settlement from theory greatly overestimates the observed settlement. It appears that this solution will provide nearly the level of settlement that was obtained from Meyerhofs revised relationships (Section 5).
Figure 6. Plot of measured versus predicted settlement based on Peck and Bazaraas method (adapted from DAppolonia et al., 1970).
7 STRAIN INFLUENCE FACTOR METHOD
Based on the theory of elasticity, the equation for vertical strain z at a depth below the center of a flexible circular load of diameter B, can be given as
[ ]BAEq
ss
sz ++= )21()1(
or
[ ]BAqEI ssszz ++== )21()1(
(20)
Where A' and B' = f (z/B); q = load per unit area; Es = modulus of elasticity; s = Poissons ratio; Iz = strain influence factor
Figure 7 shows the variation of Iz with depth based on Eq. (20) for s = 0.4 and 0.5. The experimental results of Eggestad (1963) for variation of Iz are also given in this figure. Considering both the theoretical and experimental results cited in Figure 7, Schmertmann (1970) proposed a simplified distribution of Iz with depth that is generally referred to as 2B0.6Iz distribution and it is also shown in Figure 7. According to the simplified method,
zEIqCCS
B
o s
ze =
2
21
(21)
Where q = net effective pressure applied at the level of the foundation
C1 = correction factor for embedment of foundation.
1 1 0 5 oqC .q
= (22)
qo = effective overburden pressure at the level of the foundation
856 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Figure 7. Theoretical and experimental distribution of vertical strain influence factor below the center of a circular loaded area (based on Schmertmann, 1970).
C2 = correction factor to account for creep in soil.
2 1 0 2log 0 1tC ..
= + (23)
t = time, in years For use in Eq. (21) and the strain influence factor
shown in Figure 7, it was recommended that
cS qE 2= (24) Where qc = cone penetration resistance Sivakugan et al. (1998) used the case histories of the 79
foundations given in Figure 4 and compared those with the settlements obtained using the strain influence factor shown in Figure 7 and Eq. (21), and this is shown in Figure 8. From this figure, it can be seen that Se(predicted)/Se(observed) 3.39.
Schmertmann et al. (1978) modified the strain influence factor variation (2B0.6Iz) shown in Figure 7. The revised distribution is shown in Figure 9 for use in Eqs. (21)(23). According to this,
Figure 8. Sivakugan et al.s comparison (1998) of predicted and observed settlements from 79 foundationspredicted settlement based on 2B0.6Iz procedure.
Figure 9. Revised strain influence factor diagram suggested by Schmertmann et al. (1978).
For square or circular foundation: Iz = 0.1 at z = 0 Iz(peak) at z = zp = 0.5B Iz = 0 at z = zo = 2B
For foundation with L/B 10: Iz = 0.2 at z = 0 Iz(peak) at z = zp = B Iz = 0 at z = zo = 4B
Where L = length of foundation. For L/B between 1 and 10, interpolation can be done. Also
5.0
)peak( 1.05.0
+= ozqI (25)
The value of o in Eq. (25) is the effective overburden pressure at a depth where Iz (peak) occurs.
Salgado (2008) gave the following interpolation for Iz at z = 0, zp, and zo (for L/B = 1 to L/B 10.
2.00111.01.0 )0at (
+== BLI zz
(26)
110555.05.0
+=BL
Bzp
(27)
41222.02
+=BL
Bzo
(28)
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SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Noting that stiffness is about 40% larger for plane strain compared to axisymmetric loading, Schmertmann et al. (1978) recommended that.
s)foundationcircular and square(for 5.2 cs qE = (29) and
)foundation strip(for 5.3 cs qE = (30) With the modified strain-influence factor diagram,
zEICCS
ozz
z s
ze =
=
=021 (31) The modified strain influence factor and Eqs. (29) and
(30) will definitely reduce the average ratio of predicted to observed settlement. However, it may still overestimate the actual elastic settlement in the field.
8 RECENT MODIFICATIONS IN STRAIN-INFLUENCE FACTOR DIAGRAMS
More recently some modifications have been proposed to the strain-influence factor diagram suggested by Schmertmann et al. (1978). Two of these suggestions are discussed below.
8.1 Modification Suggested by Terzaghi, Peck and Mesri (1996)
The modification suggested by Terzaghi et al. (1996) is shown in Figure 10. For this case, for surface foundation condition (that is, Df/B = 0) Iz = 0.2 at z = 0 Iz = Iz(peak) = 0.6 at z = zp = 0.5B Iz = 0 at z = zo
Figure 10. Strain influence diagram suggested by Terzaghi et al. (1996).
4log12
+=BLzo
(32)
For Df/B > 0, Iz should be modified to Iz. Figure 11 shows the variation of Iz./ Iz. with Df/B.
The end of construction settlement can be estimated as
zEIqS
ozz
z s
ze =
=
=0 (33)
The settlement due to creep can be calculated as
=
day 1log1.0 dayscreep
tz
qS o
c (34)
Where qc= weighted mean value of measured qc; values of sublayers between z = 0 and z = zo
(MN/m2)
It has also been suggested that
Figure 11. Variation of Iz./ Iz. with Df/B (after Terzaghi et al. 1996).
4.1log4.01)1/(
)/(
+== B
LEE
BLs
BLs
(35)
Where
cBLs qE 5.3)1/( == (36) Figure 12 shows the plot of Es versus qc from 81
foundations and 92 plate load tests on which Eq. (36) has been established. The magnitude of Es recommended by Eq. (36) is about 40% higher than that obtained from Eq. (29). Figure 13 shows a comparison of the end-of-construction predicted [using Eqs. (33), (35) and (36)] and measured settlement of foundations on sand and gravelly soils (Terzaghi et al., 1996).
858 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Figure 12. Correlation between Es and qc for square and circularly loaded areas [adapted from Terzaghi et al. (1996)].
Figure 13. Comparison of end of construction predicted and measured Se of foundations on sand and gravelly soils based on Eqs. (33), (35) and (36) [adapted from Terzaghi et al. (1996)].
8.2 Modification Suggested by Lee et al. (2008)
Based on finite element analysis, Lee et al. (2008) suggested the following modifications to the strain influence factor diagram suggested by Schmertmann et al. (1978). This assumes that Iz(peak) and Iz at z = 0 is the same as given by Eqs. (25) and (26). However Eqs. (27) and (28) are modified as
6at 1 of maximuma with111.05.0 =
+=BL
BL
Bzp
(37)
6at maximuma with315
cos95.0 =+
=
BL
BL
Bzo
(38)
With these modifications, the elastic settlement can be calculated using Eq. (21).
9 METHOD OF BURLAND AND BURBIDGE (1985)
Burland and Burbidge (1985) proposed a method for cal-culating the elastic settlement of sandy soil using the field standard penetration number N60. The method can be summarized as follows:
9.1 Determination of Variation of Standard Penetration Number with Depth
Obtain the field penetration numbers (N60) with depth at the location of the foundation. The following adjustments of N60 may be necessary, depending on the field condi-tions:
For gravel or sandy gravel,
6060(a) 25.1 NN (39) For fine sand or silty sand below the ground water table
and N60 > 15,
)15(5.015 6060(a) + NN (40) Where N60 (a) = adjusted N60 value
9.2 Determination of Depth of Stress Influence (z) In determining the depth of stress influence, the following three cases may arise:
Case I. If N60 [or N60 (a)] is approximately constant with depth, calculate z' from
750
41.
RR BB.
Bz
=
(41)
Where: BR = reference width = 0.3 m B = width of the actual foundation (m)
Case II. If N60 [or N60(a)] is increasing with depth, use Eq. (41) to calculate z'.
Case III. If N60 [or N60(a)] is decreasing with depth, calculate z' = 2B and z' = distance from the bottom of the foundation to the bottom of the soft soil layer (= z"). Use z' = 2B or z' = z" (whichever is smaller).
Braja M. Das 859
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
9.3 Determination of Depth of Stress Influence Correction Factor The correction factor is given as
12
= z
HzH
(42)
Where H = thickness of the compressible layer
9.4 Calculation of Elastic Settlement
The elastic settlement of the foundation Se can be calcu-lated as:
For normally consolidated soil
[ ]
+
=
a
.
R.
(a)R
e
pq
BB
BL.
BL.
NorN.
.BS
70
2
416060 250
251711140
(43)
Where L = length of the foundation, pa = atmospheric pressure ( 100 kN/m2)
For overconsolidated soil (q c; where c = overconsolidation pressure)
[ ]
+
=
a
.
R.
(a)R
e
pq
BB
BL.
BL.
N or N.
.BS
70
2
416060 250
2515700470
(44)
For overconsolidated soil (q >c)
[ ]
+
=
a
c
.
R.
(a)R
e
p.q
BB
BL.
BL.
N or N.
.BS 670
250
251570140
70
2
416060
(45)
Sivakugan and Johnson (2004) used a probabilistic approach to compare the predicted settlements obtained by the methods of Terzaghi and Peck (1948, 1967), Schmertmann et al. (1970), and Burland and Burbidge (1985). Table 3 gives a summary of their studythat is, predicted settlement versus the probability of exceeding 25 mm settlement in the field. This shows that the method of Burland and Burbidge (1985), although conservative, is a substantially improved technique to estimate elastic settlement
Table 3. Probability of exceeding 25 mm settlement in the field Predicted settlement (mm)
Probability of exceeding 25 mm settlement in field Terzaghi and Peck(1948, 1967)
schmertmann et al.(1970)
Burland and Burbidge (1985)
1 5 10 15 20 25 30 35 40
0.00 0.00 0.00 0.09 0.20 0.26 0.31 0.35 0.387
0.000.00 0.02 0.13 0.20 0.27 0.32 0.37 0.42
0.00 0.03 0.15 0.25 0.34 0.42 0.49 0.55 0.61
Compiled from Sivakugan and Johnson (2004)
10 LOAD-SETTLEMENT CURVE APPROACH BASED ON PRESSUREMETER TESTS (PMT)
Briaud (2007) presented a method based on field pressuremeter tests to develop a load-settlement curve for a given foundation from which the elastic settlement at a given load intensity can be estimated. this takes into account the foundation load eccentricity, load inclination, and the location of the foundation on a slope (figure 14). following is a step-by-step procedure of the procedure suggested by briaud (2007). 1. Conduct several Pressuremeter tests at the site at
various depths. 2. Plot the PMT curves as pressure pp on the cavity wall
versus relative increase in cavity radius R/Ro. Extend the straight line part of the PMT curve to zero pressure
and shift the vertical axis to the value of R/Ro where that strain line portion intersects the horizontal axis (Fig. 15).
3. Plot the strain influence factor diagram proposed by Schmertmann et al. (1978) for the foundation. Based on the pp versus R/Ro diagrams (Step 2) and the location of the depth of the tests, develop a mean plot of pp versus R/Ro as shown in Figure 16. The mean pp for a given R/Ro can be given as
. . . )3(3)2(2)1(1)( +++= pppmeanp pAAp
AAp
AAp
(46)
Where A1, A2, A3 . . . are the areas tributary to each test under the influence diagram
A = total area of the strain-influence factor diagram
860 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Figure 14. Pressuremeter test to obtain load-settlement curve.
Figure 15. Adjustment of field Pressuremeter test plot of pp versus R/Ro. 4. Convert the plot of pp(mean) versus R/Ro plot to q
versus Se/B plot using the following equations.
)(,/ ))(( meanpdeBL pffffq = (47)
o
e
RR
BS = 24.0
(48)
Where = Gamma function linking q and pp(mean) (see Fig. 17)
+==LBf LB 2.08.0factor shape/
(49)
(center) 33.01factorty eccentrici load
==Befe
(50)
Figure 16. Development of the mean pp versus R/Ro plot.
Figure 17. Variation of function.
(edge) 15.0
=Befe
(51)
(center) 90
(degrees) 1factor ninclinatio
==f (52)
(edge) 360
(degrees) 10.5
=f (53)
slope) 1:(3 18.0factor slope0.1
,
+== Bdf d
(54)
slope) 1:(2 17.00.15
,
+= Bdf d
(55)
5. Based on the load-settlement diagram developed in Step 4, obtain the actual Se(maximum) which corresponds to the actual intensity of load q to which the foundation will be subjected.
6. To account for creep over the life-span of the structure, 3.0
1(maximum))(
ttStS ee
(56)
Braja M. Das 861
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Where Se(t) = settlement after time t Se(maximum) = settlement obtained from Step 5 t = time, in minutes t1 = reference time = 1 minute
SETTLEMENT CALCULATION BASED ON THEORY OF ELASTICITY
11 STEINBRENNERS (1934) AND FOXS (1948) THEORY
Based on the observations made on elastic settlement calculation using empirical correlations and the wide range in the predictions obtained, it is desirable to consider alternative solutions based on the theory of elasticity. With that in mind, Figure 18 shows a schematic diagram of the elastic settlement profile for a flexible and rigid foundation. The shallow foundation measures BL in plan and is located at a depth Df below the ground surface. A rock layer (or a rigid layer) is located at a depth H below the bottom of the foundation.
Figure 18 Settlement profile for shallow flexible and rigid foundation.
Theoretically, if the foundation is perfectly flexible
(Figure 18), the settlement may be expressed as (see Bowles, 1987)
fss
se IIE
BqS21)( =
(57)
Where q = net applied pressure on the foundation s = Poissons ratio of soil Es = average modulus of elasticity of the soil under the foundation, measured from z = 0 to about z = 4B B' = B/2 for center of foundation (= B for corner of foundation) Is = shape factor (Steinbrenner, 1934)
1 21 21
ss
s
I F F
= + (58)
)(1 101 AAF +=
(59)
21
2 tan2A
nF =
(60)
( )( )11 11ln 22 2220 +++ +++= nmm nmmmA (61) ( )
111ln22
22
1 ++++++=
nmmnmmA
(62)
1222 +++=
nmnmA
(63)
==
BL
BD
fI sf
f and ,,1948) (Fox,factor depth (64)
' = a factor that depends on the location below the foundation where settlement is being calculated.
To calculate settlement at the center of the foundation, we use
4= (65)
BLm =
(66)
and
=2BHn
(67)
To calculate settlement at a corner of the foundation,
1= (68)
BLm =
and BHn =
The variations of F1 and F2 with m and n are given Tables 4 and 5. Based on the works of Fox (1948), the variations of depth factor If for s = 0.3 and 0.4 and L/B have been determined by Bowles (1987) and are given in Table 6. Note that If is not a function of H/B.
862 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Table 4. Variation of F1 with m and n
n
m
1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.8 8.0 9.0 10.0 25.0 50.0 100.00.25 0.014 0.013 0.012 0.011 0.011 0.011 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010
0.50 0.049 0.046 0.044 0.042 0.041 0.040 0.038 0.038 0.037 0.037 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036
0.75 0.095 0.090 0.087 0.084 0.082 0.080 0.077 0.076 0.074 0.074 0.073 0.073 0.072 0.072 0.072 0.072 0.071 0.071 0.071 0.071
1.00 0.142 0.138 0.134 0.130 0.127 0.125 0.121 0.118 0.116 0.115 0.114 0.113 0.112 0.112 0.112 0.111 0.111 0.110 0.110 0.110
1.25 0.186 0.183 0.179 0.176 0.173 0.170 0.165 0.161 0.158 0.157 0.155 0.154 0.153 0.152 0.152 0.151 0.151 0.150 0.150 0.150
1.50 0.224 0.224 0.222 0.219 0.216 0.213 0.207 0.203 0.199 0.197 0.195 0.194 0.192 0.191 0.190 0.190 0.189 0.188 0.188 0.188
1.75 0.257 0.259 0.259 0.258 0.255 0.253 0.247 0.242 0.238 0.235 0.233 0.232 0.229 0.228 0.227 0.226 0.225 0.223 0.223 0.223
2.00 0.285 0.290 0.292 0.292 0.291 0.289 0.284 0.279 0.275 0.271 0.269 0.267 0.264 0.262 0.261 0.260 0.259 0.257 0.256 0.256
2.25 0.309 0.317 0.321 0.323 0.323 0.322 0.317 0.313 0.308 0.305 0.302 0.300 0.296 0.294 0.293 0.291 0.291 0.287 0.287 0.287
2.50 0.330 0.341 0.347 0.350 0.351 0.351 0.348 0.344 0.340 0.336 0.333 0.331 0.327 0.324 0.322 0.321 0.320 0.316 0.315 0.315
2.75 0.348 0.361 0.369 0.374 0.377 0.378 0.377 0.373 0.369 0.365 0.362 0.359 0.355 0.352 0.350 0.348 0.347 0.343 0.342 0.342
3.00 0.363 0.379 0.389 0.396 0.400 0.402 0.402 0.400 0.396 0.392 0.389 0.386 0.382 0.378 0.376 0.374 0.373 0.368 0.367 0.367
3.25 0.376 0.394 0.406 0.415 0.420 0.423 0.426 0.424 0.421 0.418 0.415 0.412 0.407 0.403 0.401 0.399 0.397 0.391 0.390 0.390
3.50 0.388 0.408 0.422 0.431 0.438 0.442 0.447 0.447 0.444 0.441 0.438 0.435 0.430 0.427 0.424 0.421 0.420 0.413 0.412 0.411
3.75 0.399 0.420 0.436 0.447 0.454 0.460 0.467 0.458 0.466 0.464 0.461 0.458 0.453 0.449 0.446 0.443 0.441 0.433 0.432 0.432
4.00 0.408 0.431 0.448 0.460 0.469 0.476 0.484 0.487 0.486 0.484 0.482 0.479 0.474 0.470 0.466 0.464 0.462 0.453 0.451 0.451
4.25 0.417 0.440 0.458 0.472 0.481 0.484 0.495 0.514 0.515 0.515 0.516 0.496 0.484 0.473 0.471 0.471 0.470 0.468 0.462 0.460
4.50 0.424 0.450 0.469 0.484 0.495 0.503 0.516 0.521 0.522 0.522 0.520 0.517 0.513 0.508 0.505 0.502 0.499 0.489 0.487 0.487
4.75 0.431 0.458 0.478 0.494 0.506 0.515 0.530 0.536 539 0.539 0.537 0.535 0.530 0.526 0.523 0.519 0.517 0.506 0.504 0.503
5.00 0.437 0.465 0.487 0.503 0.516 0.526 0.543 0.551 0.554 0.554 0.554 0.552 0.548 0.543 0.540 0.536 0.534 0.522 0.519 0.519
5.25 0.443 0.472 0.494 0.512 0.526 0.537 0.555 0.564 0.568 0.569 0.569 0.568 0.564 0.560 0.556 0.553 0.550 0.537 0.534 0.534
5.50 0.448 0.478 0.501 0.520 0.534 0.546 0.566 0.576 0.581 0.584 0.584 0.583 0.579 0.575 0.571 0.568 0.585 0.551 0.549 0.548
5.75 0.453 0.483 0.508 0.527 0.542 0.555 0.576 0.588 0.594 0.597 0.597 0.597 0.594 0.590 0.586 0.583 0.580 0.565 0.583 0.562
6.00 0.457 0.489 0.514 0.534 0.550 0.563 0.585 0.598 0.606 0.609 0.611 0.610 0.608 0.604 0.601 0.598 0.595 0.579 0.576 0.575
6.25 0.461 0.493 0.519 0.540 0.557 0.570 0.594 0.609 0.617 0.621 0.623 0.623 0.621 0.618 0.615 0.611 0.608 0.592 0.589 0.588
6.50 0.465 0.498 0.524 0.546 0.563 0.577 0.603 0.618 0.627 0.632 0.635 0.635 0.634 0.631 0.628 0.625 0.622 0.605 0.601 0.600
6.75 0.468 0.502 0.529 0.551 0.569 0.584 0.610 0.627 0.637 0.643 0.646 0.647 0.646 0.644 0.641 0.637 0.634 0.617 0.613 0.612
7.00 0.471 0.506 0.533 0.556 0.575 0.590 0.618 0.635 0.646 0.653 0.656 0.658 0.658 0.656 0.653 0.650 0.647 0.628 0.624 0.623
7.25 0.474 0.509 0.538 0.561 0.580 0.596 0.625 0.643 0.655 0.662 0.666 0.669 0.669 0.668 0.665 0.662 0.659 0.640 0.635 0.634
7.50 0.477 0.513 0.541 0.565 0.585 0.601 0.631 0.650 0.663 0.671 0.676 0.679 0.680 0.679 0.676 0.673 0.670 0.651 0.646 0.645
7.75 0.480 0.516 0.545 0.569 0.589 0.606 0.637 0.658 0.671 0.680 0.685 0.688 0.690 0.689 0.687 0.684 0.681 0.661 0.656 0.655
8.00 0.482 0.519 0.549 0.573 0.594 0.611 0.643 0.664 0.678 0.688 0.694 0.697 0.700 0.700 0.698 0.695 0.692 0.672 0.666 0.665
8.25 0.485 0.522 0.552 0.577 0.598 0.615 0.648 0.670 0.685 0.695 0.702 0.706 0.710 0.710 0.708 0.705 0.703 0.682 0.676 0.675
8.50 0.487 0.524 0.555 0.580 0.601 0.619 0.653 0.676 0.692 0.703 0.710 0.714 0.719 0.719 0.718 0.715 0.713 0.692 0.686 0.684
8.75 0.489 0.527 0.558 0.583 0.605 0.623 0.658 0.682 0.698 0.710 0.717 0.722 0.727 0.728 0.727 0.725 0.723 0.701 0.695 0.693
9.00 0.491 0.529 0.560 0.587 0.609 0.627 0.663 0.687 0.705 0.716 0.725 0.730 0.736 0.737 0.736 0.735 0.732 0.710 0.704 0.702
9.25 0.493 0.531 0.563 0.589 0.612 0.631 0.667 0.693 0.710 0.723 0.731 0.737 0.744 0.746 0.745 0.744 0.742 0.719 0.713 0.711
9.50 0.495 0.533 0.565 0.592 0.615 0.634 0.671 0.697 0.716 0.719 0.738 0.744 0.752 0.754 0.754 0.753 0.751 0.728 0.721 0.719
9.75 0.496 0.536 0.568 0.595 0.618 0.638 0.675 0.702 0.721 0.735 0.744 0.751 0.759 0.762 0.762 0.761 0.759 0.737 0.729 0.727
10.00 0.498 0.537 0.570 0.597 0.621 0.641 0.679 0.707 0.726 0.740 0.750 0.758 0.766 0.770 0.770 0.770 0.768 0.745 0.738 0.735
20.00 0.529 0.575 0.614 0.647 0.677 0.702 0.756 0.797 0.830 0.858 0.878 0.896 0.925 0.945 0.959 0.969 0.977 0.982 0.965 0.957
50.00 0.548 0.598 0.640 0.678 0.711 0.740 0.803 0.853 0.895 0.931 0.962 0.989 1.034 1.070 1.100 1.125 1.146 1.265 1.279 1.261
100.00 0.555 0.605 0.649 0.688 0.722 0.753 0.819 0.872 0.918 0.956 0.990 1.020 1.072 1.114 1.150 1.182 1.209 1.408 1.489 1.499
Braja M. Das 863
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Table 5. Variation of F2 with m and n
n
m
1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.8 8.0 9.0 10.0 25.0 50.0 100.00.25 0.049 0.050 0.051 0.051 0.051 0.052 0.052 0.052 0.052 0.052 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053
0.50 0.074 0.077 0.080 0.081 0.083 0.084 0.086 0.086 0.087 0.087 0.087 0.087 0.088 0.088 0.088 0.088 0.088 0.088 0.088 0.088
0.75 0.083 0.089 0.093 0.097 0.099 0.101 0.104 0.106 0.107 0.108 0.109 0.109 0.109 0.110 0.110 0.110 0.110 0.111 0.111 0.111
1.00 0.083 0.091 0.098 0.102 0.106 0.109 0.114 0.117 0.119 0.120 0.121 0.122 0.123 0.123 0.124 0.124 0.124 0.125 0.125 0.125
1.25 0.080 0.089 0.096 0.102 0.107 0.111 0.118 0.122 0.125 0.127 0.128 0.130 0.131 0.132 0.132 0.133 0.133 0.134 0.134 0.134
1.50 0.075 0.084 0.093 0.099 0.105 0.110 0.118 0.124 0.128 0.130 0.132 0.134 0.136 0.137 0.138 0.138 0.139 0.140 0.140 0.140
1.75 0.069 0.079 0.088 0.095 0.101 0.107 0.117 0.123 0.128 0.131 0.134 0.136 0.138 0.140 0.141 0.142 0.142 0.144 0.144 0.145
2.00 0.064 0.074 0.083 0.090 0.097 0.102 0.114 0.121 0.127 0.131 0.134 0.136 0.139 0.141 0.143 0.144 0.145 0.147 0.147 0.148
2.25 0.059 0.069 0.077 0.085 0.092 0.098 0.110 0.119 0.125 0.130 0.133 0.136 0.140 0.142 0.144 0.145 0.146 0.149 0.150 0.150
2.50 0.055 0.064 0.073 0.080 0.087 0.093 0.106 0.115 0.122 0.127 0.132 0.135 0.139 0.142 0.144 0.146 0.147 0.151 0.151 0.151
2.75 0.051 0.060 0.068 0.076 0.082 0.089 0.102 0.111 0.119 0.125 0.130 0.133 0.138 0.142 0.144 0.146 0.147 0.152 0.152 0.153
3.00 0.048 0.056 0.064 0.071 0.078 0.084 0.097 0.108 0.116 0.122 0.127 0.131 0.137 0.141 0.144 0.145 0.147 0.152 0.153 0.154
3.25 0.045 0.053 0.060 0.067 0.074 0.080 0.093 0.104 0.112 0.119 0.125 0.129 0.135 0.140 0.143 0.145 0.147 0.153 0.154 0.154
3.50 0.042 0.050 0.057 0.068 0.070 0.076 0.089 0.100 0.109 0.116 0.122 0.126 0.133 0.138 0.142 0.144 0.146 0.153 0.155 0.155
3.75 0.040 0.047 0.054 0.060 0.067 0.073 0.086 0.096 0.105 0.113 0.119 0.124 0.131 0.137 0.141 0.143 0.145 0.154 0.155 0.155
4.00 0.037 0.044 0.051 0.057 0.063 0.069 0.082 0.093 0.102 0.110 0.116 0.121 0.129 0.135 0.139 0.142 0.145 0.154 0.155 0.156
4.25 0.036 0.042 0.049 0.055 0.061 0.066 0.079 0.090 0.099 0.107 0.113 0.119 0.127 0.133 0.138 0.141 0.144 0.154 0.156 0.156
4.50 0.034 0.040 0.046 0.052 0.058 0.063 0.076 0.086 0.096 0.104 0.110 0.116 0.125 0.131 0.136 0.140 0.143 0.154 0.156 0.156
4.75 0.032 0.038 0.044 0.050 0.055 0.061 0.073 0.083 0.093 0.101 0.107 0.113 0.123 0.130 0.135 0.139 0.142 0.154 0.156 0.157
5.00 0.031 0.036 0.042 0.048 0.053 0.058 0.070 0.080 0.090 0.098 0.105 0.111 0.120 0.128 0.133 0.137 0.140 0.154 0.156 0.157
5.25 0.029 0.035 0.040 0.046 0.051 0.056 0.067 0.078 0.087 0.095 0.102 0.108 0.118 0.126 0.131 0.136 0.139 0.154 0.156 0.157
5.50 0.028 0.033 0.039 0.044 0.049 0.054 0.065 0.075 0.084 0.092 0.099 0.106 0.116 0.124 0.130 0.134 0.138 0.154 0.156 0.157
5.75 0.027 0.032 0.037 0.042 0.047 0.052 0.063 0.073 0.082 0.090 0.097 0.103 0.113 0.122 0.128 0.133 0.136 0.154 0.157 0.157
6.00 0.026 0.031 0.036 0.040 0.045 0.050 0.060 0.070 0.079 0.087 0.094 0.101 0.111 0.120 0.126 0.131 0.135 0.153 0.157 0.157
6.25 0.025 0.030 0.034 0.039 0.044 0.048 0.058 0.068 0.077 0.085 0.092 0.098 0.109 0.118 0.124 0.129 0.134 0.153 0.157 0.158
6.50 0.024 0.029 0.033 0.038 0.042 0.046 0.056 0.066 0.075 0.083 0.090 0.096 0.107 0.116 0.122 0.128 0.132 0.153 0.157 0.158
6.75 0.023 0.028 0.032 0.036 0.041 0.045 0.055 0.064 0.073 0.080 0.087 0.094 0.105 0.114 0.121 0.126 0.131 0.153 0.157 0.158
7.00 0.022 0.027 0.031 0.035 0.039 0.043 0.053 0.062 0.071 0.078 0.085 0.092 0.103 0.112 0.119 0.125 0.129 0.152 0.157 0.158
7.25 0.022 0.026 0.030 0.034 0.038 0.042 0.051 0.060 0.069 0.076 0.083 0.090 0.101 0.110 0.117 0.123 0.128 0.152 0.157 0.158
7.50 0.021 0.025 0.029 0.033 0.037 0.041 0.050 0.059 0.067 0.074 0.081 0.088 0.099 0.108 0.115 0.121 0.126 0.152 0.156 0.158
7.75 0.020 0.024 0.028 0.032 0.036 0.039 0.048 0.057 0.065 0.072 0.079 0.086 0.097 0.106 0.114 0.120 0.125 0.151 0.156 0.158
8.00 0.020 0.023 0.027 0.031 0.035 0.038 0.047 0.055 0.063 0.071 0.077 0.084 0.095 0.104 0.112 0.118 0.124 0.151 0.156 0.158
8.25 0.019 0.023 0.026 0.030 0.034 0.037 0.046 0.054 0.062 0.069 0.076 0.082 0.093 0.102 0.110 0.117 0.122 0.150 0.156 0.158
8.50 0.018 0.022 0.026 0.029 0.033 0.036 0.045 0.053 0.060 0.067 0.074 0.080 0.091 0.101 0.108 0.115 0.121 0.150 0.156 0.158
8.75 0.018 0.021 0.025 0.028 0.032 0.035 0.043 0.051 0.059 0.066 0.072 0.078 0.089 0.099 0.107 0.114 0.119 0.150 0.156 0.158
9.00 0.017 0.021 0.024 0.028 0.031 0.034 0.042 0.050 0.057 0.064 0.071 0.077 0.888 0.097 0.105 0.112 0.118 0.149 0.156 0.158
9.25 0.017 0.020 0.024 0.027 0.030 0.033 0.041 0.049 0.056 0.063 0.069 0.075 0.086 0.096 0.104 0.110 0.116 0.149 0.156 0.158
9.50 0.017 0.020 0.023 0.026 0.029 0.033 0.040 0.048 0.055 0.061 0.068 0.074 0.085 0.094 0.102 0.109 0.115 0.148 0.156 0.158
9.75 0.016 0.019 0.023 0.026 0.029 0.032 0.039 0.047 0.054 0.060 0.066 0.072 0.083 0.092 0.100 0.107 0.113 0.148 0.156 0.158
10.00 0.016 0.019 0.022 0.025 0.028 0.031 0.038 0.046 0.052 0.059 0.065 0.071 0.082 0.091 0.099 0.106 0.112 0.147 0.156 0.158
20.00 0.008 0.010 0.011 0.013 0.014 0.016 0.020 0.024 0.027 0.031 0.035 0.039 0.046 0.053 0.059 0.065 0.071 0.124 0.148 0.156
50.00 0.003 0.004 0.004 0.005 0.006 0.006 0.008 0.010 0.011 0.013 0.014 0.016 0.019 0.022 0.025 0.028 0.031 0.071 0.113 0.142
100.00 0.002 0.002 0.002 0.003 0.003 0.003 0.004 0.005 0.006 0.006 0.007 0.008 0.010 0.011 0.013 0.014 0.016 0.039 0.071 0.113
864 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Table 6. Variation of If (Fox, 1948)*
Due to the non-homogeneous nature of a soil deposit, the magnitude of Es may vary with depth. For that reason, Bowles (1987) recommended
zzE
E iss = )(
(69)
Where Es(i) = soil modulus within the depth z
z = 5B or H (if H < 5B) Bowles (1987) also recommended that
260 kN/m )15(500 += NEs (70)
The elastic settlement of a rigid foundation can be estimated as
(rigid ) (flexible, center)0.93e eS S (71) Bowles (1987) compared this theory with 12 case
histories that provided reasonable good results.
12 ANALYSIS OF MAYNE AND POULOS BASED ON THEORY OF ELASTICITY
Mayne and Poulos (1999) presented an improved formula for calculating the elastic settlement of foundations. The formula takes into account the rigidity of the foundation, the depth of embedment of the foundation, the increase in the modulus of elasticity of the soil with depth, and the location of rigid layers at a limited depth. To use the equation of Mayne and Poulos, one needs to determine the equivalent diameter Be of a rectangular foundation, or
BLBe
4= (72)
For circular foundations,
BBe = (73) Where B = diameter of foundation Figure 19 shows a foundation with an equivalent
diameter Be located at a depth Df below the ground surface. Let the thickness of the foundation be t and the modulus of elasticity of the foundation material be Ef. A rigid layer is located at a depth H below the bottom of the foundation.
Figure 19. Mayne and Poulos procedure (1999) for settlement calculation.
The modulus of elasticity of the compressible soil layer can be given as
kzEE os += (74) Where k = rate of increase in Es with depth (kN/m2/m) With the preceding parameters defined, the elastic
settlement below the center of the foundation is
( )21 so
ERGee E
IIIqBS = (75)
Df/B L/B 1.0 1.2 1.4 1.6 1.8 2.0 5.0
Poissons ratio s = 0.300.05 0.10 0.20 0.40 0.60 0.80 1.00 2.00
0.979 0.954 0.902 0.808 0.738 0.687 0.650 0.562
0.981 0.958 0.911 0.823 0.754 0.703 0.665 0.571
0.982 0.962 0.917 0.834 0.767 0.716 0.678 0.580
0.983 0.964 0.923 0.843 0.778 0.728 0.689 0.588
0.984 0.966 0.927 0.851 0.788 0.738 0.700 0.596
0.985 0.968 0.930 0.857 0.796 0.747 0.709 0.603
0.990 0.977 0.951 0.899 0.852 0.813 0.780 0.675
Poissons ratio s = 0.400.05 0.10 0.20 0.40 0.60 0.80 1.00 2.00
0.989 0.973 0.932 0.848 0.779 0.727 0.689 0.596
0.990 0.976 0.940 0.862 0.795 0.743 0.704 0.606
0.991 0.978 0.945 0.872 0.808 0.757 0.718 0.615
0.992 0.980 0.949 0.881 0.819 0.769 0.730 0.624
0.992 0.981 0.952 0.887 0.828 0.779 0.740 0.632
0.993 0.982 0.955 0.893 0.836 0.788 0.749 0.640
0.995 0.988 0.970 0.927 0.886 0.849 0.818 0.714
* Adapted from Bowles (1987)
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Where IG=influence factor for the variation of Es
with depth E Hof , kB Be e
= =
IR = foundation rigidity correction factor
IE = foundation embedment correction factor
Figure 20 shows the variation of IG with = Eo/kBe and H/Be. The foundation rigidity correction factor can be expressed as
32
2
1064
14
++
+=
eeo
f
R
Bt
kBE
E.
I
(76)
Similarly, the embedment correction factor is
+
=61)40221(exp53
11.
DB...
I
f
es
E
(77)
Figures 21 and 22 show the variation of IR with IE as a function of the terms expressed in Eqs. (76) and (77).
Figure 20. Variation of IG with .
Figure 21. Variation of IR with KF.
Figure 22 Variation of IE with s and Df/Be.
13 BERARDI AND LANCELLOTTAS METHOD
Berardi and Lancellotta (1991) proposed a method to estimate the elastic settlement that takes into account the variation of the modulus of elasticity of soil with the strain level. This method is also described by Berardi et al. (1991). According to this procedure,
sse E
qBIS = (78)
Where
Is = influence factor for a rigid foundation (Tsytovich, 1951) Es = modulus of elasticity of soil
The variation of Is (Tsytovich, 1951) with Poissons ratio s = 0.15 is given in Table 7.
Table 7. Variation of Is L/B
Depth of influence HI /B0.5 1.0 1.5 2.0
1 2 3 5 10
0.35 0.39 0.40 0.41 0.42
0.56 0.65 0.67 0.68 0.71
0.63 0.76 0.81 0.84 0.89
0.69 0.88 0.96 0.99 1.06
Using analytical and numberical evaluations, Berardi and Lancellotta (1991) have shown that, for a circular foundation,
BH )3.1 to8.0(25 = (79)
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SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
For plane strain condition (that is, L/B 10)
(circle)2525 )1.7 to1.5( HH = (80) Where H25 = depth from the bottom of the foundation
below which the residual settlement is 25% of the total settlement
The above implies that H25 2.5B for practically all foundations. Thus the depth of influence HI can be taken to be H25. The modulus of elasticity Es in Eq. (78) can be evaluated as (Janbu, 1963)
50
50.
a
oaEs p
.pKE
+= (81)
Where
pa = atmospheric pressure o and ' = effective overburden pressure and net
effective stress increase due to the foundation loading, respectively, at a depth B/2 below the foundation KE = dimensionless modulus number
After reanalyzing the performance of 130 structures foundations on predominantly silica sand as reported by Burland and Burbidge (1985), Berardi and Lancellotta (1991) obtained the variation of KE with the relative density Dr at Se/B = 0.1% and KE at varying strain levels. Figures 23 and 24 show the average variation of KE with
Dr at Se/B = 0.1%
and
%)10/()/( / .BSEBSE ee KK =
with Se/B.
In order to estimate the elastic settlement of the foundation, an iterative procedure is suggested which can be described as follows: 1. Determine the variation of the blow count N60 from
standard penetration tests within the zone of influence, that is H25.
2. Determine the corrected blow count (N1)60 as 3.
+= oNN
01.012)( 60601
(82)
Where o = vertical effective stress in kN/m2
Figure 23. Variation of KE with Dr and N60 (adapted from Berardi and Lancellotta, 1991).
Figure 24. Plot of %)10/()/(/ .BSEBSE ee KK = with Se/B (adapted
from Berardi and Lancellotta, 1991). 4. Determine the average corrected blow count from
standard penetration tests 601 )(N and hence the average relative density as
5.01
60
= NDr (83)
5. With a known value of Dr, determine %)10/( .BSE eK = from Figure 23 and hence Es from Eq. (81) for Se/B = 0.1%
6. With the known value of Es (Step 4), the magnitude of Se can be calculated from Eq. (78).
7. If the calculated Se/B is not the same as the assumed value, then use the calculated value of Se/B from Step 5 and Figure 24 to estimate a revised )/( BSE eK . This value can now be used in Eqs. (81) and (78) to obtain a
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revised Se. The iterative procedures can be continued until the assumed and calculated values are the same. Based on a probabilistic study conducted by Sivakugan
and Johnson (2004), the probability of exceeding 25 mm settlement in the field for various predicted settlement levels using the iteration procedure of Berardi and Lancellotta (1991) is shown in Table 8. When compared with Table 3, this shows a promise of improved prediction in elastic settlement. Table 8. Probability of exceeding 25 mm settlement in the field procedure of Berardi and Lancellotta (1991) Predicted settlement (mm)
Probability of exceeding 25 mm in the field (%)
1 5 10 15 20 25 30 35 40
6 19 32 43 52 60 66 72 77
(based on Sivakugan and Johnson, 2004)
14 GENERAL COMMENTS AND CONCLUSIONS
A general review of the major developments over the last sixty years for estimating elastic settlement of shallow foundations on granular soil is presented. Based on the above review, the following general observations can be made. 1. Meyerhofs relationship (1965) is fairly simple to use.
It will probably yield predicted settlements that are 50% higher on the average than those observed in the field. Peck and Bazaraas method (1969) provides results that are almost similar to those obtained from Meyerhofs method (1965).
2. Burland and Burbidges solution (1985) will provide more reasonable estimations of Se than those obtained from the solution of Meyerhof (1965). However it will be difficult to determine the overconsolidation ratio and the preconsolidation pressure for granular soils from field exploration.
3. The modified strain influence factor diagrams presented by Schmertmann et al. (1978), Terzaghi et al. (1996), and Lee et al. (2008) will all provide reasonable estimations of the elastic settlement provided a more realistic value of Es is assumed in the calculation. The authors feel that the empirical relationships for Es provided by Eqs. (35) and (36) are more reasonable.
4. The relationships for Es provided by Eqs. (35) and (36) are based on the field cone penetration resistance. These equations can be converted to expressions in terms of N60 and D50 (mean grain size). Figure 25
shows some of the relationships available in the literature. Based on the data of Burland and Burbidge et al. (1985)
305.050
60
8DNpq
a
c
=
(84)
Based on the data of Robertson and Campanella (1983)
and Seed and DeAlba (1986)
Figure 25 Variation of (qc/pa)/N60 with D50. (a) Adapted from Terzaghi et al. (1996); (b) Adapted from Anagnostopoulos, 2003).
228.050
60
6DNpq
a
c
=
(85)
Based on the data of Anagnostopoulos et al. (2003)
26.050
60
6429.7 DNpq
a
c
=
(86)
868 Developments in elastic settlement estimation procedures for shallow foundations on granular soil
SOCIEDAD MEXICANA DE INGENIERA GEOTCNICA A.C.
Where pa = atmospheric pressure (same unit as qc) D50 = mean grain size, in mm. 5. The procedure for developing the load-settlement plot
based on pressuremeter tests is a versatile technique; however, the cost effectiveness should be taken into account.
6. Relationships for elastic settlement using the theory of elasticity will be equally as good as the other methods, provided a realistic value of Es is adopted. This can be accomplished using the iteration method suggested by Berardi and Lancellotta (1991). In lieu of that, the Es relationship given by Terzaghi et al. (1996) can be used. In his landmark paper in 1927 entitled The Science of
Foundations, Karl Terzaghi wrote Foundation problems, throughout, are of such character that a strictly theoretical mathematical treatment will always be impossible. The only way to handle them efficiently consists of finding out, first, what has happened on preceding jobs of a similar character; next, the kind of soil on which the operations were performed; and, finally, why the operations have lead to certain results. By systematically accumulating such knowledge, the empirical data being well defined by the results of adequate soil investigations, foundation engineering could be developed into a semi-empirical science, . . . .
What is presented in this paper is a systematic accumulation of knowledge and data over the past sixty years. In summary, the parameters for comparing settlement prediction methods are accuracy and reliability. Reliability is the probability that the actual settlement would be less than that computed by a specific method. In choosing a method for design, it all comes down to keeping a critical balance between reliability and accuracy which can be difficult at times knowing the non-homogeneous nature of soil in general. We cannot be over-conservative but, at the same time, not be accurate. We need to keep in mind what Karl Terzaghi said in the 45th James Forrest Lecture at the Institute of Civil Engineers in London: Foundation failures that occur are not longer an act of God.
REFERENCES
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Bazaraa, A.R.S.S. 1967. Use of the standard penetration test for estimating settlements of shallow foundations on sand. Ph.D. Thesis, University of Illinois, Champaign-Urbana, Illinois.
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