Auvinet State of The Art 0

 

Rigid inclusions in Mexico City soft soils: history and  perspectives. G. Auvinet & Rodríguez J.F.  Instituto de Ingeniería, UNAM

ABSTRACT:  This paper presents an overview of ri rigid gid inclusions in Mexico City soft cl clays. ays. These element elementss are used in order to reduce foundations settlements and/or to improve the soil bearing capacity. It is shown that reinforcing soft soils with rigid inclusions is hardly a new concept in Mexico City since such a system was commonly applied by preColumbian constructors and by engineers of the New Spain era. Some similar ideas proposed during the twentieth piles are also examined. Finally, the reasons behind the century, including negative skin friction piles and overlapping  overlapping   piles recent surge in the application of this technique in Mexico City are discussed. RESUMEN: Esta contribución presenta un panorama del uso de inclusiones rígidas en las arcillas del valle de México  para reducir los asentamientos de las cimentaciones y/o mejorar su capacidad de carga. Se muestra que el refuerzo de suelos blandos con inclusiones rígidas no es un concepto nuevo en México donde sistemas de este tipo ya fueron empleados por constructores precolombinos y por ingenieros de la época de la Nueva España. Otras ideas similares desarrolladas en el siglo XX, incluyendo los pilotes de fricción negativa y los pilotes entrelazados se examinan también. Finalmente, se analizan las razones que explican el reciente auge de la aplicación de esta técnica en la capital mexicana. Key words: Geotechnical Engineering, Soft Soils, Mexico City clays, Rigid Inclusions, Analysis, Design, Finite Element Method.  

1  INTRODUCTION

Foundations on soft soils constitute a difficult challenge for Geotechnical engineers. Unfortunately, many areas left for development in existing urban centers are zones of  poor subsoil. Design of foundations on compressible soils cannot be based on bearing capacity considerations only; rather, it is generally governed by soil deformations and their effect on the structure. Design can become still more intricate when extreme adverse environmental conditions  prevail. The high compressibility and low shear strength of the lacustrine clays of Mexico City, together with the existence of regional subsidence and seismic activity, have led to the development of specific foundation solutions in which an impressive amount of creativity was involved. Among these solutions, an old one which has surged again in the last decade as an attractive technique is the reinforcement of soft soils by rigid inclusions. This paper presents a review of the use of rigid inclusions in Mexico City soft clays aimed at reducing foundations settlements and improving bearing capacity. It is shown that reinforcing soft soils with rigid inclusions is not a new idea in Mexico City since such a system was commonly applied by pre-Columbian constructors and by engineers of the New Spain era. Some similar ideas applied during the twentieth century, including negative skin friction  piles and overlapping  piles, are also examined. Finally, the reasons behind the recent surge in the application of this technique in Mexico City are discussed.

2  MEXICO CITY SUBSOIL th

Until the end of the XVIII  century, the valley of Mexico was a closed basin, with a number of shallow lakes, amongst them the Texcoco and Xaltocan lakes. It became an open basin when the Nochistongo cut was completed in 1789. Progressively, the lakes were drained, mainly through the Tequisquiac and Deep Drainage ( Emisor Central) tunnels, and practically disappeared. A large part of the city was then built on lacustrine sediments. These are highly plastic soft clays interbedded with layers of silt, sand and sandy gravels of alluvial origin. The urban area can thus be divided in three main geotechnical zones (Marsal and Mazari, 1975): Foothills (Zone I), Transition (Zone II) and Lake (Zone III). Figure 1 shows the three zones as defined in the present building code. In the foothills, very compact but heterogeneous volcanic soils and lava are found. These materials contrast with the highly compressible soft soils of the Lake Zone. Generally, in between, a Transition Zone is found where clayey layers of lacustrine origin alternate with sandy alluvial deposits erratically distributed. In Figure 2, typical soil profiles are presented (Marsal, 1975). Borehole Pc-28 corresponds to the Lake Zone. The water table is close to the surface. Three clayey layers are to be distinguished, denominated upper (Formación  Arcillosa Superior , FAS), lower (Formación Arcillosa  Inferior , FAI) and deep deposits ( Depósitos Profundos, DP). clays of, FAS separated from FAI by a hard layer The (Capa Dura CD),are a sandy clayey stratum, some 3m thick, lying at a typical depth of 30 to 35m. Generally, FAS is covered by a desiccated crust and/or an artificial

 

fill several meters thick. Average values of index  properties for borehole borehole Pc 28 are presented in Ta Table ble I. 19.60

   D      U    T    I    T    A19.55    L

" C A R A R A C OL "  T E X C O C O

P       E        R       I        F      É        R       I        C       O     

  P P.  T O A U

 . E X  T  E  - T  .  M É X

   A       M     R    O     F        E     R

    C     O       X     E      T     -     S      E      Y      E     R

 O  T O  A  D U C T  V  V  I A

    O     C      I        R      É        F      I      R      E        P

19.35

    S          E          T           N           E     G          R          U C I R C U I T   O     S I N T E T E R I O R          N          I

    N    A      P     L     A     L        T

19.30

P      R      O      L     .  D      I      V       .  D      E      L      N      O      R      T       E     

    O     C          L     A          U          H          E          Y          L          U          T       C     A          U          H     A          L          T

                   L                   O          A                    R                             IC                    E                    X                    D                        É                    E                     M                     F                    E                   O                    D                    I T                   O                    R                    D                    T                   A                             IS                    T                    D                             ES T L AH  C .  X   AH U  I  C  O  U    C   AC   A -  C H  H AL   LC   A C O  O 

19.20

-99.25

CD

FAI

Water content, %

270

58

191

Liquid limit wL, %

300

59

288

Plastic limit, wP, %

86

45

68

Density of solids, S s 

2.30

2.58

2.31

Initial void ratio, e 0 

6.17

1.36

4.53

85

24

160

Due to exploitation of underground potable water supplied to the population, and to other factors, in the course of the  present century, Mexico City has suffered a general subsidence that in some locations has reached 10m. Recent data show that the rate of subsidence tends to decrease in certain areas. However, in newly developed urban zones such as the center of the former Texcoco lake and former lakes of Xochimilco and Chalco, in the south of the valley, the consolidation process is only in its first stage and the rate of subsidence attains 30cm per year.

Z    A   R      A   G    O    Z     A  

   O      C     I        R       É     F      I   A V . T L     R    A  A H      E  U  A     P C 

 O  A L C  E H U  T U L Y  - T  O L C O  M I  L  H I M  X O C

19.25

19.15 -99.30

FAS

Unconfined compressive strength, q u, kN/m2 

    O     C

 AE RO P U E RT O

19.40

(Borehole Pc-28, Marsal, 1975) PROPERTY

N

19.50

19.45

Table I. Typical average values of index properties in Lake Zone

-99.20

-99.15

-99.10

-99.05

-99.00

-98.95

-98.90 -98.85 LONGITUD

Zona I Zona II

3  HISTORICAL REVIEW

Escala gráfica 0 1 2.5

5

10

Zona III

Figure 1. Geotechnical zones in Mexico City

Figure 2. Soil profiles in Mexico City (Marsal, 1975)

15

20 Km

  In their state-of-the-art report, Briancon et al. (2004) consider that typical rigid inclusions systems are formed  by two main elements: vertical rigid inclusions transferring loads to deeper, less compressible materials and a platform of granular materials ensuring transfer of the structural load to the head of the inclusions. Both elements were already present in some preColumbian constructions. Fig. 3 shows for example the foundation of the aqueduct that carried potable water from the Chapultepec hill to the center of the Aztec capital, Tenochtitlan, now Mexico City (DGCOH, 1994). The rigid inclusions were short wood piles (estacas) and the distribution platform was constituted by a mixture of volcanic sand   (tezontle) and fragments of volcanic rock stabilized with lime. The wood piles were intended to mitigate the settlements induced by the shear and volumetric strains of the unconsolidated superficial materials.

Figure 3. Schematical representation of the foundation of Chapultepec-Tenochtitlán Chapultepec-Tenochtit lán aqueduct (circa 1465).

The same solution was adopted for some of the most important constructions during the New Spain era. One of

 

the most famous is certainly Mexico City Metropolitan Cathedral. Again, both elements: a distribution platform (rockfill) and wood inclusions are present (Fig. 4). The inclusions were however much too short to prevent the very large settlements that were observed during and after the construction.

Box foundation

Masonry beams 3.5m height 2.5m width

Inclusions Rock Fill 1.2 to 2.0m thick,

Compressible clay

Wood inclusions 3 to 3.5m length 22 to 30cm section 45 to 60cm spacing

6 6 6 m      m

Section

Rock fill

Hard layer 

   m  1 2 2

Figure 6 Negative skin friction piles

Masonry beams Wood inclusions

Figure 4 Original foundation of the Metropolitan Cathedral in Mexico City.

Fig. 5 shows the foundation of the School of Mines Palace, an outstanding neo-classical construction by architect Manuel Tolsa. In this case, the transfer of structural load to the short piles is through a wooden beam supporting the masonry of the structure.

 

Other engineers proposed connecting similar negative skin friction piles to the foundation substructure through a control system  (González Flores, 1948 and 1981). This idea gave birth to the control pile concept, a solution still widely used for building foundations in Mexico City to control the load carried by each pile as well as the total and differential movements of the foundation. The control system is a mechanical or hydraulic device that regulates the load received by each pile. Each pile can be unloaded  by removing the mechanism in order to correct any tilting of the building. As a matter of fact, depending on whether the control system is connected or not, the foundation switches from a classical point-bearing pile foundation to a negative skin friction piles foundation.

Figure 5 Foundation of the School of Mines Palace.

During the twentieth century, the idea of reinforcing the soil with rigid inclusions for building foundations was again proposed in different forms. Correa (1961) suggested reinforcing the soil with rigid inclusions consisting of point-bearing prefabricated piles not connected to the substructure. Taking into account that the weight of the foundation and the natural consolidation of the upper clay formation induce downward oriented shear stresses on the shaft of the piles, these piles received the name of negative skin friction piles. This type of inclusions was indeed useful to mitigate settlement and prevent the apparent protruding observed in classical point-bearing piles foundations. However, their limited bearing capacity in seismic conditions was considered a serious drawback, especially for slender  buildings. Finite element modeling of this type of piles has been  presented recently (Rodríguez, 2001). Spacing of the piles appears to be the most significant design parameter.

Figure 7 Control pile

A system combining traditional friction piles and rigid inclusions was proposed by Girault (1964, 1980), Fig. 8. This type of foundation includes conventional friction  piles (“A” Piles) together with end bearing negative skin friction piles (“B” piles). This arrangement reduces stress increments in the soil and consequently mitigates the settlements; any protruding of the foundation is also avoided. This system (known as overlapping or interlaced  piles)  piles) has been used in a number of projects in Mexico City both as a foundation and as an underpinning solution.  New interest for this system has arisen during the last years (Menache, 2006).

 

reinforced by injecting mortar in the hydraulic fractures generated radially radially around the inclusi inclusion. on. (Fig. 10, Santoyo & Ovando, 2000;  2000; Santoyo & Ovando 2006).

Box foundation

Friction piles

Compressible clay

Inclusions

Har Hard d laye layer  r 

  Figure 8 Overlapping piles

In a limited number of cases, preloading has been used in Mexico City to improve the mechanical characteristics of the upper clay formation (Fig. 9, Auvinet, 1979).

Ballast Ballast

1.0m

Tezontle 

1.0m

18.5m

Ballast Tezontle

2.3m 1.0m 1.0m

sand drain 30cm, @3.75m

1rst Stage (19 kPa)

Figure 10 Rigid inclusion and induced soil fracturing

2d. Stage (32 kPa)

Figure 9 Preloading of Mexico City soft clays

 

Sand drains were installed to accelerate the consolidation rate. The observed drastic reduction of the total settlement and very small differential movements of the foundation suggest that the sand drains also reinforce and homogenize the soil and that they behave in some degree as rigid inclusions. This should probably be considered a serious advantage of sand drains on flexible wick drains. A mention should be made also of some proposals that have been madeany to filling use “air” inclusions,  borings without intended to softeni.e. thevertical soil in specific areas to induce differential settlements in order to straighten tilted buildings (Gutiérrez, 2005). The experience with this kind of solution, closely related to the now classical underexcavation  technique seems very limited.

Parametric studies were performed to evaluate the  possibility of using rigid inclusions (without soil fracturing) to control future differential movements of the structure associated to piezometric changes in the subsoil. Using an analytical model, iterative calculations were  performed to define the distribution and number of inclusions required. It was concluded that this technique  presented a real potential (Auvinet, (Auvinet, 2000). The problem of  predicting future piezometric piezometric changes changes   constitutes however a difficult challenge for long term designs. Initial condition

1st. Iteration

2nd. Iteration

3rd. Iteration

4th. Iteration

5th. Iteration

4  RECENT EXPERIENCES

During the restoration works on Mexico City Metropolitan Cathedral performed during the last decade of the twentieth century, it was considered necessary to introduce some complementary improvement techniques of the soil along with the basic underexcavation method used to correct the large differential settlements of the structure (Támez et al.  1997). The soil was locally reinforced by rigid inclusions made of mortar injected into a geotextile sleeve previously placed in a vertical boring stabilized with bentonite slurry. The soil was also

Figure 11 Design of an inclusion system for Mexico City Metropolitan Cathedral by trial and error.

 

During the same period, the author of this paper and several young Mexican collaborators were involved in the Rion-Antirion Bridge project on the Corinthian Gulf in Greece. This was an opportunity to learn more and  perform some research on rigid inclusions for foundations on soft soils. The foundation system proposed for the bridge piers (Pecker & Salencon 1998; Simon & Schlosser, 2006) is shown on Fig. 12. A granular material platform was built on the sea floor and tubular metallic inclusions, typically 25m long, 2m in diameter and 20mm thick, were driven into the soil in order to improve its bearing capacity, especially in seismic conditions.

Figure 13 Stress distributions underneath piers footings.

Figure 12 Footing on soil reinforced by inclusions. RionAntirion Bridge, Greece. A geostatistical model, describing spatial variations of the physical and mechanical properties of the marine and alluvial subsoil underneath each footing, was developed (Auvinet, 1998; Auvinet 2002). This model showed that, in spite of the sharp local variations observed (from soft clays to gravel), the soil mass was practically statistically homogeneous. The model was also used to compute the settlements of the piers. The stress distribution beneath each footing (90m diameter) was estimated using a 3D finite element model taking into account the footing stiffness and the presence of all inclusions individually. The results of the 3D model were complemented for large depths with Boussinesq stress distributions, taking into account Saint Venant’s principle (Fig. 13). The stress and compressibility fields were then combined following the traditional soil mechanics  procedure to assess the settlements. The order of magnitude of the computed total (20 to 40cm) and differential settlements (less than 0.003) was found to be in good agreement with the results of the measurements  performed during the the bridge construct construction. ion. In this particular case, it could be concluded that the inclusions were useful to improve the bearing capacity of the soil under eccentric and inclined loading, as verified using centrifuge models. On the other hand, the inclusions did not contribute so effectively to reduce settlements due to the large spacing (7m) between these elements and to the existence of compressible materials below the tip of the inclusions (Auvinet, 1998).

5  PRESENT TREND.

The above experiences led to the development in Mexico of simple analytical and numerical models representing the behavior of the soil-inclusions systems for different geometric and soils conditions (Auvinet & Rodriguez, 2006) and to basic research on lateral deformations of the soil surrounding inclusions (Ortiz & Ovando, 2006) For inclusions in the lacustrine zone of Mexico City, all models should take into account the general consolidation of the clayey subsoil due to changes in the piezometric conditions as a result of pumping of potable water in deep  pervious deposits. deposits. Generally, the analysis is performed uncoupling the  problem in two two stages: Stage 1: consolidation of the soil-inclusions system submitted to the weight of the construction Stage 2: long term effects on the system of the general subsidence associated to estimated future piezometric variations. Analytical models developed for analysis of friction  piles (Zeevaert, 1972; Reséndiz & Auvinet, 1973) can be easily adapted to model the behavior of inclusions in consolidating soils (Auvinet & Rodríguez, 2006). Limit values of skin friction on the inclusion shaft to be introduced in these models can be reasonably assessed  based on previous experiences (Auvinet & Hanel, 1981). A much better insight in this problem is obtained however with approximate axisymmetric finite element models (Rodríguez 2001; Auvinet & Rodríguez 2006), based on the influence cell concept (Schlosser, 1984), or with true 3D models (Auvinet & Rodríguez, 2006). For stage 2

 

evaluations, the progressive increase of soil shear strength due to consolidation must be taken into account. A surge in the use of rigid inclusions is now observed in Mexico City. This solution has been recently adopted for example for a large housing project in the lacustrine zone of Mexico City (Fig. 14 & 15, Schmitter, 2005; Rodríguez & Auvinet, 2006). Building surface

Reticular beams Retaining wall

Embankment

Friction piles

Dried crust

Internal inclusions

21m 19m

Hexagonal distribution

Upper clay formation

Inclusions

6m

Hard Layer 

Figure 16 Embankments on inclusions in Mexico City soft soil

The main reasons for the surge in using rigid inclusions seem to be the following:

Extra perimeter inclusion row

a) 

Obvious economic advantages are obvious when inclusions systems are compared to traditional foundations with reinforced piles and structure connections.  b)   New reliable construction methods, especially for unreinforced cast-in-place rigid inclusions, have  been developed. c)  Experience was acquired in different projects as described in the previous section. d)  Reasonably accurate analytical and numerical models for analysis and design of inclusions systems have been developed, although more feedback from instrumentation is required.

Figure 14 Inclusion system for housing project (plan view) Dried crust

Mat

Extra perimeter inclusion row 2m

21m

The application field of inclusions in Mexico City soft soils is now limited to light to medium constructions. For Upper clay formation Hard Layer 

0.4m circular inclusions

8m

 

Figure 15 Inclusion system for housing project (cross section)

Cast-in-place unreinforced inclusions, combined with traditional prefabricated friction piles, were also used to control the expected settlements of large embankments  built on soft soil in the surroundings of the new National Library project (Fig. 16; Rodriguez & Auvinet 2006). In both cases, construction of a distribution platform was not considered necessary due to the good mechanical characteristics of the desiccated crust found near the surface of the subsoil. More applications of inclusions are described in other  papers presented in this symposium.

higher bearing capacity becomes a problemwork and seismicstructures, behavior is a serious concern. The research  being performed on the seismic behavior of inclusions (Mayoral 2006; Rangel 2006) will certainly be helpful to extend the application domain of this technique. The need for specific standards on inclusions orienting designers and constructors is also obvious (Luna, 2006). 6  REFERENCES Auvinet G. (1979) Precarga en las arcillas del valle de México, Memoria, México,  Memoria, Simposio sobre "Mejoramiento masivo de suelos",  suelos",  Sociedad Mexicana de Mecánica de Suelos, Mexico, D. F. , pp. 100-102, Auvinet, G. & Hanel, J. J. (1 (1981). 981). Negative skin friction on piles in Mexico City clay, Proceedings, Xth International Conference on Soil  Mechanics and Foundation Engineering Engineering,, Stockholm, Sweden, pp. 599-604. Auvinet G. & Medina Medina Z. (1998) Geostatistical analysis of soil data on the site of the Rion-Antirion bridge, Greece. Final report  submitted   submitted to Géodynamique et Structure, France. Auvinet, G. (2000). Reforzamiento de suelos con inclusiones rígidas,  Memoria,    Memoria, Tercer Simposio Consultores-Constructores;

 

Cimentaciones profundas.  profundas.  Sociedad Mexicana de Mecánica de Suelos, México, D.F Auvinet, G. (2002). Uncertainty in Geotechnical Engineering. Sixteenth  Nabor Carrillo Lecture Lecture,, Special bi-lingual publication, SMMS, Querétaro, México. Auvinet & Rodríguez (2006). Modeling of rigid inclusions in consolidating soils. This symposium. Briancon L. et al. (2004). al. (2004). Etat des connaissances: amélioration des sols  par inclusions rigides, Proceedings, Proceedings,    Internationa  Internationall Symposium on Ground Improvement, ASEP-GI 2004, 2004, Paris, september, Presses de l’Ecole Nationale des Ponts et Chaussées. Correa, J.J., (1961). The application of negative friction piles to

Santoyo E. & Ovando E. (2000). Catedral y Sagrario de la Ciudad de México. Corrección geométrica y endurecimiento del subsuelo, TGC Geotecnia, México, D.F. Santoyo, E. & Ovando E. (2006). Geotechnical considerations for hardening the subsoil in Mexico City’s Metropolitan church. This symposium. Schlosser F., Jacobsen H. M. & Juran I., (1984). Le renforcement des sols (1), Revue (1), Revue Française de Géotec Géotechnique hnique,, No. 29, pp. 7-32 Tamez, E., Ovando, E. & Santoyo E., (1997). Underexcavation of Mexico City’s Metropolitan Cathedral and Sagrario Church, Special invited lecture. Proceedings, XIV ICSFE, Hamburg. Schmitter, J.M., (2005). Inclusiones reductoras de asentamiento, Revista

reduction of settlement, Proceedings Fifth International Conference , Paris, France. on Soil Mechanics and Foundation Engineering Engineering, DGCOH, SOP, Departamento del Distrito Federal (1994). Evolución de la Ingeniería Sanitaria y Ambiental en México. México D.F. Girault, P., (1964). A new type of pile foundation, Proc. Conf. on Deep Foundations,, Mexican Society of Soil Mechanics, Vol. 1, Mexico, Foundations D.F. Girault, P., (1964). Discussion, Proc. Conf. on Deep Foundations,  Mexican Society Society of Soil Mec Mechanics, hanics, Vol. 1, Mexico, D.F. Girault, P., (1980). Pilotes entrelazados, Teoría y funcionamiento,  Memoria de la Reunión conjunta ConsultoresConsultores-Constructores Constructores Cimentaciones profundas, profundas, Sociedad Mexicana de Mecánica de Suelos, México, D.F González Flores, M., (1948). Level control in buildings by means of adjustable piling, Proc. Second International Conference on Soil  Mechanics and and Foundati Foundation on Engineerin Engineering g, Rotterdam, Vol. IV, p. 152 González Flores, M., (1981). Raise of a side-settled XVIII Century Church in Mexico City, Proc. X th  International Conference on Soil  Mechanics and Foundation Engineering Engineering,,  Stockholm, Sweden, pp. 101-105. Gutiérrez C. (2005). Proposal for a building underpinning in Mexico City. Mexico D.F. Luna O. & Auvinet G. (2006) Elements for the elaboration of standards for inclusions. This symposium. Marsal, R.J. & Mazari, M. (1975). The Subsoil of Mexico City, City.   Engineering Faculty, UN UNAM, AM, Mexico City.  Mayoral, J..M. et al.  al.  (2006). Effect of layered clay deposits on the seismic behavior of a single rigid inclusion. This symposium Menache A. (2006) New investigations in design and application of interlaced piles into high compressibility and very low shear strength soil deposits. This symposium. Menache A. (2006) Rigid inclusions to reduce the vertical deformation in a commercial store set on highly compressive lacustrine soils, with low shear stress resistance. This symposium. Ortiz E. & Ovando E. (2006) Lateral subsoil deformations due to construction of inclusions. This symposium Paulin Aguirre, J. & Riveroli Rivera H., (2004). Cimentación Cimentación de silos con inclusiones rígidas.  Memoria de la XXII Reunión Nacional de  Mecánia de Suelos. Suelos. Guadalajara. Sociedad Mexicana de Mecánica de

de la Sociedad Mexicana de Mecánica de Suelos, Número 196, Ene/Feb. Simon B & Schlosser F. (2006). Soil reinforcement by rigid inclusions in France.This symposium. Zeevaert L. (1972). Foundation Engineering for Difficult Subsoil Conditions, Van Nostrand-Reinhold, Cap. Cap. VIII, IX, X, 335-460.

Suelos, D.F A parametric study of the factors involved in Rangel J.L.México, J.L.    et al.  al.  (2006) the dynamic response of soft soil deposits when rigid inclusions are used as a foundation solution. This symposium. Reséndiz, D. & Auvinet, G., (1973). Analysis of pile foundations in consolidating soil, Proceedings, VIIIth International Conference on Soil Mechanics and Foundation Engineering, Engineering, pp. 211-218, Moscow, USSR. Rodríguez, J.F. & Auvinet G. (1998). Uso de inclusiones para el control de asentamientos, Memoria asentamientos, Memoria de la XIX Reunión Nac Nacional ional de Mec Mecánica ánica de Suelos. Puebla. Sociedad Mexicana de Mecánica de Suelos, pp. 40 a 46. Rodríguez, J.F. & Auvinet G. (1999). Uso de inclusiones para el control de asentamientos debidos a abatimientos piezométricos. Proc. XI Panamerican Conference on Soil Mechanics and Geotechnical Engineering, Fos de Iguazu, Brasil. Rodríguez, J.F., (2001). Uso de inclusiones rígidas para el control de asentamientos en suelos blandos,  Master degree thesis, DEPFI, UNAM, México D.F. Rodríguez, J.F. & Auvinet G. (2002). Cap. 9: Inclusiones. Inclusiones . Manual de Construcción Geotécnica, Geotécnica, Sociedad Mexicana de Mecánica de Suelos, México, D.F, Vol. II, pp. 403-406. Rodríguez & Auvinet G. (2006). Rigid inclusions in Mexico City soft clays. Case histories. This s ymposium