Consolidation process and stress-path-dependant deformations in excavations in soft soils

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1 Consolidation process and stress-path-dependant deormations in excavations in sot soils Berhane Gebreselassie & P. Becker Institute o Geotechnics and Geohydraulics, University o Kassel, Germany BSTRCT: Back analysis o well instrumented excavations showed that the short term behavior o excavations is best expressed in terms o eective stress analysis. The three-dimensional consolidation theory, introduced by Biot (9), assumes solely a one-dimensional loading, namely a change o stresses in vertical direction but drainage o the pore water in all directions. The complex relationships between the threedimensional change o stresses due to the excavation and the resulting wall movements are not yet considered in the current available computation methods. Thereore, the simultaneous inluence o the stress relie due to excavation and the stress-path-dependent displacements on the consolidation process o an excavation has to be yet quantiied. The paper introduces the research work currently running at our institute that investigate this problematic based on small scale model tests and controlled stress path triaxial tests. INTRODUCTION One o the elementary question in excavations in sot soils is the consolidation behaviour in the initial condition. The knowledge o the inluences o the deormation o the excavation wall and the relie o stresses due to excavation on pore pressure development and thereore the resulting time dependant change o eective stresses in sot soils is o undamental importance in the design o excavations. Comparative calculations o well monitored excavations show that the initial condition can best and realistically be described with the eective stress analysis. The application o the eective stress analysis, however, requires the knowledge o the excess pore pressure, which is crucially aected by the stress path dependant deormations. Both the redistribution o the stresses due to the excavation and the resulting wall deormation determine the consolidation behaviour and thus the rate o change o the eective stress in an excavation in sot soils. PROBLEM FORMULTION In an excavation, the soil transerred into a new equilibrium condition because o the relie o stresses due to excavation. The excavation wall supports the soil above the bottom o the excavation, which in turn get its support through the mobilization o the passive resistance throughout the embendement depth o the wall and through struts or anchors. Thus, there arise an additional changes in the horizontal stresses apart rom the vertical stress changes due to excavation. The amount o the mobilized horizontal earth pressure depends in turn on the wall movement, which can not be in principle ully avoided in an excavation in normally consolidated sot soils. The resulting multidimensional deormation state is thereore dependent on the stress paths and aects the consolidation behavior o the soil in as much as so ar not quantiiable extent. The undamental o the solution o consolidation problems in soils was irst carried out by Terzaghi & Fröhlich (936) based on the well known diusion equation in physics. Thereby, however, a number o assumptions has been taken to simpliy the real mechanical behaviour o soils. mong other things, or example, the compressibility o the soil is not constant as supposed by Terzaghi, but in reality it changes with the eective stress and also depends on the pre-consolidations history. possible inluence o the viscosity o the soil is also not considered. Moreover, the Darcy low law is ormulated with the assumption o a constant permeability. Investigations by Scherzinger (99) show, however, that the permeability is not constant, rather it is dependant on the void ratio e. The equilibrium o the orces also neglects the weight o the soil itsel. In addition, the volume balance assumes an incompressibility o the solid and pore luid. part rom the general simpliications o the consolidation theory, there are additional conlicting assumptions by excavations. These are:

2 - Beside the vertical deormations, horizontal deormations can be induced, which result rom the wall deormation due to the redistribution o stress as a result o excavation. - The permeability o the soil depends on the volume change, i.e. on the deormation behavior o o the soil. The relie o stresses due to excavation is to be understood as a negative load, which causes a volume increment o the soil and an increase o the pore volume. Depending on the permeability and the stiness o the soil, a negative pore pressure can be developed. The unloading stiness o the soil is taken in this case as governing stiness. question may however arise that to what extent will the permeability o the soil be aected by the heave o the soil due to the excavation - The assumed linear elastic material behavior does not consider the irreversible deormations and the possible coupling between shearing and volume change. Moreover, the linear elasticity theory is independent o the stress paths. To date no theoretical approach is available that reasonably describes the consolidation process in excavations. The three-dimensional consolidation theory o Biot (9) considers the same assumptions and conditions as Terzaghi s one-dimensional theory. The dierential equations o the three-dimensional consolidation analysis are based on the equilibrium and continuity conditions o a volume element o a soil. The continuity condition describes the relationship between the volume change o the soil particles o a given volume element and the amount o water lowing out o the element. It should be noted, however, that the volumetric deormations due to the drainage o the pore water in soil in all directions in three-dimensional consolidation theory are caused by loading in one direction only, namely the vertical direction. The increase in volume is described here by the Poisson s ratio ν. The complex behaviour o a three-dimensional change o stresses due to excavation cannot thereore be described on the basis o the Biot theory. 3 STTE OF THE RT The most unavorable condition or excavations in sot soils is apparently the drained (end) condition, since the relie o stresses due to excavation produces a negative pore pressure, which contributes to the stability o the excavation at initial state. It should be noted however that by temporarly supported excavations the construction time may not be long enough to deine the state o the excavations as drained or may not be short enough to deine it as undrained. The real condition o an excavation in sot soils lies somewhat between these two extreme cases, which can only be solved with the help o an accurate consolidation theory. Such theory, however, is not available at present or analytical computation o excavations. It is a well known act that the behaviour o soils is primarily governed by the eective stresses independent o the drainage condition. Based on this principle, Kempert and Gebreselassie (); Gebreselassie (3) attempted to develop an approach to calculate the active and passive pressure using the eective shear parameters and the pore pressure coeicient at ailure. They used the eective angle o the over all shear strength ϕ' s instead o the ϕ' and c. This assumption is a common practice in Germany. On the basis o stress paths o a consolidated undrained triaxial test, relationships have been derived between the angle o the overall shear strength ϕ' s and the normalized undrained strength λ cu and or various type o stress paths according to Figure (Table ). This relationships have the advantage o making use o the huge experience and data available on the undrained strength c u in the ield o geotechnical engineering. The possible ideal stress paths are shown in Fig.. Table. Relationship between ϕ s and c u or dierent stress paths according to Fig. (ater Gebreselassie (3)) Stresspath sinϕ s (O) (K + ( K ) ) + (OB) ( + ( K )) (OE) ( + ( K )) + (OD) (K + ( K )) + 3 ; and -n 3 * (+ K + β(k ) ( K )) + β λ cu *n is proportionality constant between v and H ; and β (n-)/(n+). It should be noted that the stress path within the passive zone o an excavation can not easily be identiied to the ideal stress paths in Fig.. Since there is a change o the vertical stress in addition to the change o the horizontal stress during construction (undrained), the total stress ollows another path than that normally assumed or passive case (OE). I ailure has to occur during excavation, the changes in vertical pressure should also be taken in to account. The relative rate o change o the vertical

3 q c u c u /ξ K - line (eective) α α B Figure. Idealized stress paths O C K - line D F E β β β - p, p stress and horizontal stress during excavation is not yet known, but it lies somewhat between the two extreme cases: the passive case (OE) and the extension case (OD) and it is dependant on on the type o the soil, the excavation depth and the wall type. The pore pressure coeicient at ailure is not a unique value or a given soil, rather it is dependent on the direction o the principal stresses, the initial stress state and the plastic volumetric strain (Franke (98); Schweiger ()), while the eective shear parameters, in this case the angle o the overall shear, may be assumed independent o the stress path to a large extent. On the other hand the order o the magnitude o is well-known or the standard triaxial compression case (O). Thereore, it is worthwhile to develop a relationship between the s value or standard triaxial case (O) and other stress paths (Table ) (Gebreselassie (3); Kempert and Gebreselassie ()). Table. Estimation o the pore pressure coeicient or dierent stress paths according to Fig. (ater Gebreselassie (3)) Stress- s [-] paths* (O) s (OB) s K ξ + s( K,s ) (OE) ( ξ( K ) +,s ) K ( ξ ) +,s + s( K,s ) (OD) ( ξ( K ) + λ ) cu,s 3 ; β,s ξ /+ s( K,s ) + K ( ξ /) and + (,s ξ(k )) -n 3 s are λ cu,s are the pore pressure coeicient at ailure and the normalized undrained shear strength respectively or a standard triaxial compression test (Path O). β (n-)/(n+) Since the un/reloading modulus o elasticity o sot soils is 5 to 7 times higher than the modulus o elasticity in primary loading, the time required to reach an approximate steady condition ater excavation is usually measured in weeks or months, i.e. during the normal construction periods. Freiseder (998) presented a ield pore pressure measurements during the construction o a 6.3 m deep excavation or underground park in Salzburg. It appears that the excess pore pressure stabilizes to a steady state in a time o to 6 days ater excavation. The eective stress path B in Fig. below corresponds to undrained loading and B C corresponds to swelling and reduction in the mean normal eective stress. The pore pressure immediately ater construction u i is less than the inal steady state pore pressure u c and so there is an initial excess pore pressure which is negative. s time passes the total stresses remains approximately unchanged at B but the pore pressure rises. The wall will ail in some way i the states o all elements along the slip suraces reach the ailure line; i B reaches the ailure line the wall ails during the undrained excavation and i C reaches the line the wall ails some time ater construction. The igure demonstrate that unlike ooting oundations or embankment oundations or retaining walls loaded by ill, where the oundation becomes stronger with drainage, the actor o saety o a retaining walls supporting an excavation will decrease with time. C u c Bruch linie u i B B, C, u u/γ w u/γ w Figure. Change o stresses and pore pressure in an excavation (ater tkinson (993) ter reviewing six open excavations (5 to m deep) case records in clay, Janbu (977) concluded that the stability is best expressed in terms o eective stress analysis. He reasoned that the readjustment o stresses and pore water pressures to correspond with a state o steady seepage may oten take place in the course o ew days or ew weeks or at most some months. He urther commented that the simple total stress analysis or excavations in clay will requently lead to erroneous results both or saety actor and shear surace location. Laleur et al. (988) had also examined the behavior o a well instrumented, 8 m deep excavation

4 slope in sot Champlain clay. They reported that the eective stress approach may give a reasonable estimate o the actor o saety. On the other hand, all the stability analyses using a short term approach overestimated the actor o saety o the ailed slopes. Kempert and Gebreselassie (); Gebreselassie (3) came to the conclusion that the drained analysis results the most unavorable situation or excavations in sot soils in most cases. For the proo o the saety o the excavation in short term, it is advisable to use the eective stress analysis together with the pore pressure coeicient than the total analysis with undrained shear strength c u. Based on an excvation with strut support at the top o the wall and ree end support condition, Hettler et al. () also showed that the total analysis method using c u may lead to large interpretation diiculties in the determination o the penetration depth o the wall. PRELIMINRY EXPERIMENTL STUDY. Excess pore pressure development in excavations The development o the excess pore pressure in an excavation in sot soil has been studied using an extensive small scale model tests at our institute. The models contain three stages o excavtion. In the irst series o model tests the eects o wall support, the surcharge load and the construction stages on the development o the pore pressure has been investigated. In the case o the wall support, it was dierentiated between ixed end and a ree end support condition with additional strut support at wall head. The pore pressure change was measured at representative locations in the excavation model. The ollowing results present the development o the excess pore pressure change in an excavation model with a ixed end support condition in comparison with analytical and numerical analysis results (Becker (3)). The analytical analysis or the primary approximation o the consolidation process was perormed based on the one-dimensional consolidation theory o Terzaghi. Figure 3 shows typical course o the excess pore pressure during and ater the execution o the excavation or the three selected measuring points and its comparison with the results o the analytical and numerical analysis. The general tendency o the excess pore pressure at the measuring point (Fig. 3a), which is located on the passive side at the level o the assumed sliding surace below the bottom o the excavation, corresponds to the computation results. It appears rom this igure that the vertical relie o stresses are dominant in this area o the excavation model, which can be explained by the immediate drop o the excess pressure. This drop o excess pore pressure corresponds to the eective change o the vertical stress due to excavation, i.e., u γ z, kn/m². On the basis o the gradual pore pressure drop in model test V5 in the irst hours, however, a possible inluence o the wall movement and the resulting deormation in the soil body can be observed, although it can not be yet quantiied. The result o the analytic computation supplies a urther indication o the inluence o the horizontal change o stress due to the excavation process on the development o the excess pore pressure ater the irst hours. Here a pure relie o stresses is assumed and a stronger dissipation o the negative pore pressure is calculated than it can be conirmed experimentally. Thereore, the one-dimensional consolidation theory is not in a position to describe clearly the inluence o the wall deormation, which produces a positive excess pore pressure in this zone, on the permeability and thereore on the drainage behavior o the soil. The problem o a consolidation analysis o an excavation becomes particularly clear at the measuring point B (Fig. 3b). This point is located at the passive side near the wall toe. The exact knowledge o the development o the excess pore pressure is particularly important or calculation o the stability o the excavation around this point. The inluence o the displacement and rotation o the wall toe on the consolidation process can be demonstrated on the basis o the test results. Depending on the horizontal deormation o the wall a positive excess pore pressure may develop which may overlay the developed negative excess pore pressure due to the excavation and thus reduces the development o the excess pore pressure as in the case o the model tests V and V or even ully dominates the negative excess pore pressure as in the case o the V3 and V. Such phenomenon can by no means be simulated by any analytical computation methods. The measured excess pore pressure at the measuring point C (Fig. 3c), which is located on the active side o the wall, conirms the validity o the above statements. For example, the rotation o the wall toe causes a pore pressure increase on the active side o the wall, which produces a positive excess pore pressure in the case o model test V. The rise o the positive excess pore pressure is an indication o the inluence o the wall deormation in this zone in contrast to the inluence o the stress relie due to excavation. Thereore, the model tests conirm the moderate agreement o the computation results based on the generally accepted one-dimensional consolidation theory with the experimentally measured development o the excess pore pressure at the middle o

5 st nd 3 rd excavation step - V V5 V - st step nd 3 rd Pore pressure u [kn/m²] B V C V3 V V B C Modell test results V V V3 V V5 analytical result - V V5 V V3 V - numerical result Time [h] Figure 3. The develpement o the excess pore pressure in an excavation amodel the excavation just below the bottom o the excavation. The eect o the horizontal wall deormation on the change o the eective stress in an excavation remains a determining actor in the consolidation analysis o excavations in sot ground, which is still not quantiied.. Stress path controlled Triaxial tests series o stress path dependent triaxial tests on normally consolidated lacustrine soil had been carried out at our institute to investigate the development o the excess pore pressure (Gebreselassie (3)). Typical test results or the total stress paths OB and OC according to Fig. are presented as ollow. The postulated total stress path OB at a slope o : was eected by decreasing the horizontal stress and maintaining the vertical stress constant. Similarly, the postulated total stress path OC at a slope o ininity was eected by increasing the vertical stress and simultaneously decreasing the horizontal stress. The development o the excess pore pressures are shown in Fig. a & 5a. The excess pore pressure or the stress path B is negative or the eective con- Excess pore pressure u [kn/m²] ( - 3 )/ [kn/m²] (a) 3 kn/m² kn/m² kn/m² (b) xial strain ε [%] total eective ( - 3 )/ ; ( + 3 )/ [kn/m²] Figure. Excess pore pressure development and the stress paths in a stress path (OB) controlled triaxial test (Gebreselassie 3)

6 Excess pore pressure u [kn/m²] ( - 3 )/ [kn/m²] (a) (b) xial strain ε [%] total eective 3 kn/m² kn/m² kn/m² K - line 3 5 ( - 3 )/ ; ( + 3 )/ [kn/m²] Figure 5. Excess pore pressure development and the stress paths in a stress path (OC) controlled triaxial test (Gebreselassie 3) solidation pressure o and kn/m², and it is positive or 3 kn/m². It shows a general tendency o shiting the excess pore pressure rom negative to positive as the eective consolidation pressure increases. The excess pore pressure or the stress path C with eective consolidation pressure o and kn/m² reached their maximum value at an axial strain o.5% beore they dropped gradually to minimum value at large axial strain, while the excess pore pressure with 3 kn/m² reaches its maximum value at 7.5 % axial strain and remains almost constant through out the test. The stress paths are shown in Fig. b & 5b. The test paths in all the specimens are very similar to the postulated stress paths till they approximately reach the ailure stress (( - 3 ) max ), ater which the paths begins to deviate rom the postulated paths. Since the horizontal and vertical stresses had been eected in a stepwise ashion, the actual stress path reproduced in the laboratory have a zig-zag pattern. However, the general trend o the stress condition is aithully reproduced. 5 CONCLUSION The presented results, in particular the model tests, show the substantial dierences between the theory and practice concerning the computation o the development o the excess pore pressure in excavations in sot soils. s ar as the current stand o the science is concerned, the exact knowledge o the stress path dependent excess pore pressure development is indispensable or a realistic eective stress analysis based on the eective shear strength or the initial condition o excavations in sot ground. On the basis o the identiication o the typical total stress path zones in an excavation, which characterize the threedimensional deormation behavior, it is possible to perorm an eective stress analysis or the initial condition with the help o the derived relationships or the angle o the overall shear strength and the pore pressure coeicient at ailure. In this way, the saety reserve in the computation o excavations in sot soils can be optimized The research work to this basic soil mechanics problem, namely the consolidation process in an excavation in sot soils, is currently running and will be published in the near uture. LITERTUR tkinson, J. (993). n introduction to the mechanics o soils and oundations. London: McGraw-Hill. Biot, M.. (9). General Theory o Three-Dimensional Consolidation. Journal o pplied Physics, Vol. : Becker, P. (3). Porenwasserüber- und Unterdruckverlau bei Baugruben in weichen bindigen Böden. Diplomarbeit, Universität Kassel, Fachgebiet Geotechnik, unpublished. Franke, E. (98). nwendbarkeit der undränierten Scherestigkeit im Vergleich zur nwendbarkeit der eektiven Scherparameter. Vorträge der Baugrundtagung 98: Freiseder, M. (998): Ein Beitrag zur numerischen Berechnung von tieem Baugrund in weichen Böden. Institut ür Bodenmechanik und Grundbau, Technische Universität Graz, Het 3. Gebreselassie, B. (3). Experimental, analytical and numerical investigations o excavations in normally consolidated sot soils. University o Kassel, Institute o Geotechnics, Dissertation, Booklet No.. Hettler,. et al. (). Zur Kurzzeitstandsicherheit bei Baugrubenkonstruktionen in weichen Böden. Bautechnik 79, Het 9: Janbu, N. (977). Slopes and excavations in normally and lightly overconsolidated clays. Proc. o the IX ICSMFE, Tokyo, Vol. : Kempert, H.-G. & Gebreselassie, B. (): Zur Diskussion von dränierten und undränierten Bedingungen bei Baugruben in weichen Böden. Bautechnik 79, Het 9: Laleur, J. et al. (988). Behaviour o a test excavation in sot Champlain Sea clay. Can. Geotech. J. 5: Scherzinger, T. (99). Materialverhalten von Seetonen Ergebnisse von Laboruntersuchungen und ihre Bedeutung ür das Bauen in weichem Untergrund. Veröentlichung des Instituts ür Bodenmechanik und Felsmechanik der Universität Karlsruhe, Het. Terzaghi, K. & Fröhlich, O. K. (936). Theorie der Setzung von Tonschichten. Leipzig-Wien: F. Deuticke.