ࡱ> G kbjbjَ ]]    $ l` D 0*  <0>0>0>0>0>0>0$13b0i \b0g'  g'g'g'V <  <0     <0g'g'}-:/gT | 00 , E$"&0 Modeling of an anchored diaphragm wall A. Szavits-Nossan & M.S. Kova evi University of Zagreb, Faculty of Civil Engineering, Zagreb, Croatia Vlasta Szavits-Nossan University of Zagreb, Faculty of Geotechnical Engineering, Vara~din, Croatia ABSTRACT: The paper describes a case history and numerical modeling of an anchored diaphragm wall designed to secure an 18m deep excavation pit for the construction of an underground garage and mall in downtown Zagreb. The numerical analysis performed by FLAC included detailed modeling of staged excavation and prestressing of ground anchors. The soil behavior, ranging from large stiffness at very small strains to low stiffness at large strains, was accounted for by a new elasto-plastic model, which was incorporated into FLAC by the FISH programming language. The new model allows for adjustments to arbitrary shear stiffness reductions, depending on shear strains during loading. The required soil parameters were determined from filed and laboratory tests, including triaxial tests with measurements of small strains and field geophysical tests. The wall deflections, observed during different construction stages, compared very well with the predicted behavior. InTroduction The finite element and finite difference methods are powerful tools for a rational analysis of anchored soil retaining structures. However, these methods often overpredict ground movements and wall displacements, when simple elastic models are used, with stiffness parameters determined in conventional laboratory tests. Thus, the limit analysis and the Winkler spring model are still predominantly used in practice. Only recently, it became apparent that conventional laboratory tests overpredict strains, due to the strong non-linearity of soil behavior in the small to medium strain range (e.g. Jardine et al. 1986, Burland 1989, and Simpson 1992). The paper presents the results of a numerical analysis intended to overcome this problem. The analyzed anchored diaphragm wall is a cast in place reinforced concrete structure, constructed in the downtown area of Zagreb in Croatia. Existing buildings sensitive to possible ground movements closely surrounded the construction site. Ground settlements and anchored wall displacements were monitored during the excavation and wall construction. The numerical analysis was conducted by FLAC (Version 3.22), using the new elasto-plastic soil model described in the paper. The FISH programming language incorporated the new constitutive relationship into FLAC. The main features of this model are, (a), accommodation of any given relationship between shear stiffness and shear strain including the strong non-linearity of soil behavior in the range from small to large strains, and (b), proper modeling of the increased soil stiffness upon unloading. The second feature is important, because it can cover the increase in stiffness of the soil-structure system during the ground anchor prestressing. The selection of soil parameters, required for the numerical analysis, was based on laboratory and field test results. In situ measurements of shear wave velocity by seismic down-hole tests, was an important source of data. Several investigators recently proposed that the shear stiffness determined from shear wave velocity could represent static shear stiffness at very small strains (e.g. Tatsuoka & Shibuya 1991, Tatsuoka & Kohata 1995). The shear strength of fine-grained soils was determined in laboratory direct shear, and triaxial UU and CIU tests. Field standard penetration tests were used for strength characteristics of gravely soils. The triaxial tests were performed with and without local strain measurements. A limited number of triaxial tests with small strain measurements provided data for modeling the strong non-linearity of soil behavior in the small to medium strain range. The calculated displacements of the anchored diaphragm wall were compared to observed wall displacements during different construction stages. soil profile and wall layout The soil profile at the construction site is shown in Figure 1. It was obtained from standard laboratory and field tests. In addition, Figure 1 shows the measured and modeled shear wave velocities. The average strength parameters used in the numerical analysis are listed in Table 1, along with the analysis type, for each soil layer. The referent shear modulus and the modulus exponent, also presented in Table 1, are variables used in the described new soil model. Their values were determined from the measured shear wave velocity.  Table 1. Design soil parameters (soil profile from Figure 1) and related analysis types. ___________________________________________________ Soil ( c' (' cu G0 m Analysis _____ _____ ___ _____ ______ __ layer kN/m3 kN/m2 deg. kN/m2 MN/m2 - ___________________________________________________ Fill 19 5 30 -- 60 0.5 drained Firm clay 19 15 22 -- 170 0.5 drained Gravel 21 5 38 -- 170 0.5 drained Stiff clay 20 -- -- 150 320 0.0 undrained ___________________________________________________ ( = unit weight; c' = cohesion; (' = friction angle; cu = un-drained strength; G0 = referent shear modulus for mean effective stress s0 = 100 kN/m2; m = modulus exponent. The cross section of the anchored diaphragm wall is shown in Figure 2. The wall is a 22m high and 0.8m thick structure. The Young modulus of concrete was assumed 3x107kN/m2. Commercial ground anchors of high strength steel, with a nominal Young modulus of 1.95x108kN/m2, were used. The excavation and ground anchor prestressing proceeded in stages, as indicated in Table 2. Table 2. Construction stages and anchor characteristics. ___________________________________________________ Stage Description z L GL ( a A F0 _ _ __ ___ _ ___ __ m m m deg. m cm2 kN ___________________________________________________ 1 Excavation -5 2 1st anchor row -4 27 7 20 2.6 6.6 420 3 Excavation -11 4 2nd anchor row -10 20 7 12 2.6 9.7 400 5 Excavation -16 6 3rd anchor row -15 17 7 15 2.6 9.7 400 7 Excavation -18 ___________________________________________________ z = depth; L = anchor length; GL = anchor grouted length; (=anchor inclination; a = horizontal distance between anchors; A = anchor cross section area; F0 = anchor prestressing force. The soil model Shear stiffness The new soil model was developed for the plane strain condition. Plane stress invariants t and s', defined as  EMBED Equation  (1) were used, where t = maximum shear stress; d = deviator stress tensor; (' = effective stress tensor; s'=mean effective stress; and ( = the two-dimensional unit tensor (indices may take values 1 and 2). The effective stress analysis was performed by introducing the effective stresses as  EMBED Equation  (2) where ( = total stress tensor; and u = pore water pressure. The standard continuum mechanics sign convention is used, as in FLAC. Three features characterize the shear stiffness of the new soil model: The elastic shear modulus, the shear strength, and a target shear modulus function. The elastic shear modulus Ge defines the maximum tangential shear stiffness of the soil at a given stress state, and will be covered in the next section. The Mohr-Coulomb law given by  EMBED Equation  (3) governs the shear strength, where tf = t at failure; c'= the cohesion intercept; and (' = the friction angle. The target shear modulus function rt is a normalized function with a normalized argument. It is given by  EMBED Equation  (4) where G = secant shear modulus for monotonic loading, defined as  EMBED Equation  (5) ( = the maximum shear strain, defined as  EMBED Equation  (6) e = deviator strain tensor; ( = strain tensor; and v=volumetric strain. The referent shear strain is defined as  EMBED Equation  (7) The target backbone function t/tf = bt(x) is related to the shear modulus function rt by  EMBED Equation  (8) Two assumptions are made on the form of the target backbone function, i.e. two limits are imposed. The first limit is the elastic limit (el, below which the target backbone function is equal to x (rt=1). The second limit is the failure shear strain (f, beyond which the target backbone function is equal to unity (rt = 1/x). Within these two limits, the target backbone function bt can assume any form. It is assumed unique for a given soil. The uniqueness of this function complies with the experimental evidence provided by Anderson & Richart (1976), and Richart (1977, 1978, and 1982). Puzrin ( Burland (1996) discussed specific forms of backbone functions for different soils. A normalized backbone function for Toyoura sand was developed by Szavits-Nossan ( Kova evi (1994). Elastic strains The proposed soil model incorporates a plane strain case of the simple nonlinear elastic constitutive equation proposed by Vermeer (1978, 1984),  EMBED Equation  (9) where ((e = elastic strain tensor; and the elastic shear modulus Ge is given as a function of the stress invariant I(, or the elastic strain invariant I(  EMBED Equation  (10) with  EMBED Equation  (11) The soil parameter G0 is the referent elastic shear modulus, defined for a referent stress state given by t= 0 and s' = s0; v0 is the referent volumetric strain given by v0=s0/G0, and m is the shear modulus exponent. Equation (9) may also be written as  EMBED Equation  (12) where ve and (e are the volumetric strain and the maximum elastic shear strain, respectively. It can be shown that this elastic constitutive equation has a strain energy potential U given by  EMBED Equation  (13) The effective stress is the gradient of this potential. The tangential form of equation (9) may be written as  EMBED Equation  (14) where  EMBED Equation  (15) ('1 and ('2 are the principal effective stresses. It can be seen that equation (9) is isotropic with a zero Poisson's ratio, whereas its tangential form is orthotropic with a nonzero Poisson's ratio. Kinematic hardening In the proposed new soil model, the kinematic hardening follows the concept of Iwan's array of parallel elasto-plastic elements (Iwan 1967). The described model consists of n parallel elements undergoing the same strain history. If the element strains are decomposed into elastic and plastic components, it follows that  EMBED Equation  (16) where (m)(e, (m)(p = elastic and plastic strain tensor for the m-th element, respectively. The elastic range of each element is bounded by a limit strain (m)(l, so that  EMBED Equation  (17) The m-th limit shear strain defines a cylindrical yield surface in the elastic strain space of the m-th element. The axis of this cylinder is the zero shear strain line ((m)(e = 0). Plastic strains may develop when elastic strains reach the yield surface. The following flow rule is obtained by assuming normality  EMBED Equation  (18) where <> denote Maculay brackets ((x( ( x for x ( 0; and (x( ( 0 for x ( 0). Because of the cylindrical yield surface, and the associated flow rule, the model does not develop plastic volumetric strains. The elastic strain rates are then calculated as  EMBED Equation  (19) The kinematic hardening is introduced by assuming that the elastic strain is a weighted average of element elastic strains  EMBED Equation  (20) where (m)w = weight of the m-th element. It is readily verified that this model has a piece wise linear backbone function of the form  EMBED Equation  (21)   Weights are determined from a given target backbone function bt. Requiring that the model backbone function bm coincides with the target backbone function bt at n points, for which ( = (m)(l, the following expressions for weights are obtained (provided the limit shear strains (m)(l form an increasing order)  EMBED Equation  (22) where (m)y = bt((m)x); and (m)x = (m)(l/(r. It is to be noted that the weights are not constant. They are functions of the referent strain (r, which is, in turn, a function of the current stress state. Figure 3 shows a target and a model backbone function, and the corresponding modulus reduction functions. The model backbone function is plotted for a set of five element limit shear strains and a given referent strain. It is obvious that a better approximation of the target backbone function is obtained for a greater number of elements. It is to be noted that, for a given number of elements, a better approximation of the target backbone function is obtained by a convenient selection of element limit shear strains.  If the first and the last limit shear strain satisfy the following inequalities  EMBED Equation  (23) where (el and (f were defined in Section 3.1, it can be shown that  EMBED Equation  (24) The strain tensor of the model can then be decomposed into an elastic and a plastic component, so that  EMBED Equation  (25) and the stress tensor can then be calculated using the elastic constitutive equation (9). This new model satisfies the Masing rules for regular cyclic loading (Masing 1926, Pyke 1979), expressed by  EMBED Equation  (26) where (x0, y0) are the coordinates of the unloading (or reloading) point on the stress-strain hysteresis. Furthermore, the new model naturally extends the Masing rules to irregular cyclic loading, without resorting to any arbitrary rules (Pyke 1979). Due to constant element limit shear strains, the apparent yield surface of the model is characterized by the constant shear strain surface, which complies with experimental evidence for sands (Tatsuoka ( Ishihara 1974). Implementation of the model into the FLAC code  The constitutive equation described in previous sections was implemented into FLAC by the use of the FISH language. Version 3.22 of the code was used at the design stage, but the results presented in this paper are from reruns by Version 3.4. Although the constitutive equation may use any number of parallel or overlaying elements, the code was developed for five elements only. It is the authors' opinion that five elements may model any backbone function with sufficient accuracy for practical purposes.  Being developed for plane strain only, the five-element model has to store ten deviator elastic strain components, two for each local element, and one elastic volumetric component. Since FLAC automatically stores the global stress components, from which the elastic volumetric strain may be calculated, ten variables remain to be stored for each of four triangular subzones of the FLAC quadrilateral zone, giving a total of forty variables. These forty variables were stored using variables declared by the f(prop statement. Any target backbone function may be given as input to FLAC by a table of (x, y) pairs. The table function was used for this purpose. Material functions and parameters Four material parameters and one material function are used in the constitutive equation: the referent shear modulus G0, the modulus exponent m, the cohesion c(, the friction angle ((, and the target backbone function bt(x). The material parameters for the analysis of the diaphragm wall are listed in Table 1. The design shear wave velocities (vs = (Ge/()1/2, ( = soil density), calculated from these material parameters, are shown in Figure 1. The same backbone function, shown in Figure 4, was used for all soil layers. This function was developed from extensive studies of numerous laboratory data on Toyoura sand (Szavits-Nossan & Kova evi 1994). Figure 4 also shows typical data from triaxial CIU tests, with local strain measurements, performed on the stiff clay from the site of the diaphragm wall. CIU triaxial tests were performed in the hydraulic triaxial apparatus from GDS, UK. Hall effect transducers (Clayton & Khatrush 1986) were used to measure local vertical and lateral strains on soil specimens. Despite the fact that the backbone function was developed for a specific sand, it approximates the stiffness of the stiff clay fairly good. The constitutive model uses element limit shear strains, for which the model backbone function matches the target backbone function (see Section 3.3). For the five element model used in the presented analysis, the following element limit strains were found appropriate: (m)(l = 10-5, 10-4, 10-3, 10-2, and 10-1. construction stages: predictions and observations  All construction stages indicated in Table 2 were modeled by FLAC. A rectangular mesh of 28 horizontalx35 vertical zones (56mx35m) was used for the spatial discretization. The initial vertical stresses were calculated using the soil unit weights. The initial horizontal stresses were assumed equal to vertical stresses. The drained conditions were assumed for the upper three soil layers, as indicated in Table 1. The drained state was modeled by fixed values of pore water pressure, zero bulk modulus of water, and strength parameters related to effective stresses. It was assumed that the undrained state is more appropriate for the bottom stiff clay layer. The undrained condition was modeled by a stiff bulk modulus of water, and strength parameters related to total stress. Hydrostatic water pressures were assumed in the gravel layer. Predictions by the numerical model were made at the design stage, i.e. before the construction of the anchored diaphragm wall. Wall movements were measured during the excavation of the construction pit, and compared to predicted values. Surveying methods and several inclinometers installed in the concrete wall were used for the measurement. At the end of Stage 7, the maximum horizontal displacement at the top of the wall, measured by surveying methods, was about 1cm, which is less than the corresponding predicted displacement of about 2.5cm. Taking into consideration the low accuracy of the used surveying method, and the uncertainty of soil parameters, this prediction is considered satisfactory. As for the displacements along the whole wall length, it has to be noted that it was not possible to rectify reliably the inclinometer measurements, because there was no fixed point either on the top, or on the bottom of the wall, to refer them to. Therefore, only relative displacements of the wall with respect to its top can be compared to predicted values. Figure 5 shows computed horizontal displacements of the wall at the end of stages 2, 4 and 7. It also shows horizontal displacements of the wall measured by inclinometers. These values were rectified by adding a constant displacement, in order to have the computed and measured values coincide at the wall top. The resulting curves show a good agreement of predicted and measured values. The bending moments were also well predicted. Figures 6 to 9 show some typical FLAC output. Figure 8 is interesting in showing the lines of equal maximum shear strains. Shear strains are about 0.4% close to the wall, and then they rapidly decrease by an order of magnitude, or more, with the distance from the wall, indicating the corresponding increase in shear stiffness of the soil. Conclusions From the presented case history and numerical analysis of an anchored diaphragm wall, with the emphasis on constitutive modeling and the determination of soil parameters, the following conclusions are proposed: The shear wave velocity determined in field tests, which is a ready available and reliable, but not commonly required parameter in soil-structure interaction projects, can be used to determine the static soil stiffness at very small strains; this is one of the few soil parameters required by the proposed new soil model. The new kinematic hardening constitutive equation is capable of modeling any measured relationship between the soil shear stiffness and shear strain in the range from very small up to the failure strains; this is very important in soil-structure interaction analyses; good predictions of the behavior of an anchored diaphragm wall were obtained when this relationship was properly chosen. The new soil model requires a normalized shear-stress-shear-strain backbone function, which results from special laboratory tests on undisturbed soil specimens; the presented analysis has shown that good predictions of wall displacements can even be obtained by using a normalized backbone function from the literature. The new soil model was incorporated into the FLAC code, and used to solve a complicated practical problem of a non-linear soil-structure interaction in the design stage; the observed behavior during the construction stage compared very well with the predictions. References Anderson, D.J. & Richart Jr., F.E. 1976. Effects of straining on shear modulus of clays. ASCE Jour. Geotechnical Engineering Division 102(9): 975-987. Burland, J.B. 1989. "Small is beautiful"-the stiffness of soils at small strains. Canadian Geotechnical Journ. 26: 499-516. Clayton, C.R.I. & Khatrush, S.A. 1986. A new device for measuring local axial strains on triaxial specimens. Gotechnique 36: 593-597. Iwan, W.D. 1967. On a class of models for the yielding behavior of continuous and composite systems. Journ. of Applied Mechanics 34(3): 612-617. Jardine, R.J., Potts, D.M., Fourie, A.B. & Burland, J.B. 1986. Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction. Gotechnique 36: 377-396. Masing, G. 1926. Eigenspannungen und Verfestigung beim Messing. In Proc. 2nd intern. congr. applied mechanics, Zrich. Puzrin, A.M. & Burland, J.B. 1996. A logarithmic stress-strain function for rocks and soils. Gotechnique 46(1): 157-164. Pyke, R.M. 1979. Nonlinear soil models for irregular cyclic loadings. ASCE Jorn. Geotechnical Engineering Division 105(6): 715-726. Richart Jr., F.E. 1977. Part 1 of "Soil dynamics and its application to foundation engineering" by Y. Yoshimi, F.E. Richart Jr., S. Prakash, D.D. Barkan, & V.A. Ilychev; Proc. IX intern. conf. soil mechanics and foundation engineering, Tokyo, Vol. 2: 605-612. Richart Jr., F.E. 1978. Field and laboratory measurements of dynamic soil properties. In B. Prange (ed.), Proceedings int. symp. dynamical methods in soil and rock mechanics, Karlsruhe. Rotterdam: Balkema, Vol. 1, 3-36. Richart Jr., F.E. 1982. Discussion. In S. Prakash (ed.), Recent advances in geotechnical earthquake engineering and soil dynamics; Proc. intern. conf., St. Louis. St. Louis: University of Missouri-Rolla, Vol. III, 914-915. Simpson, B. 1992. Retaining structures: Displacement and design. Gotechnique 42: 541-576. Szavits-Nossan, A. ( Kova evi, M.S. 1994. A kinematic hardening soil model for wide shear strain ranges. International Journal for Engineering Modelling 7(3-4): 55-63. Tatsuoka, F. & Kohata, Y. 1995. Stiffness of hard soils and soft rocks in engineering applications. University of Tokyo, Report of the Institute of Industrial Science 38(5). Tatsuoka, F. ( Ishihara, K. 1974. Yielding of sand in triaxial compression. Soils and Foundations 14: 63-76. Tatsuoka, F. & Shibuya, S. 1991. Deformation characteristics of soils and rocks from field and laboratory tests. Key note lecture for session no. 1. Proc. 9-th Asian regional conf. on soil mechanics and foundation engineering, Bangkok. Vermeer, P.A. 1978. A double hardening model for sands. Gotechnique 28(4): 413-433. Vermeer, P.A. 1984. A five-constant model unifying well established concepts. In Gudehus et al. (eds.), Constitutive relations for soils. Rotterdam: Balkema, 175-197. Figure 1. Soil profile at the site of the anchored diaphragm wall. Figure 2. Cross section of the cast in place diaphragm wall with three rows of prestressed ground anchors.  EMBED Visio.Drawing.4  Figure 3. A target and a model shear modulus function, and the corresponding target and model backbone functions (z = normalized shear modulus; y = normalized shear stress; x = normalized shear strain). Figure 4. The design (target) shear modulus function and typical results from CIU triaxial tests with local strain measurements on the stiff clay at the diaphragm wall site. Figure 5. Predicted horizontal displacements of the anchored wall after completion of stages 2, 4 and 7, and displacements measured by inclinometers, rectified to coincide with the computed displacements at the top of the wall. Figure 6. Vertical displacements at the end of Stage 7. Figure 7. Horizontal displacements at the end of Stage 7. Figure 8. Maximum shear strains at the end of Stage 7. Figure 7. Horizontal displacements at the end of Stage 7. Figure 9. 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F | |Ole :CompObj-/;\ObjInfo0=Ole10Native>_983229762,63 F `| `|Ole ACompObj24B\ FMathType Equation Equation Equation9q G e =G 0 )I s s 0 () m =G 0 )I e v 0 () ObjInfo5DOle10NativeE_9832297828 F `|P|Ole J)m(1-m)#F#a FMathType Equation Equation Equation9q  I s =)"s ij "s ij 2() )12 ,CompObj79K\ObjInfo:MOle10NativeN$_983229797E= FP|P|I e =2e ije e ije () )12 FMathType Equation Equation Equation9q 2s=G e v e ,t=Ole SCompObj<>T\ObjInfo?VOle10NativeWG e g e FMathType Equation Equation Equation9q U= 1-m2-m G e I e2<C:\P_983229811B F}}Ole ZCompObjAC[\ObjInfoD]Ole10Native^_983531865YG F}}Ole aCompObjFHb\ FMathType Equation Equation Equation9q "e 11e "e 22e "e 12e []=12G e )2G e ObjInfoIdOle10Nativee_983726617L FL-}L-}Ole pE 1t )-2m 2t G e E 2t 0)-2m 1t G e E 1t )2G e E 2t 0001[]\\\\\s\\\ \\1\1\ \\s\\\ \\2\2\ \\s\\\ \\1\2\ \[\] FMathType Equation Equation Equation9q )E it (2G e )=)(1+R 2 )A i ,R=)"s 1 "s 2 m it =)mRA i ,)mCompObjKMq\ObjInfoNsOle10Nativet_983229978@TQ F@t6}@t6} 2t m 1t =)E 2t E 1t ,A 1 =1+1-m()R 2 ,A 2 =1-m()+R 2 FMathType Equation Equation Equation9qOle }CompObjPR~\ObjInfoSOle10Native , (m) e ije +, (m) e ijp =e ij ,m=1,...,n  FMathType Equation Equation Equation9q_983229997V F@N}@N}Ole CompObjUW\ObjInfoX , (m) g e =2, (m) e ije , (m) e ije () )12 , (m) g l&2t FMathType Equation Equation Ole10Native_983230010Oc[ FX}h}Ole CompObjZ\\Equation9q  , (m) "e ijp =, (m) g l-2 2, (m) e kle "e kl ef, (m) e ijees New Roman#-ObjInfo]Ole10Native$_983230022` Fh}8}Ole CompObj_a\ObjInfobOle10Native_983230033^re F8}࢙} FMathType Equation Equation Equation9q , (m) "e ije ="e ij -, (m) "e ijp FMathType Equation Equation Ole CompObjdf\ObjInfogOle10NativeEquation9q e ije =, (m) w, (m)m=1n  e ije FMathType Equation Equation Equation9q_983755819'j Fʢ}4}Ole CompObjik\ObjInfol y=b m (x)=, (m) w), (m) g e g r () m=1n  FMathType Equation Equation Equation9qOle10Native_983726864o F4}4}Ole CompObjnp\ObjInfoqOle10Native_983230082wt F}@%}Ole  , (1) w=, (1) y, (1) x-, (2) y-, (1) y, (2) x-, (1) x,, (n) w=, (n) y-, (n-1) y, (n) x-, (n-1) x, (m) w=, (m) y-, (m-1) y, (m) x-, (m-1) x-, (m+1) y-, (m) y, (m+1) x-, (m) x FMathType Equation Equation Equation9qCompObjsu\ObjInfovOle10Native_983230094y F }@} , (1) g l g el ,, (n) g l g f FMathType Equation Equation Equation9q , (m) w=1 m=1n Ole CompObjxz\ObjInfo{Ole10Native FMathType Equation Equation Equation9q e ije =e ij -e ijp ,e ijp =, _983726784Jm~ F@}@}Ole CompObj}\ObjInfoOle10Native_983756490 F!~!~Ole CompObj\(m) w, (m) e ijpm=1n   FMathType Equation Equation Equation9q y-y 0 =2b m )ObjInfoOle10Native_983725724FH~ -Ole (x-x 0 )2() FVISIO 4 DrawingVISIO 4.0 ShapesVisio.Drawing.49qOh+'08CompObjiObjInfoVisioDocument.VisioInformation"Visio (TM) Drawing RTќ@d !fffMMM333;q0;T _Arial)-dTimes New _Roman)-L":5T?? 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All 2s reserved.32f!t0032, lUa@@rb -D @40XAqR@g| `r/Ar((   =@X2TAqdga$ i rxF41HOHo!@40@u2P l AoD!E@@@ioTNz`e ``MNWY\uGP RsP BnKPP,E hWRO ` &gOr.I BZB H?O i m!De_>hF'`B@yP$* TP B_/[&S$'XQc /A^V A JrWjkM0wNXmsT)`U%&' dq \10Z)/911Choose the displayed prec1n fortmenq0` Pu~`0;0.rP0y4V qp+&/ '/c.DKqdqvY vx+1#xuni0 qUݏq UpDrawing Page's ;.Feet-Inch (1'-0"#")Ճ'܁eԄftMil-lpterCentMKilor$/j"r1drc0Ei] dqƇqvu<14twhepsr z0 tou abbrevUi2s0q Ds#qDon't ShCowτCU3^Y2E;/)qo$a`Both11)iހexts lines are v0ble0qEL(q {;End only;BeginףNeiQ!@d.A.Ad )e&X[$?$Dtg 3@qA&-scalalue@tQ`otR 7uAA(e) ^ 4 cN` Arrsizɡ0@ F%uk?u/`P {Gz?aǿ[5d4eq.ԝtA!7 = =R3uACUͬ4gXw?offsetĤPPqaAH =4@ƿZ_뿳ߓ#2pfyf0w u `.\XOM_` Sign1} [@AT%#0Oc"ԿaZm@`Dim0PP@3@e BH! ] Xr0`T outsid?31)MڃlZ s|1Xq"q@uB~ 80d$ d$  3@iBzXJУ1㞢Jar:#@0B _  B}7<>@p@!h_C73!SQޑqVrHðOc!q43@p`Changu He1ap/rUqVpa"!M%rw"p!q  =@'@ `Reposui1 U" U2#- * T"yv Qi 4O|']ǘ!DG``}q0T7P BOX2B>fEF#p?)8=0(`?"" @? z0= @l9r!|3-0cpc06qX=8h7- SQq# 2P!~5'S?>d!$4'h(OE/E|t BnD@~Aff`(Tw`9+r@"@f pDtsW#vnv &&σ..G?ʓՠwСtŀuy)?Prop.Lq1~@b @hOx`SAsȂ Defaul PHQthis shaṕw#Qʒ;opג assSҔpʀӷTheɁ!rbSrDvP` ^WfValuQ` kri!a` ^S`Ph>f jVd;ac^Rg`k>e_AvRevertW To\[S[w sopat ̐usY_0WofYq&o8jfoxooooFv_Re7" P0$5-Mov tVit̀Uloc֒> Controls.X2` Scratch.X1s CYM~rL` RX_jWu[ <0)  h w ,m@T N& -O>` Draw5PbP.Feet-In(1'-0")u.00'd|etftWMil-l7terCe~=MKiloOIR$0ORQYkORO?Don't aQ $  5 杨g@0QNOVۀ*+ ,<0n$ ./ %00@1& 2m@3ޠ4@05u67"K LWB4h@]b`.0;0FT 0wIN;FT;MI;0 MMCűűKMW@4,@QYB%hB-A\c1, `\'!0bS  `u` )4A8FB@R/& s24As0r*bS|@5I2 h r)A$BF6pjB 4 c`A0Գu* "ar GForma3R SCtrRpU$@h pUA/Მ[$r$Г04S,B@%׶Ѵ(Wٕh%p1Σ{%C+ #0=Dwg, 1=Arch, 2=Dec Ft, 3+ ={ o>Pr.IwՓ H׶Cg*f&p3A&2ڐѴ"8׶2@0TcˌorB3(@ `#\'\-)4r0D? 5`0/#r7A`\""60 #405ESgJc;O3ýSb =@513SeNc?75ĸ5 wPT+0;`Annotate.hlp!#2803A`9Copyright 1996 Visio Corporation. 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