Program COLANY Stone Columns Settlement Analysis 1 User Manual
Contents
1. 8 3898E 06 Sigma rr Li22 19E 01 Sigma 00 1 2275E 01 Slgma zz 320423E700 Strain zz 5 9478E 05 Surface deflection delta 1 4870E 03 CLAY Sigma zz L 12205 0L KAXKKKXKXKKKXKXKKKXKKKKXKXKKXKKKXKKKXXKk AR INITIAL EFFECTIVE STRESS STATE KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKEKK Element Sigma zz Sigmal rr A Gao C420 2 1875 1875 3 AS Sia ZO 4 AS ee Alo 5 AS NAS 6 O8 15 68 75 7 81 25 81 25 8 9375 93 75 9 106 25 O ARAS 10 LS 29 11875 11 TS Lazo Tolsa 12 AS ES IE MS 13 156 25 156 25 14 168 75 168 75 15 151425 io awe ne 16 193 75 193 15 17 2004 25 20625 18 218 795 218 75 19 231 25 251325 20 24 o 243475 22 Program COLANY Stone Columns Settlement Analysis KKKKKKKKKKKKKKKKKKKKKKKKKKKHK LOAD SETTLEMENT RESPONSE KKKKKKKKKKKKKKKKKKKKKKKKKKKEK Column Load Load Average Surface Step Pressure Settlement 1 eae 0 0078 2 Fogal 0 0308 o 29 09 0 0633 4 43 45 0 1043 9 Do 69 Os LoS 6 Le Lo Us 2 big J DZ sdo One 160 8 11156 03538 9 a O 0 4375 10 ESA E 045298 11 ES le 26507 12 LIS 00 0 7401 Lo 223 43 0 8580 14 249 36 0 9845 13 276 48 Lil doo 16 304 79 LL 203 a 17 334 29 1 4153 18 364 98 Laos 19 SI 00 ls 7452 20 429 97 la 2233 kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxxkxk kxx xxk COLUMN FULLY PLASTIC KKKKKKKKKKKKKKKKKKKKKKKK For an increment in deflection of 1 0 le an increment in strain of the following increments occur CLAY d Sigma rr 1042. FRICTION ANGLE DILATANCY ANGLE COEFFICIENT OF LATERAL EARTH PRESSURE SOIL MODULUS 2000 Ole SOIL POISSON S RATIO 3 20 Program COLANY Stone Columns Settlement Analysis 4 4 Output File Example Problem The content of the output file for the example problem is KAXKKKKXKXKKXKXKKXKKKKKKKKAKKAAAAAAARAAARAAARARAAAAAA AAA AAA AAA AAA AAA Balaam and Booker 1985 ES Settlement of Rigid Raft on Clay Stabilized by Stone Columns KKKAKKKKKKKKKKKKKKKKKKKKKKKKKKK KKK KKK KKKKKKKKKKKKKKKKKKKKKKKKKKEKKEK Output File C COLANY Data Files Manual out KKKKKKKKK lt ese KKKKKKKKK Settlement analysis of a water tank on stabilised clay KKKKKKKKKKKK GEOMETRY KKKKKKKKKKKK Triangular Grid Spacing MO a 0 500 b 1 024 de 2 047 KKKKKKKKKKKKKKKKK STONE COLUMNS KKKKKKKKKKKKKKKKK Length of column h 25 00 Diameter d 100 Number of elements 20 Friction angle phi 35 00 Submerged unit weight 10 00 Coefficient KO iL 00 Dilatancy angle psi 0 00 Young s Modulus 60000 0 Poisson s ratio O30 KKKKKKKK CLAY KKKKKKKK Young s Modulus 2000 00 Poisson s ratio 0430 21 Program COLANY Stone Columns Settlement Analysis KKKKKKKKKKKKKKKKKKKK ELASTIC SOLUTION KKKKKKKKKKKKKKKKKKKK Elastic Solution Balaam amp Booker 1981 For unit applied pressure the solution is gt TONE COLUMN Radial displacement u r
3. and references to figures and the appendix in this section are from this paper Stone Columns Diameter do im tm NR Poisson s ratio wa 03 03 Frctionangle o a a oS Ditaancyange y o Clay Young s modulus 2 000 kPa Poisson s ratio Step 1 Calculation of one dimensional settlement no stabilization For the purpose of illustration the settlement of the tank founded on unstabilized clay can be estimated from 1 D settlement theory using an average m calculated from the average value of E The settlement S is S z h Ez My Ao Program COLANY Stone Columns Settlement Analysis For 1 D conditions E 1 v 1 2v a Eel 7 V s E 1 3 0 4 2000 x 0 7 my 0 000371 m kN The 1s given by E My Aoz 0 000371 x 20 x 9 8 The e is given by 0 0727 The settlement S amp z h 0 0727 x 25 S 1 82m Step 2 Calculate settlement of tank founded on stabilized clay assuming stone columns and clay are elastic The elastic settlement is calculated using the equations in Appendix I 1 Elastic parameters of stone column E E 60 000 kPa Vi Vp 0 3 E E we is 1 2v 1 v1 0 4 x 1 3 Program COLANY Stone Columns Settlement Analysis Goo 2 _ 23077kp 1 204 v 26 gt a 11 Elastic parameters of clay E E s 2 000 kPa V2 Vs 3 _ v E gt _ 03 2000 ap 1 G 2v 4 v 04x13 a 0 _ 769kP 2 20 v 26 i 111 Constan
4. Selas _ E 0 43 _ 0 292 0 436 Settlement of Tank 6 0 679m This settlement corresponds to a settlement ratio 0 679 1 82 0 373 0 679m Some Comments This example illustrates quantitatively that an analysis in which the stone columns and clay are assumed to be elastic throughout the range of applied load overestimates the effectiveness of the stone columns in reducing settlement The hand calculated value for the settlement ratio 0 373 is close to the value calculated by COLANY 0 40 and the error of 7 is expected considering the interpolation of values read from figures in the publication Finally at sites where numerous tanks are constructed e g refineries or where the load is widespread the use of 1 D settlement theory is justified However in the example considered if the tank were isolated the elastic settlement theory predicts a settlement of 1 37m when the clay is not stabilized In these situations the settlement of the tank founded on the stabilized clay can be predicted with sufficient accuracy by applying the settlement reduction factor 0 373 to the elastic displacement theory settlement 1 37m Therefore for an isolated tank the predicted settlement theory 1s Settlement 6 0 373 X 1 37 0 512m 12 Program COLANY Stone Columns Settlement Analysis 4 COLANY 4 1 Data Entry After starting COLANY and selecting File New Project the data entry screen shown in Figure 2
5. the load deflection values are calculated at which each of the column elements yield Therefore the more elements the column is divided into the more points are plotted on the load settlement curve The analysis is described in Balaam and Booker 1985 Finally the solution is computed for the settlement response of the stabilized clay when all the column elements have yielded These solutions enable the complete load settlement response to be predicted for the specified applied pressure In these analyses a unit cell 1s considered and it consists of a stone column and the surrounding clay within the column s zone of influence It is therefore assumed that the response of this unit cell adequately represents the response of the clay layer stabilized by large numbers of stone columns 2 PROBLEM DEFINITION A regular pattern of stone columns can be analyzed by considering a typical column clay unit Figure 1 For a triangular arrangement each column has a hexagonal zone of influence whereas a square arrangement results in each column having a square zone of influence In order to reduce the complexity of the analysis the zone of influence is approximated by a circle of effective diameter de 2b 1 05s where s is the column spacing A square arrangement of columns has d 1 13s A consideration of the interaction between the stone columns and the surrounding clay indicates that the major principal stress direction will be close to t
6. 3 d Sigmalzz T207 d Load clay 302 7 COLUMN d u r 9 0111E 03 d Sigma rr 104 3 qd Sigma zz 384 8 d Load column 302 2 d Load clay column 604 9 d q A 183 7 4 Q0000E 02 L05 Sal LS LS EEN LIGs LOS le SOU 426 AO LOs SoU 2 Program COLANY Stone Columns Settlement Analysis gt REFERENCES Balaam N P and Booker J R 1981 Analysis of Rigid Rafts Supported by Granular Piles International Journal for Numerical Methods in Geomechanics Vol 5 pp 379 403 Balaam N P and Booker J R 1985 Effect of Stone Column Yield on Settlement of Rigid Foundations in Stabilized Clay International Journal for Numerical Methods in Geomechanics Vol 9 pp 331 351 24
7. 5 0 Length 0 Diameter MN 1 95 Spacing e Triangular grid Square grid 0 Number of elements 60000 Stone Modulus 3 Poisson s Ratio 0 0 Submerged unit weight En 5 0 Friction angle Degrees Dilatancy angle Degrees 0 Coefficient of lateral earth pressure atrest T Soil Data Average Soil Modulus 3 Poisson s ratio pa Pa ama a m Display Default Values Figure 3 Example Problem Data Analysis start Analysis J Pressure Settlement Unreinforced Settlement Reinforced Settlement Ratio Volume Column Soil Grid Design 15 Program COLANY Stone Columns Settlement Analysis 4 2 Results The analysis is performed when the Start Analysis command button is clicked The results are shown in Figure 4 The results are Settlement Unreinforced 1 820 1 D settlement of unreinforced clay 1 82m Settlement Reinforced Settlement of stone column reinforced clay 0 727m i MO Sa Settlement Ratio J Settlement ratio 0 727 1 82 0 400 SO S Volume Column Soil 23 39 Ratio of stone column volume to total volume of the unreinforced clay layer 23 9 16 Program COLANY Stone Columns Settlement Analysis COLANY v1 0 C COLANY Data Files Project1 dat Settlement analysis of a water tank on stabilised clay Settlement En CN po e 60000 pa r 0 pa pp See eee eee eee ee
8. Program COLANY Stone Columns Settlement Analysis COLANY User Manual Program COLANY Stone Columns Settlement Analysis CONTENTS SYNOPSIS 1 INTRODUCTION 3 2 PROBLEM DEFINITION 4 2 1 Material Properties 6 2 2 Dimensions 7 2 3 Units 7 3 EXAMPLE PROBLEM 8 3 1 Description 8 3 2 Hand Calculation 8 13 4 COLANY 4 1 Data Entry 13 4 2 Grid Design 18 4 3 Data File Example Problem 20 4 4 Output File Example Problem 21 5 REFERENCES Program COLANY Stone Columns Settlement Analysis SYNOPSIS COLANY computes the load settlement response of a rigid foundation supported by a layer of clay stabilized with stone columns An example problem is considered A complete hand solution to this problem and the results produced by COLANY are included The hand solution is included in an attempt to ensure the correct interpretation of the results generated by COLANY Nigel Balaam May 2012 Program COLANY Stone Columns Settlement Analysis 1 INTRODUCTION COLANY computes the settlement response of a rigid raft supported by a layer of clay which has been stabilized with a large number of stone columns The results from an analytical solution Balaam and Booker 1981 for the settlement assuming no yield occurs in the clay or column are calculated The program also computes the load settlement response of the stabilized clay The column is divided into a specified number of cylindrical elements and
9. The values on this row are Ac As 35 of the soil has to be replaced with stone columns Settlement 0 47m satisfies maximum allowable settlement 0 5m SR Settlement Ratio Settlement of Reinforced Soil Settlement Unreinforced n Improvement factor n 1 SR Triangular s Columns on triangular grid spaced at 1 61m Specify 1 6m Square Columns on square grid spaced at 1 5m COLANY v1 0 Grid Help _ Print Report Back To Analysis R Ac As Settlement n Triangular s Square s 1 82 1 00 0 00 1 52 0 84 1 20 4 26 3 96 1 26 0 69 1 44 3 01 2 80 1 04 0 57 1 75 2 46 2 28 0 85 0 47 2 14 2 13 1 98 0 69 0 38 2 62 1 90 1 77 0 57 0 31 3 21 1 74 1 62 0 47 0 26 3 91 1 61 1 50 40 0 38 0 21 4 75 1 51 1 40 45 0 32 0 17 5 75 1 42 1 32 50 0 26 0 14 6 90 1 35 1 25 55 0 22 0 12 8 22 1 28 1 19 60 0 19 0 10 9 71 1 23 1 14 65 0 16 0 09 11 35 1 18 1 10 Pile spacing 70 0 14 0 08 13 19 1 14 1 06 100 0 06 0 03 30 00 Figure 5 Grid Design Screen 18 Program COLANY Stone Columns Settlement Analysis The file produced for the example problem when the Print Report button is pressed is COLANY v1 0 Grid Design Balaam amp Booker 1985 Job Description Settlement analysis of a water tank on stabilised clay Loading Applied Pressure q 196 0 Stone Columns Length of column h 25 0 Diameter d 1 0 Friction angle phi 35 0 Submerged unit weight 10 0 Coef
10. e eee eee eee ee ee ee eee ee ee Balaam and Booker 1985 Settlement of Rigid Raft on Clay Stabilized by Stone Columns ee ee ee ee ee ee a a ee ee ee ee a a a a Output File C COLANY Data Files Projecti out RAS TITLE ERRRAAARA q Settlement analysis of a vater tank on stabilised clay Figure 4 Screen Displayed After Start Analysis Button Clicked 17 Program COLANY Stone Columns Settlement Analysis 4 2 Grid Design When the Grid Design button highlighted in Figure 4 is clicked multiple analyses of the problem are performed The loading column diameter column length material properties etc all remain unchanged The only parameter that is changed is the column spacing and analyses are performed for both triangular and square arrangements of the columns These multiple analyses are summarized in tabular form and are shown in Figure 5 The first row in the table corresponds to the unreinforced soil and then each row below this summarizes the results for a 5 increases in stone column material The values in the grid can be used to select an appropriate arrangement and spacing of columns to meet a specific design criterion For example in the example problem considered in this manual if the maximum allowable settlement of the tank is 0 5m then referring to the highlighted row in Figure 5 this arrangement of columns would satisfy the requirement because the predicted settlement is 0 47m
11. ficient Ko 1 0 Dilatancy angle psi 0 0 Young s Modulus 60000 0 Poisson s ratio 0 3 Soil Young s Modulus 2000 0 Poisson s ratio 0 3 Ac As Settlement SR n Triangular s Square s 0 1 82 1 00 0 00 Unreinforced soil 5 1 52 0 84 1 20 4 26 3 96 10 1 26 0 69 1 44 3 01 2 80 t5 1 04 Q97 Tera 2 46 Aado 20 0 85 0 47 2 14 2 13 1 98 25 0 69 0 38 2 62 1 90 Lat 30 0 57 0 31 3 21 1 74 1 62 39 0 47 0 26 3 91 1 61 1 50 40 0 38 0 21 4 15 Laal 140 45 0 32 0 17 Dera Teda La 50 0 26 0 14 6 90 1 35 1 25 55 0 22 0 12 uz Laa Tey 60 0 19 0 10 9 71 ledo Te 65 0 16 0 09 11 35 1 18 La LO 70 0 14 0 08 13 19 1 14 1 06 100 Ri Os 03 3000 Soil fully replaced Ac Area of columns As Area of soil SR Settlement Ratio Settlement Reinforced Settlement Unreinforced Improvement factor Settlement Unreinforced Settlement Reinforced s Column spacing 19 Program COLANY Stone Columns Settlement Analysis 4 3 Data File Example Problem The content of the data file for the example problem is TITLE Settlement analysis of a water tank on stabilised clay APPLIED PRESSURE 196 COLUMN 2550 COLUMN 1 0 COLUMN ig COLUMN 1 NUMBER 20 COLUMN 60000 COLUMN Ome COLUMN 10 0 COLUMN Cora COLUMN 0 0 COLUMN LeU LENGTH DIAMETER SPACING PATTEREN 1 Triangular 2 Square OF ELEMENTS MODULUS POISSON S RATIO SUBMERGED UNIT WEIGHT
12. he vertical direction and that while there may be significant yielding of the stone columns due to the high stress ratios there will be little yield in the surrounding clay This suggests that the problem can be idealized by assuming that the stone column is in a triaxial state but that perhaps part of it may yield that there is no shear stress at the stone column interface and that there is no failure in the surrounding clay so that its behavior is entirely elastic Program COLANY Stone Columns Settlement Analysis Soft Clay Y I i N Figure la Plan oe ee y Da w y y w APA PO PA PR CAA CAA CAA S amp B Oe Os MA 00 VEN 900 900 0 none SY RA RA Yt BA OA BA OY A O DA O DA O DA PRN PRN PRN PRN PORO piba piba PORO 10 10 10 10 DAL VAX DAL DAL ESA a Unit Cell Stone Column iaa Stone Columns Installed in Large Numbers Smooth Rigid Foundation Boundaries of unit cell Figure 1b Elevation Stone Columns Installed in Large Numbers iil Program COLANY Stone Columns Settlement Analysis b d 2 Smooth Rigid 08 4 400 Interface Outer a shear free Boundary Smooth Rigid a DES FAS a d 2 Smooth Rigid Figure 1c Boundary Conditions on Unit Cell 2 1 Material Properties The material properties required for this analysis are Stone Column Clay E Young s modulus Es Y oung s modul
13. is displayed Figure 3 shows the data that has been entered for the example problem described in Section 3 The data is self explanatory except the value of 20 entered for the number of elements This is the number of equal sized cylindrical elements the column is divided into and is used to calculate the progressive yielding of the column For example when 20 elements are specified there are 21 points defining the load settlement response one for each element yielding and the final 21 point defining the response when the column has fully yielded 13 Program COLANY Stone Columns Settlement Analysis ICOLANY 1 0 Ci coLANY Source Code Projectl dat File Help Description Stone Columns Analysis Length Start Analysis Diameter Spacing i Triangular grid Pressure Square grid I Settlement Number of elements Unreinforced Stone Modulus Settlement Poisson s Ratio Reinforced l Submerged unit weight Settlement Ratio Friction angle Degrees Dilatancy angle Degrees e Volume Column Soilh Coefficient of lateral earth pressure atrest AL Soil Data Average Soil Modulus Grid Design i Poisson s ratio il Display Default Values Figure 2 Data Entry Screen 14 Program COLANY Stone Columns Settlement Analysis lil COLANY v1 0 2 COLANY Data Files Project1 dat I Fie Help Description Settlement analysis of a water tank on stabilised clay Stone Columns 2
14. t F equation 10 A A2 b as Ax x Aa 2 la F G gt Ay G F b F Gy F G For a triangular spacing of 1 95m the diameter de of the unit cell is given by de 1 05s 1 05 x 1 95 2 05m b d 2 1 025m The diameter d 2a of the stone columns is Im E 34615 1154 x 1 025 x 1 025 0 5 x 0 5 200 5 x 0 5 x 1154 769 34615 23077 1 025 x 1 025 34615 23077 769 F 282 F 10 Program COLANY Stone Columns Settlement Analysis iv Strain from equation 11 q b A 2G a 2 2G b a 2a A A Fle 196 x 1 025 x 1 025 34615 2 x 23077 x 0 5 x 0 5 1154 2 x 769 1 025 x 1 025 0 5 x 0 5 2 x 34615 1154 x 0 282 e e 0 01168 The elastic total final settlement of the tank founded on stabilized clay is sias 0 01168 x 25 Settlement sias 0 292m Step 3 Correct settlement to take account of contained yielding in the stone columns The non dimensional load level 1s q4 20x98 4 22 0 784 Vsub h 10 x 25 Referring to Figures 6 to 9 the following settlement correction factors can be tabulated TABLE 1 Settlement Correction Factors elas Note The tabulated values are for the modular ratio E E s 30 Linear interpolation for de d 2 05 and 35 results in a settlement correction factor 11 Program COLANY Stone Columns Settlement Analysis
15. us Vp Poisson s ratio Vs Poisson s ratio Angle of internal friction Dilatancy angle Ko Coefficient of lateral stress Ysub Submerged unit weight Program COLANY Stone Columns Settlement Analysis 2 2 Dimensions The geometry is defined by these parameters a Radius of the stone columns b Radius of the column s zone of influence h Depth of the clay layer and this is also the length of the stone columns because the analysis only considers columns constructed to the base of the clay layer 2 3 Units Any consistent set of units can be used 1 e the dimensions specified must be consistent with the units for the applied pressure q and the applied pressure units must be consistent with the units specified for the Young s modulus of the stone and clay The example problem uses metres for the dimensions and kPa for the applied pressure and Young s modulus Program COLANY Stone Columns Settlement Analysis 3 EXAMPLE PROBLEM 3 1 Description In this example a prediction is made of the settlement of a 40m diameter water tank supported by a rigid foundation founded on clay stabilized by stone columns The maximum height of water stored in the tank is 20m The stone columns have an average diameter of 1m and are installed on a triangular grid with a spacing of 1 95m The water table is at the ground surface 3 2 Hand Calculation This hand calculation illustrates the use of the solutions Balaam and Booker 1985
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