Stress distribution strip foundation final - UMass Lowell GSP 94 2000_Paikowsky... · methods are...

Geotechnical Engineering Research Laboratory Samuel G. Paikowsky, Sc.D. One University Avenue Professor Lowell, Massachusetts 01854 Tel: (978) 934-2277 Fax: (978) 934-3046 e-mail: [email protected] web site: http://geores.caeds.eng.uml.edu DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

Visual Observation and Measurement of Areal Stress Distribution under a Rigid Strip Footing

By: Samuel G. Paikowsky, Christopher J. Palmer and Albert F. DiMillio

Performance Verification of Constructed Geotechnical Facilities ASCE Geotechnical Special Publication No. 94, pp. 148-169

Lutenegger A.J. and DeGroot D.J. edittors Amherst 2000: G-I / ASCE Specialty Conference

April 9 - 12, 2000 University of Massachusetts, Amherst

148 Paikowsky, Palmer and DiMillio

VISUAL OBSERVATION OF AREAL STRESS DISTRIBUTION UNDER A RIGID STRIP FOOTING

By: Samuel G. Paikowsky1, Christopher J. Palmer1 and Albert F. DiMillio2

ABSTRACT Recent advances in tactile sensor technology have produced very thin sensors allowing the simultaneous measurement of normal pressure at multiple points. Such sensors were used under the base of a laboratory model of a rigid strip footing (76.2mm x 609.6mm). The developed contact stresses are peaked along the centerline and lower along the edges. This distribution, visually observed for the first time, matches well the anticipated theoretical distribution and is quite different than the even distribution routinely assumed in design. The insight obtained by the observed contact stress distribution can assist in a better geotechnical and structural economical design of shallow foundations. BACKGROUND

A successful and economic design of a shallow foundation requires the knowledge of the maximum bearing pressure of the soil under the footing. Design methods are based on Bearing Capacity theories assuming that the contact pressures beneath a footing are uniform. In the case of eccentric loading conditions, the design methods are simplified and a linear approximation of the actual stress distribution is used. In reality, however, the distribution of contact stresses is neither constant nor linear.

_______________ 1 Professor and formerly a Graduate Research Assistant, (respectively), Geotechnical Engineering Research Laboratory, Department of Civil and Environmental Engineering, University of Massachusetts - Lowell, 1 University Avenue, Lowell, MA 01854 Email - [email protected] 2 Highway Research Engineer, Federal Highway Administration HNR-30 Construction, Maintenance and Environmental Design Division, 6300 Georgetown Pike, McLean, VA 22101 Email – [email protected]


Elastic analysis (Borowika, 1936, 1938) and measurements (Schultze, 1961 and Barden, 1962) indicate that the stress distribution beneath symmetrically loaded footings is not uniform (see Bowles, 1996).

Terzaghi and Peck (1948) described the problem of the distribution of contact pressure on the base of uniformly loaded rigid footing, in the following way:

“Since the settlement of the base of a perfectly rigid footing is by necessity

uniform, the distribution of the load required to produce uniform settlement of the loaded area. If the sub-grade consists of a perfectly elastic material, of clay, or of sand containing thick layers of soft clay, a uniformly loaded area assumes the shape of a shallow bowl or trough. In order to obtain uniform settlement it would be necessary to shift part of the load from the center of the loaded area toward the edges. Hence, the contact pressure on the base of a rigid footing resting on such a sub-grade increases from the center of the base toward the rim (see Figure 1). On the other hand, if a uniformly loaded area is underlain by sand, the settlement is greater at the edges than at the center. Uniform settlement can be obtained only by distributing the load so that its intensity decreases from a maximum at the center to a minimum at the rim. Hence, the distribution of the contact pressure on the base of a rigid footing on sand has the same characteristics.” (see Figure 2)

The relationship depicted in Figure 1 is based on the theory of elasticity and suggests stresses at the edges approaching infinity (in theory) but limited to the yield stress, (in practice) as shown in Figure 2a. The state of stress depicted in Figure 2 represents the conditions expected under a rigid footing on cohesionless soils. An ideal flexible footing on the other hand would develop uniform stresses while experiencing uneven settlement. In practice, the building of a rigid foundation is feasible while testing of flexible foundations encounters the problem of a ‘flexible’ loading system, which is not easily achievable.

Figure 1: Distribution of contact pressure on base of uniformly loaded rigid footing of very great length, resting on perfect elastic, homogeneous and isotropic subgrade (Terzaghi and Peck, 1948)

Figure 2: Distribution of contact pressure on base of smooth rigid footing supported by (a) real, elastic material; (b) cohesionless sand; (c) soil having intermediate characteristics. Curves Cu refer to contact pressure when footing is loaded to ultimate value. (Terzaghi and Peck, 1948)


A revolutionary technology enabling the measurement and presentation of normal stress distribution over an area in real time was recently developed. A flexible, grid-based, tactile pressure sensor allows pressure to be measured in up to 2288 (51 x 44) sensing locations. The overall shape and size of the measured area can vary with sensors up to 427 by 488 mm in size. Pressure ranges are possible up to 172 MPa (25 ksi). The system was first developed for dental purposes and has been used in other medical and mechanical applications as well. The original examination and application of the system to granular materials was presented by Paikowsky and Hajduk (1997). Further technological developments continue to evolve and some are utilized in the present study.

OBJECTIVE

The objective of the study presented in this paper was to investigate the possibility of applying the tactile technology to examine the stress distribution beneath shallow foundations. The placement of tactile sensors on the bearing surface of the foundation allows the direct measurement of the contact pressures (stress distribution) in real time during the foundation loading.

SCOPE

The present preliminary research focuses on tests conducted in the laboratory on a model rigid strip footing, examining the feasibility of such tests, the adequacy of the measuring systems and the potential of the study.

TEST SETUP Overview

The test setup includes three mechanical and four data acquisition components. The mechanical components are: (i) the testing container and granular material, (ii) the load application system, and (iii) the model foundation. The four data acquisition systems (with three separate PC's), measure: (i) contact stress distribution, (ii) applied load, the displacement response of the foundation and the granular material at the surface, (iii) digital imaging system to monitor detailed exterior soil displacement, and (iv) general observation using a regular video camera. Figure 3 presents a schematic of the test setup components and Figure 4 shows a cross-section of the foundation and the related setup. The Mechanical Components

Testing Container and Granular Material A 63.5 x 116.8 x 94 cm deep (25 x 46 x 37 inch) box was constructed of 0.5 inch PLEXIGLASS® to fit into an INSTRON testing machine being used for load application. Ottawa sand has been used in all tests and was selected for its standardization, grain size and grain shape. Its uniform particle size and round grain


- Footing LVDTs- Sand surface LVDTs

- Load cell

0

0

0

video camera

OPTIMAS digitalimaging camera

TEKSCAN tactile pressuresensors placed on the bearingsurface of the model footing

0

0observation wall on PLEXIGLAS box

extent of black sand layers(approximate)

0

0 model foundation

61 cm

7.6 cm114.3 cm

Schematic of model foundation test setup.Figure 3

connection bar (to load cell)loading bar

ball bearingmodel foundation splice piecesstabilizing rollers

model foundation

sand surface

alternating black and white sand layers

B=76.2 mm

25.4 mmD=50.8 mm

76.2 mm

Profile view of model foundation setup (LVDT's not shown).Figure 4


shape make it ideal for use with the tactile sensor, providing non-puncturing edges and approximately equal contacts per sensel. This sand has been used extensively in the Geotechnical Engineering Research Laboratory at the University of Massachusetts Lowell (e.g. Paikowsky et al., 1995) and has the following characteristics: 99.7%SiO2, D50=0.50mm, Cc=1.08, Cu=1.40 The sand was placed through a pullivation (raining) process, through a set of wire meshes (45ο to each other). The sand was poured evenly from a constant height and at a constant rate to achieve a uniform density. At 10 cm (3.94 in) below the final height of the sample, the surface was leveled and a 1-cm (0.39-in.) thick layer of black (dyed) sand was rained and leveled along the observation side of the box below where the footing will be placed. A 2-cm high regular Ottawa sand was then rained on top of the black layer and so on. This process produced a total of five black sand layers. The final surface is leveled for footing placement. Figure 4 presents the alternating black and white sand layers below the model foundation.

Load Application System

The load is applied to the footing in the form of a constant rate of displacement using an electro-mechanical INSTRON universal testing instrument Model No. 1127. The INSTRON has an integral load cell attached to the center of the crosshead (which is positioned between two vertical tracks) capable of measuring loads to 250 kN (56202 lbs.). In order to allow for a clear view of the failure plane beneath the foundation, the container had to be placed off-center in relation to the testing machine. This required the design of a special load application system consisting of a horizontal arm fabricated from aluminum channel stock, bolted to the INSTRON load cell. The underside of the arm had an adjustable plate with a ball-type connection for moment free exact alignment with the model. The vertical loading system consisted of three elements: a connecting rod from a direct shear machine, a 4.448 kN (1000-pound) load cell, and the model loading bar. The loading bar connects to the model foundation through two ball bearings placed 304.8 mm (12 inches) apart. The bearings provide the foundation with a moment free load application and the 304.8mm (12-inch) spacing allows for uniform moments along the model itself, (acting as a beam).

The Model Foundation The size of the model foundation was dictated by the size of the testing container and the extent of the expected failure zone (to prevent boundary effects). The maximum length of the model was governed by the interior width of the box to be 60.69-cm (24 inches), as illustrated in Figure 3. The failure zone calculations were based on Terzaghi’s (1943) and Hansen’s (1970) log spiral failure mode and Rankine’s wedges, determining the maximum width of the foundation to be 7.62-cm (3 inches) thereby resulting in a length to width ratio of eight (L/B=8) characteristic of a strip footing. The foundation is comprised of a bearing plate and a wall plate constructed of 25.4 x 76.2 mm (1 x 3-inch) aluminum stock.


The model was built as two separate pieces to allow the sensors to be placed through the bearing plate in the middle of the footing. The wall plates were attached to the bearing plates with a total of eleven bolts and the two sections were connected using 8 bolts and two coupling 12.7-mm (0.5-inch) plates. Figure 5 presents the design of the model foundation and a photograph. The two circles with crosshairs on the top edge of the wall plate are ball bearing seats for the load application system. The model is aligned with the cross section of the footing against the transparent (observation) wall of the testing box (see Figures 3 and 4). Placement of pressure sensors on the shorter 203.2-mm (8-inch) section as well as the center of the footing is accomplished through the slot between the two coupling plates. The footing design allows the use of a third sensor. This sensor is placed on the outer end of the longer model section. The sensor is wrapped around the end of the foundation and the connections are passed through a recessed channel between the model and the wall of the testing container, (see Figure 5b). The photograph in Figure 6 presents the footing with an attachment of two sensors covering two 203.2 mm (8-inch) sections. The Data Acquisition Systems Contact Stress Distributions and Tactile Pressure Sensors TEKSCAN tactile pressure sensors are constructed of two polymeric sheets with pressure sensitive semi-conductive ink printed on one side of each sheet. The sheets are then laminated together with the printed sides facing each other. Usually, the ink is printed in rows on one sheet and columns on the other. When the two sheets are pressed together a grid of sensing areas is formed. A "handle" which is clapped to the end of the sensor and connected to a data acquisition card installed in a PC that reads the sensor. The computer scans the sensor sequentially by rows and columns and records the change of resistance in each of the sensels. This resistance change is then converted into Raw Sensor Data (RSD) units, which are then correlated to a pressure using a calibration process. Each individual sensor has its own unique properties and must be calibrated separately. For additional details and procedures, see Paikowsky and Hajduk (1997). The 9800 TEKSCAN sensor was selected for the model foundation tests due to its size, sensel dimensions, and excellent performance in the calibration process. The sensing area of the 9800 measures 76.2 x 203.2 x 0.1 mm thick (3 x 8 x 0.00393 inches) and consists of 6 columns and 16 rows of sensels for a total of 96 sensing locations. Each sensel measures 9 x 11 mm and has an effective sensing area 12.7 x 12.7 mm (161.3 mm2). Images of two 9800 sensors mounted at the bottom of the foundation are shown in Figure 6.


b) Photograph of model foundation

Figure 5 Model rigid strip footing.

16 in. 8 in.24 in.

1 in

3 in.

3 in.

1 in.

Plan view

Plan view (from bottom)

Profile

a) Assembly diagram

76.2 mm

76.2 mm

25.4 mm

25.4 mm

20 32 cm40 64 cm

60.96 cm


Figure 6 Tactile sensors attached to the base of the strip footing, arrangement for model test #2 and #3.

Foundation and Soil Instrumentation for Monitoring Total Load and Displacement

The footing was instrumented both before and after placement in the testing

box. The TEKSCAN pressure sensors must be attached prior to the placement of the model in the container (see Figure 6). Following the placement of the model an additional layer of overburden sand was rained around the footing to provide embedment depth, and roller guides were bolted to the side of the box to ensure linear vertical displacement and prevent tilting of the foundation during the test (see Figure 4). Displacements and applied load were monitored by a Hewlett – Packard, HP7500, VEE Data Acquisition System, (DAS). Four linear voltage displacement transducers (LVDTs) were attached to the corners of the bearing plate, and an additional three LVDTs were placed on the sand surface in the middle of the footing at distances 76.2, 152.4, 228.6 mm away from the edge of the bearing plate as shown in Figure 3. All LVDTs are connected to a frame attached to a reference frame and are independent of movements of the testing box. A 4.448 kN (1000 lb.) load cell connected to the loading bar was used to measure the total load applied to the foundation. Digital Imaging System

High resolution Kodak Megaplus Model 4.2 (MP 4.2) CCD camera, Bit Flow imaging board, Data Raptor – VL frame grabber (single slot local BUS board) and OPTIMAS digital imaging processing and analysis software were used to measure the displacement of the sand beneath the footing. The digital images have a


resolution of 2000 pixels x 2000 pixels and are taken at a frequency of about one frame every 15 seconds. For the size of the image taken in these tests, the resolution is high enough to identify individual grains of the Ottawa sand. A grid was placed over the transparent observation wall of the box to provide reference points for both the video and OPTIMAS cameras prior to the test. The imaging camera was set-up normal to the box surface and at the average height of the expected displacement field. After the test, the imaging system is calibrated using points of known coordinates (e.g. the grid) in the initial frame. Points, or individual grains of sand, can then be tracked in subsequent frames and the displacements can be determined. Details of motion monitoring techniques utilizing image processing and analysis system are presented by Paikowsky and Xi (1997, 1999). Video Photography An analog color 8mm CCD camera was used to monitor and record the entire process, and provide, via a monitor, visual information of the overall foundation response during the test. TESTING PROCEDURE

Following the placement of the footing, the overburden sand rained, the data acquisition systems are connected and stabilized and the test can be started. Initial image frames and zero-load data bursts are taken by both the TEKSCAN and the HP DAS systems. The data acquisition systems are then setup for the test and double-checked. Next, the INSTRON testing machine is set for a constant displacement rate of 1 mm per minute. The INSTRON displacement is started and the tests proceeds and followed up via a strip chart graphing the load-displacement relations. The test proceeds well into the post peak or to total displacement of at least 25.4-mm (1 inch). CALCULATED BEARING CAPACITY

The bearing capacity and ultimate load were calculated using Terzaghi’s, Meyerhof’s, Hansen’s, and Vesic’s bearing capacity equations. The ultimate loads and contact pressures for the model at an embedment depth of 25.4-mm (1-inch) ranged from 2127 to 3239N (478 to 728 lbs.) and 45.52 to 69.66kPa (6.6 to 10.1 psi). At a depth of 50.8 mm (2 inch), the calculated ultimate load ranged from 3.34 to 4.45kN (750 to 1000 lbs.). These calculations allowed the mechanical design of the loading system connections and the determination of the measurement ranges of the monitoring system (e.g. load cells) and the tactile sensors. TEST RESULTS Overview

Four model foundation tests have been conducted to date. The first test did

not have alignment rollers and as a result, the foundation tilted and failed typically of


eccentric loading. New equipment was acquired and used for Test 4. Three sensors were mounted under the entire bearing area of the footing. Test 4 complex results were not yet analyzed and as such, this manuscript presents the results for the second and third tests. The major difference between the two tests were the sand density influencing the foundation behavior, stress distribution, and the conditions next to the boundaries. Two 9800 tactile sensors were used in both tests 2 and 3. One sensor measured the stress distribution on the 203.2mm (8 inch) segment of the footing adjacent to the observation wall and another was placed under the middle 203.2 mm (8 inch) segment of the footing such that two thirds of the footing's contact stresses were observed. The Foundation's Load vs. Displacement Response

In both tests, the load and displacement of the foundation were measured and the typical load - displacement curves were plotted. Figures 7a and 7b show the load vs. displacement relationship for tests 2 and 3 respectively. Ultimate failure in the second test occurs at a displacement of 10 mm and a corresponding load of 2.50 kN. The shape of the curve suggests that the model underwent a local shear failure. In the third test, the foundation failed at a displacement of 16.1 mm and a corresponding load of 5.09 kN. The shape of the curve for Test 3 suggests a general shear failure. Post failure stick-slip behavior is seen in both tests. The sand densities for the second and third tests were 16.51kN/m3 (105 pcf) and 17.61kN/m3 (112 pcf) respectively. Although small, this difference is significant in relation to the sand's uniformity and hence the density variation effects on the behavior of the model foundation can be clearly seen. In Test 2, the load increased almost linearly with the displacement until failure and then continued to gain capacity with additional large displacements. In Test 3, the load increases linearly with a greater stiffness. After failure the load decreases rapidly to a residual value, indicative of a dense sand strain softening behavior. Figures 8 and 9 show the detailed displacement (of the various LVDTs) vs. load for Tests 2 and 3 respectively. The detailed load – displacement behavior allows for evaluation of the tilting of the foundation. It can be seen that the foundation tilted along its short axis in Test 2, with a differential settlement of approximately 2-mm from one end to the other. In Test 3, only slight tilting occurred along the long axis.


Figure 7 Load vs. displacement for Test 2 and Test 3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Load (kN)

0

2

4

6

8

10

12

14

16

18

20

Dis

plac

emen

t (m

m)

(a) Load vs. displacement plot for Test #2.

Test #2

Failure at10.0 mm, 2.50 kN.

t = 641 sec.

t = 105 sec.

t = 44 sec.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Load (kN)

0

5

10

15

20

25

30

35

40

45

Dis

plac

emen

t (m

m)

(b) Load vs. displacement plot for Test #3.

Test #3

Failure at16.1 mm, 5.09 kN.

t = 300 sec.

t = 600 sec.

t = 800 sec.

t= 100 sec.


0 1 2 3 4 5 6

Load (kN)

0

5

10

15

20

Dow

nwar

d di

spla

cem

ent (

mm

)

Figure 8 Load vs. displacement curves for the footing LVDTs for Test #2.

Corner

R3

L3

R1

L1

Foundation corners anddirection of rotation

L1 R1

L3 R3

Longitudinal distortion = 0.00394Sectional distortion = 0.01312

Test #2

0 1 2 3 4 5 6

Load on foundation (kN)

0

5

10

15

20

Dow

nwar

d di

spla

cem

ent (

mm

)

0

5

10

15

20

Corner

R3

L3

R1

L1

Figure 9 Load vs. displacement curves for the footing LVDTs for Test #3.

Test #3Foundation corners and

direction of rotation

L1 R1

L3 R3

Longitudinal distortion = 0.00038Sectional distortion = 0.03221


Soil's Response at the Surface

The behavior of the sand surface adjacent to the footing also differed between tests 2 and 3. Figures 10 and 11 show load vs. displacement for the three LVDTs mounted on the sand surface (see Figure 3 for details). In interpreting the information presented in Figures 10 and 11, one needs to correlate the data to Figures 8 and 9. The 0 (zero) displacements of the sand surface represent initial loading, permanent displacements represent the final condition of the soil at the surface (e.g. about 2.5 mm in Test 3). Only slight movement of LVDT S3 can be seen in Test 2 while all the surface LVDTs moved between 2 and 3 mm in Test 3. These differences are also associated with the variation in the sand density for the two tests and the resulting mode of failure. The general shear failure in the sand exhibit larger surface deformation (e.g. heave) while local shear failure result in little or no surface deformations.

Aerial Stress Distribution vs. Load Cell Measurements The data collected from the tactile sensors is stored in a movie file and can only be viewed using the TEKSCAN software. The data can then be converted into a graph file and the sensor response vs. time is displayed. Similarly, the data from the movie file can be converted into a frame file that allows the analysis of an individual data frame. Both the graph and the frame files can then be exported as data files and imported into a spreadsheet program. The appropriate calibration for the sensor is applied and the actual pressure measured by the sensor is obtained. Three frames were selected for analysis of Test 2 and four frames were selected for the analysis of Test 3. The locations of these frames relative to the applied load and time (i.e. in direct relations to the displacement) are shown as part of Figures 7a and 7b for tests 2 and 3, respectively. The post failure data analysis of Test 3 is problematic due the to stick-slip behavior and the unloading conditions and hence is not presented. The average bearing pressure can be calculated from the load cell data for each frame, providing an independent evaluation of the aerial stress measurement. Figure 12 shows the average cross-sectional stress distributions and the average bearing pressures from both the tactile sensors and the load cell for the three selected frames of Test 2. Figure 13 shows the same for the four selected frames of Test 3. Recall that in Test 2 the foundation tilted lengthwise about its short axis (and not to the side) as detailed in Figure 8. The stress profiles shown in frames 1 through 3 of Test 2 indicate a symmetric stress distribution, confirming that side-to-side tilting about the long axis did not take place. The stress profiles shown in frames 1-4 of Test 3 suggest the opposite. In frame 3 (t=600 sec.), the stress is higher toward the right side of the footing. This is also seen in frame 4 indicating that the footing is tilting toward the side with higher stresses. The foundation LVDT data for Test 3 confirms tilting in the clockwise direction.


0 1 2 3 4 5Load (kN)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Dsi

plac

emen

t (m

m)

DCDT

S1 (3")

S2 (6")

S3 (9")

Figure 10 Load vs. displacement curves for LVDTs on the sand surface for Test #2.

Test #2

0 1 2 3 4 5 6Load (kN)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Dsi

plac

emen

t (m

m)

DCDT

S1 (3")

S2 (6")

S3 (9")

Figure 11 Load vs. displacement curves for LVDTs on the sand surface for Test #3.


Figure 12 Average cross-sectional stress distributions and the average bearing pressures from TEKSCAN sensors and the load cell for the three frames analyzed of

6.35 19.05 31.75 44.45 57.15 69.85Foundation width (mm)

3035404550556065707580

Pres

sure

(kPa

)

Avg. Columns

Tekscan absolute avg.

Load cell calculated avg.


3035404550556065707580

Pres

sure

(kPa

)

Avg. Columns




3035404550556065707580

Pres

sure

(kPa

)

Avg. Columns



(a) Frame 1 (t=44s)

(b) Frame 3 (t=105s)

(c) Frame 3 (t=641s)


Figure 13 Average cross-sectional stress distributions and the average bearing pressures from TEKSCAN sensors and the load cell for the three

frames analyzed of Test #3.


102030405060708090

100110120

Pres

sure

(kPa

)

Avg. Columns




102030405060708090

100110120

Pres

sure

(kPa

)

Avg. Columns




102030405060708090

100110120

Pres

sure

(kPa

)

Avg. Columns



(a) Frame 1 (t=100s) (b) Frame 2 (t=300s)

(c) Frame 3 (t=600s) (d) Frame 4 (t=800s)


102030405060708090

100110120

Pres

sure

(kPa

)

Avg. Columns




The absolute average of the tactile sensors, as marked in Figures 12 and 13, is the average pressure at all sensing locations. This number, when compared to the calculated average from the load cell, provides an independent assessment of the accuracy of the tactile sensors. In general, a very good agreement between the two measurements. For Test 3, a maximum difference occurs in frame 3 at only + 6%. In Test 2, the maximum difference occurs early in the test and is shown in frame 1. This large (relatively) difference of approximately + 14%, is due to the small magnitude of the loads acting on the foundation for this frame. As a larger load is placed on the footing, the percent error decreases as shown in frames 2 and 3 of Test 2.

Actual 2D and 3D Stress Distributions

Figures 14 and 15 show two and three dimensional stress distributions for the peak contact stresses, i.e. frames 3 and 4 in Tests 2 and 3, respectively. Notice the localized high stresses adjacent to the boundary in Test 2 and the higher stresses in the central region of the model in Test 3. Due to the low density of the sand, the stresses at the observation wall (length = 0) are lower in test 2 than in the center of the footing. As the footing displaced downwards, the sand is moved and densified. At the wall, lateral strains are prevented in one direction, resulting in higher contact pressures. Non-uniform density of the sand may also contribute to this condition. The stresses for Test 3 are lower near the observation wall indicating that the condition at the boundary seems to be opposite to those of Test 2. This was caused in part by the increased density of the sand (as the lateral spreading was limited normal to the wall) and by a space between the end of the footing and the observation wall. Sand trapped between the wall of the box and the footing and caused increased friction. This end friction on the foundation reduces the contact stresses under the footing at the boundary and detected by the measurements presented in Figure 15. SUMMARY AND CONCLUSIONS

The presented model tests are unique due to the presence of the tactile sensors. For the first time, the actual stress distribution at multiple discrete points below a rigid strip footing could be recorded and analyzed. Due to the sensors small thickness (0.1 mm), the disturbance in the stress behavior in the granular material is minimal. The results of the two model foundation tests presented in this paper lead to the following conclusions:


Figure 14 Two and three dimensional presentation of the stress distribution in frame 3 of Test #2.

a: 2-dimensional image

c: 2-dimensional

Sensor Output (kPa)

0 10 20 30 40 50 60 70 80 90

b: 3-dimensional

12.7 50.8

Foundation width (mm)

50.8

101.6

152.4

203.2

254.0

304.8

355.6

406.4

457.2

508.0

558.8

Foun

datio

n le

ngth

(mm

)

No d

ata

colle

cted

in

this

area

.

12.7

38.1

63.5

Foundation w

idth (mm

)

50.8 101.6 152.4 203.2 254.0 304.8 355.6 406.4 457.2 508.0 558.8

Foundation length (mm)

No data collected in this area.


Figure 15 Two and three dimensional presentation of the stress distribution in frame 4 of Test #3.

a: 2-dimensional image

c: 2-dimensional

Sensor Output (kPa)

0 20 40 60 80 100 120 140

b: 3-dimensional

12.7 50.8

Foundation width (mm)

50.8

101.6

152.4

203.2

254.0

304.8

355.6

406.4

457.2

508.0

558.8

Foun

datio

n le

ngth

(mm

)

No d

ata

colle

cted

in

this

area

.

12.7

38.1

63.5

Foundation w

idth (mm

)

50.8 101.6 152.4 203.2 254.0 304.8 355.6 406.4 457.2 508.0 558.8

Foundation length (mm)

No data collected in this area.


1. The application of the tactile sensing technology to geo-materials is revolutionary and very promising. The presented preliminary tests revealed visual and quantitative data that could not have even being imagined only short time ago. The stress distributions measured accurately by the sensors reflect those predicted by foundation and stress distribution theories. The general accuracy of the sensors was shown to be on the average within ± 10% (although higher errors were seen at very low pressures). These values need, however, to be reviewed in light of the very large variation in stresses between one zone under the foundation to another and hence reflect very high accuracy.

2. The variations in the stress distributions due to the influence of the boundaries and

sand density can be easily and clearly measured and quantified for the first time. The sand density greatly affects the distribution of the contact stresses on the bearing surface of the footing and therefore the load-displacement behavior. The effect of the boundaries was also seen to vary greatly with only a slight change in sand density. A relatively small variation in the sand density caused a different failure mode in each test. Sand raining tests using the Ottawa sand determined that lower raining rates result in denser sand. Sample uniformity, however, is troublesome to predict due to the difficulty in controlling the density of a uniform round material and installation procedures (e.g. leveling of the sand) required for the placement of the black sand layers.

3. The 9800 type sensors used in the present study have large sensing areas relative to

the particle size of the sand. The large sensels are very suitable for stress distribution measurements within granular materials. The use of sensors with larger number of sensels will result in a higher resolution when used with a larger foundation.

4. The digital imaging system was utilized in both tests but the results have not been

analyzed yet. Difficulties exist in identifying representative displacements along the sand/wall interface (where the displacements are observed) and accurate point selection for frame analysis. The initial points on the transparent grid can be used for initial calibration of the camera but tracking the displacement of individual particles proved difficult. The installation of a greased rubber membrane between the sand and the wall of the box with a printed grid (on the membrane) is the preferable solution. The grid intersections could be easily tracked by the high resolution CCD but the application of the technique requires effort beyond that possible under the current preliminary study.

5. The limited tilting of the foundation in one direction during all tests suggests that it

is caused by an eccentric load problem in the loading system. The deflection of the cantilever-loading arm (bolted to the load cell of the Instron loading machine) seem to be the source of the introduced eccentricity. As a result, the load is applied to the right of center, causing a clockwise rotation in all tests. Stiffening of the loading arm may be required to eliminate foundation tilting.


REFERENCES Atkinson, J.,1993. The Mechanics of Soils and Foundations. McGraw Hill. Barden, L. 1962. Distribution of Contact Pressure under Foundations. Geotechnique,

Vol. 18, no. 1, March, pp.1-24. Borowicka, H. 1936. Influence of Rigidity of a Circular Foundation Slab on the

Distribution of Pressures over the Contact Surface. Proc. 1st International Conference of Soil Mechanics. Cambridge. Vol. 2, pp. 144-149.

Borowicka, H. 1938. The Distribution of Pressure under a Uniformly Loaded Elastic

Strip Resting on Elastic-Isotropic Ground. 2nd Cong. Int. Assoc. Bridge and Structural Eng.. Berlin. Final Report

Bowles, J. E., 1996, Foundation Analysis and Design, Fifth Edition, McGraw Hill. Das, B. M. 1990. Principles of Foundation Engineering, 3rd edition. PWS-KENT

Publishing Company, Boston MA. Das, B. M. 1990. Principles of Geotechnical Engineering, 2nd edition. PWS-KENT

Publishing Company, Boston MA. Fang, H. Y. 1991. Foundation Engineering Handbook, 4th edition. Van Nostrand

Reinhold, New York. Hansen J.B., 1970, "A Revised and Extended Formula for Bearing Capacity", Danish geotechnical Institute, Bulletin 28. Lambe, T. W., and Whitman, R. V. 1969. Soil Mechanics, Wiley, New York. Paikowsky, S.G. and Hajduk E.L., 1997 “Calibration and Use of Grid-Based Tactile

Pressure Sensors in Granular Material,” Geotechnical Testing Journal, GTJODJ, Vol. 20, No. 2, June, pp. 218-241.

Paikowsky, S.G., and Xi, F., 1977, "Photoelastic Quantitative Study of the Behavior of

Granular Material with Application to the Problem of Friction Along an Interface", Research Report submitted to the Air Force Office of Scientific Research, September 1997.

Paikowsky, S.G. and Xi, F., 1999, Particle Motion Tracking Utilizing High Resolution

Digital CCD Camera, in print, ASTM Geotechnical Testing Journal. Paikowsky, S.G., Player C. M., and Connors P.J., June, 1995, “A Dual Interface

Apparatus for Testing Friction of Soil Along Solid Surfaces”, ASTM,


Geotechnical Testing Journal, Vol. 18 No. 2, pp. 168-193 Schultze, E. 1961. Distribution of Stress beneath a Rigid Foundation. 5th ICSMFE. Vol.

1, pp. 807-813. Tatsuoka, F., Molenkamp, F., Torii, T., and Hino T. 1984. "Behaior of Lubricated

Layers of Platens in Element Tests," Soils and Fondations. Vol. 24, No.1, JSSMFE, Tokyo, Japan. pp. 113-128.

Terzaghi K., 1943, "Theoretical Soil Mechanics", John Wiley and Sons Terzaghi K. and Peck R. B., 1948, "Soil Mechanics in Engineering Practice", John Wiley

and Sons. Terzaghi, K., Peck, R. B., and Mesri, G. 1996. Soil Mechanics in Engineering Practice.

3rd edition, John Wiley and Sons, Inc., New York. ACKNOWLEDGEMENT An initial support of the presented research was provided by the Federal Highway Administration (FHWA), by the National Science Foundation (NSF), NYI Grant MSS-5398090, and the University of Massachusetts Lowell. Continuation of the research is possible through the support of the NSF Grant No. CMS-9908612 with a complementary support by the Tekscan Corp., Boston, MA.

Stress distribution strip foundation final - UMass Lowell GSP 94 2000_Paikowsky... · methods are...

Documents

Transcript of Stress distribution strip foundation final - UMass Lowell GSP 94 2000_Paikowsky... · methods are...