GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

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2 GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of Civil Engineering, IIT Bombay, Powai, Mumbai , India. Tel

3 Module-13 LECTURE- 62 Designing with Geofoam

4 Recap of previous lecture.. Design of embankment using geofoam Overturning due to seismic effect Translation due to wind Testing of Geofoam Apparent Density Test Water Absorption Test Compressive Strength Test

5 Proposed unconfined compression test (PUCT) on EPS geofoam Proposed compressive strength Test on EPS geofoam (a) Schematic diagram (b) Test specimen

6 Unconfined compression test on EPS geofoam with different densities: (a) ρ = 15 kg/m 3 (b) ρ = 20 kg/m 3 (c) ρ = 22 kg/m 3 (d) ρ = 30 kg/m 3

7 Compressive Stress (kpa) kg/m 3 22 kg/m 3 20 kg/m 3 15 kg/m Strain (%) Stress-strain relationship for proposed unconfined compression test on EPS geofoam

8 Density of EPS geofoam (kg/m 3 ) Compressive strength test results: Size of the specimen (mm) Compressive strength Yield Initial tangent modulus (kpa) φ 150 ht φ 150 ht φ 150 ht φ 150 ht

9 Compressive strength (kpa) Compressive 10% strain σ c = 5.799ρ R² = Density of EPS geogoam (kg/m 3 ) Relationship between density of EPS geofoam (ρ) and compressive 10% strain

10 Compressive strength (kpa) Compressive yield σ c = 4.689ρ R² = Density of EPS geogoam (kg/m 3 ) Relationship between density of EPS geofoam (ρ) and compressive yield

11 Compressive strength test results as per different test specifications Density Compressive strength (kpa) (kg/m 3 ) ASTM D IS: DIN represents compressive strength value of EPS geofoam calculated at 5 and 10 percent of axial compression of test specimen. PUCT - Proposed Uniaxial Compression Test.

Tensile Properties of Geofoam (ASTM: D1623 09) Objective To determine the tensile

Type-A test specimen with its dimensions is shown below Tensile strength test

12 Tensile Properties of Geofoam (ASTM: D ) Objective To determine the tensile strength properties of geofoam Test Specimen Specimen Type A The recommended Type-A test specimen with its dimensions is shown below Tensile strength test specimen of Geofoam (Density of the geofoam from left to right are 15, 20, 22 and 30 kg/m 3 )

13 Gripping Assembly Tensile strength test on EPS geofoam Failed specimens in tension

14 (a) Before (b) After Tensile strength test on EPS geofoam (Density of the geofoam material are from left to right 15, 20, 22 and 30 kg/m 3 ) (a) Before and (b) after failure

15 Tensile Strength: The tensile strength is calculated by dividing the breaking load by the original minimum cross-sectional area of the specimen. Tensile stress, (σ t ) Calculations t F D 2 F = Tensile force applied to the specimen (kn) D = Minimum diameter of the test specimen (m) Considering Density of EPS geofoam = 20 kg/m 3, 4 Tensile stress Breaking Load Cross sectional area kpa

16 Stress-strain behavior of EPS geofoam in tension

17 Test Results of tensile Strength on EPS geofoam Density of EPS ASTM D geofoam (kg/m 3 ) Tensile strength (kpa) Strain at failure (%)

18 500 Tensile strength (kpa) σ t = 17.14ρ R² = Density of EPS geofoam (kg/m 3 ) Correlation between tensile strength and density of EPS geofoam

19 Proposed Test Specimen for Tensile testing of Geofoam: In the proposed tensile strength test, the test specimen has thickness of 25 mm with a flat section. Figure shows the schematic representation of the test specimen. Schematic representation of tensile strength test specimens

20 Tensile strength test specimens (Density of the geofoam materials are from left to right as 15, 20, 22 and 30 kg/m 3 ) Tensile strength test gripping assembly

21 Tensile strength test on EPS geofoam

22 (a) Before (b) After Tensile strength test on EPS geofoam (Density of the geofoam material are from left to right 15, 20, 22, and 30 kg/m 3 ) (a) Before and (b) after failure

23 Tensile Stress (kpa) Strain (%) 30 kg/m 3 15 kg/m 3 22 kg/m 3 20 kg/m 3 Tensile stress - strain behavior of EPS geofoams

24 Tensile strength test results and comparison Density of EPS geofoam (kg/m 3 ) ASTM D Tensile Strain at strength failure (kpa) (%) PTST (IITB) Tensile strength (kpa) Strain at failure (%)

The test specimens shall be 300 mm 50 mm 25 mm Schematic

25 Shear Properties of Geofoam (ASTM: C273/C273M-07a) Objective: To determine the shear strength parameters of geofoam Test Specimen: The test specimens shall be 300 mm 50 mm 25 mm Schematic representation Shear strength test specimen with different densities (kg/m 3 )

26 Shear test assembly for Geofoam Plate Shear Specimen of Geofoam and Force Line of Action Shear Strength Test on EPS geofoam

27 Calculations: Shear Stress (τ) of the geofoam material: P L b τ = core shear stress (kpa), P = instantaneous force on specimen (N), L = length of specimen (m) and b = width of specimen (m). Maximum shear stress (τ max ) max P Lb

28 Considering Density of EPS geofoam = 20 kg/m 3, P = kn, L = 0.3 m and b = 0.05m; max kpa Shear Strain (γ) of the geofoam material: u t u = Deformation at peak shear load (mm) t = Thickness of core (mm) mm / mm

29 Core Shear Modulus (G) of the geofoam material: G P x u L b t P/ u = slope of the force-displacement curve (N/mm) from mm/mm to mm/mm effective engineering shear strain Now, P/ u = , t = m, L = 0.3 m and b = 0.05 m; G kpa

30 Density of EPS geofoam (kg/m 3 ) Maximum load at failure (N) Shear strength test results Shear strength (kpa) Deformat ion at peak load (mm) P/ u (From graph) Core shear modulus (kpa)

31 Breaking Load and Flexural Properties of Geofoam (ASTM: C203-05a) Objective: To determine the breaking load and flexural properties of the geofoam. Methods available Three point method Four point method Flexural strength test methods for EPS geofoam

32 Test Specimen: The test specimen shall be 300 mm 100 mm 25 mm. Schematic representation Flexural strength test specimen (Density of the geofoam material from left to right are 15, 20, 22 and 30 kg/m 3 )

33 Flexural Test Assembly for Geofoam Span length = 250 mm

34 (a) Before (a) After Flexural Strength Test on Geofoam (a) Before and (b) After failure (Density of the geofoam material are from left to right 15, 20, 22 and 30 kg/m 3 )

35 EPS geofoam specimens after failure Flexural strength test results: Density (kg/m 3 ) ASTM C Flexural Strength (kpa) Deformation (mm)

36 Maximum Fiber Stress (S): S 2 3P L 2 bd S = stress in the outer fibers (kpa) P = load at a given point on the load-deflection curve (N) L = support span (m), b = width of beam tested (m), and d = depth of beam tested, (m)

37 Considering Density of EPS geofoam = 20 kg/m 3, P = kn, L = 0.25 m, b = 0.1 m and d = 0.025m. Flexural strength 3PL 2 2bd Flexural strength kPa

38 Maximum Strain (ε): The maximum strain in the outer fibers occurs at mid span. 6Dd 2 L ε = maximum strain in the outer fibers (mm/mm), D = maximum deflection of the center of the beam (mm) L = support span (mm) and d = depth (mm). Here, D = m, d = m and L = 0.25 m Maximum strain ( ) mm/ mm

39 Moment of Inertia: The moment of inertia is calculated as follows: I b d 12 3 I = moment of inertia (mm 4 ) b = specimen width (mm), and d = specimen thickness (mm) Here, b = 0.1m and d = m I x10 7 m 4

40 Elastic Modulus of geofoam material can be given as, E P L I D E = elastic modulus (kpa), D = corrected deflection at center of sample (m), I = moment of inertia (m 4 ), L = support span (m), and P = load at a given deformation within the proportional limit of the specimen (kn). P = kn, L = 0.25 m, I = m 4, and D = m E kpa

41 Flexural strength test results Density of EPS geofoam (kg/m 3 ) Maximu m load at failure (kn) Flexural strength (kpa) Deform ation at center (m) Maxim um strain (mm/m m) Moment of Inertia (m 4 ) Modulus of elasticity (kpa)

42 Please let us hear from you Any question?

43 Prof. J. N. Mandal Department of civil engineering, IIT Bombay, Powai, Mumbai , India. Tel

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally