Water-Induced Swelling Displacements in Core Drilling Method

(ProQuest Information and Learning: ... denotes formulae omitted.)

INTRODUCTION

The core drilling method is a nondestructive test method that can be used to evaluate stresses in concrete.1 In the core drilling method, a circular core hole is cut in to the concrete in a structure, and the

displacements that occur in the concrete as the hole is cut are measured. These measured displacements are then related to the in-place state of stress in the structure. The proposed method is nondestructive because the ability of the structure to perform its intended function is not impaired and the core hole is repaired. The method is similar to the ASTM Hole-Drilling Strain Gauge Method (ASTM 837 1994) that consists of measuring strains at the surface of a specimen as a hole is drilled. Reference 1 contains a comprehensive theoretical background for the core drilling method and summarizes the results of research that showed that digital image correlation and industrial photogrammetry may be used to capture the displacements that result from applying the method.

The typical current practice for cutting a core hole in concrete involves flushing the core hole with water to cool and lubricate the coring drill bit, flush coring debris from the core hole, and minimize air-borne dust. Hardened concrete typically swells when exposed to water.2 This swelling, however, is not accounted for in the core drilling method equations for relating relieved displacements to in-place stresses. This swelling induces displacements around a core hole that are difficult to differentiate from displacements due to stress relief, resulting in errors in in-place stress predictions when applying the method.

Water moves into porous materials such as concrete in a manner that may be predicted using transport theory. In this study, a simplified prediction of this movement using the concept of sorptivity and a Sharp Front Model3 is used to predict the depth of the water penetration during core drilling. Sorptivity is a measure of the ease with which a porous material absorbs liquid and is covered in detail subsequently. This is combined with an estimate of the magnitude of concrete swelling strain due to moisture uptake to yield expected displacement values around the core hole measurement circle due to the use of water in the coring process. These displacements are hereafter referred to as moisture displacements to differentiate them from relieved displacements that arise from stress relief. These moisture displacement values are then converted into apparent stresses using the core drilling method equations that relate displacements to stresses. These apparent stresses are then removed from the stresses calculated when applying the core drilling method.

To demonstrate the applicability of the approach, this technique is applied to correct in-place stress predictions from a hole drilling study of concrete slabs performed by Buchner at the University of Surrey.4 The current work involves a reanalysis of the original reported results from the Buchner slabs to account for the effects of core drilling water on those tests. Correction of the Buchner results using the procedure outlined herein reduced average errors in in-place stress prediction over a series of nine tests from 47% prior to correction to 14% afterward.

RESEARCH SIGNIFICANCE

The core drilling method1 is an emerging technique for the nondestructive evaluation of in-place stresses in concrete structures. The method involves drilling a small hole in the concrete and measuring the deformations that result. The typically wet core drilling process induces previously unaccounted for swelling in the wetted concrete adjoining the hole. The current work provides a method to account for this swelling, thereby potentially significantly increasing the accuracy of the overall technique.

THEORETICAL BACKGROUND

Core drilling method

Elasticity methods treating a small through hole in an infinite thin plate are used to derive the relationship between the stresses and displacements in a loaded object subjected to the drilling of a core hole. Assumptions made in the derivations are that the material is linear elastic, isotropic, homogenous, and that the load is distributed uniformly through the plate thickness. The problem is treated as a two-dimensional problem of linear elasticity and solved for plane stress and plane strain assumptions, similar to the approach of the ASTM hole-drilling strain gauge method, except that displacements rather than strains are the quantities of interest. Turker and Pessiki5 performed finite element analyses to investigate the validity or consequences of many of these assumptions, such as the effects of blind holes, of plates of finite size, and of stresses that vary through the thickness of the plate.

The two-dimensional elasticity problem is solved using the potential function of complex method as outlined by Muskhelishvili.6 For a core hole of radius a, this approach yields relieved displacements in the radial u and tangential v directions around the core hole of

... (1)

... (2)

where

...;

and µ and ? are material parameters; r and a are the radius and angle to the measured point; and s^sub x^, s^sub y^, and t^sub xy^ are the in-plane normal and shear stresses, respectively. Relieved displacements give the displacement of a point relative to the center of the through-hole. In practice, however, a displacement measurement would likely be taken between two points, neither of which is the center of the hole. Many different measurement configurations are presented in Reference 5. In this study, the measurement configuration shown in Fig. 1 was used to convert from displacement to stress, where U1, U2, and U3 represent relative relieved displacements between two points and are denoted as measured displacements.

To solve for the three unknown stresses in a plate with a constant biaxial and shear stress field, (s^sub x^, s^sub y^, and t^sub xy^), three measured displacements are required. Using Eq. (1) and (2), the three measured displacements noted in Fig. 1 are expressed in terms of the relieved displacements, and then three simultaneous equations are solved for the unknown stresses, resulting in

... (3)

... (4)

... (5)

Transport theory

Reference 3 contains an excellent treatment of moisture movement in building materials. A summary of only those concepts necessary for the current work is presented in the following.

Moisture movement in nonsaturated porous materials may be described by the nonlinear diffusion equation, which for one dimensional flow may be written as

... (6)

where ? is the moisture content and D the capillary diffusivity. The boundary conditions on this equation are such that ? = ?^sub s^ for x = 0 and time t == 0; ? = ?^sub d^ for x > 0, t = 0. ?^sub s^ and ?^sub d^ are the saturated and dry moisture contents, respectively. Using the Boltzmann transformation, where

[straight phi] = xt^sup 1/2^ (7)

allows this equation to be rewritten as an ordinary differential equation whose solution is

x(?,t) = [straight phi](?)t^sup 1/2^ (8)

This result indicates that as liquid is absorbed into a porous solid, the liquid profile maintains a constant shape, [straight phi](?), and advances as the square root of time.3

The total amount of liquid absorbed i in a given time t may be calculated from Eq. (8) and is given by

... (9)

The sorptivity S is defined by Eq. (9) and may be expressed as

... (10)

Sorptivity is often measured through simple testing according to the direct gravitmetric method, which seeks to engender a situation that is consistent with all the parameters involved in the derivation of Eq. (8). In particular, the test is intended to simulate one-dimensional flow into a semi-infinite porous material, where the initial and boundary conditions match those noted previously. A prismatic concrete specimen, usually cylindrical, is suspended above a pan of water so that its bottom face is in contact with the water. All other faces of the specimen are previously sealed. The specimen is initially dry, as sorptivity measurements can be sensitive to initial moisture content.3 The specimen is weighed periodically, and the weight gain divided by the crosssectional area of the specimen and the density of the water is plotted versus the square root of time. The slope of this plot corresponds to the sorptivity. Deviation from straight line behavior is possible. The interested reader is directed to Reference 3 for detailed discussion of this topic.

A review of the literature (References 7 through 9 among many others) shows that sorptivity values for neat cement tend to be higher than those for concretes, and further, that sorptivity values can vary by orders of magnitude from concrete to concrete, although typically the trends are for values between 0.1 and 5 mm/[radical]min (0.004 and 0.197 in./[radical]min). There are various test procedures that have been developed for measuring the water absorption properties of concrete in-place.10-13

The focus of the current research is the advance of the wetted front. For many porous materials, the capillary absorption profiles vary sharply with water content ?, and the leading part of the wetting profile is very sharp. These properties mean that the wetted region may be represented by a step function, that is, the material is considered either saturated (? = ?^sub s^) or dry (? = ?^sub d^).3 In this way, the wetted region is represented by a rectangular profile, and thus the Sharp Front Model of absorption. It may be shown3 that the distance to the wetted front t^sub w^ is given by

... (11)

where f is the porosity. Equation (11) is a key equation used throughout this work to estimate the distance advanced into a concrete specimen by the wetted front and, consequently, the volume of wetted specimen.

It is apparent then that the distance to the wetted front is dependent on three parameters, the porosity f, the sorptivity S, and the time of exposure to water t. For example, the distance to the wetted front is calculated as 1.89 mm (0.074 in.) for a concrete exposed to water for 60 minutes, with sorptivity of 0.03 mm/[radical]min (0.001 in./[radical]min) or 2.58 mm (0.102 in.) for a concrete exposed for 10 minutes with S = 0.1 mm/[radical]min (0.004 in./[radical]min). In all cases herein, the porosity f has been assumed to be f = 0.1225, a reasonable value for concrete.14

Expansion of cementitious materials exposed to water

It is well known2 that hardened concrete will continue to shrink upon drying. Furthermore, concrete that is subsequently re-exposed to water expands. Neville gives as a guide that the swelling strain a^sub w^ is on the order of 1/3 to 1/2 of the overall shrinkage strain a^sub s^.

Note that for any concrete specimen except those of the most minimal dimensions, the shrinkage due to aging or expansion upon water exposure will increase for some time. This increase is due to the fact that moisture movement in concrete is a relatively slow process. Aging shrinkage is a function of the drying out of a concrete specimen. The interior of a massive specimen will remain at a higher moisture content ? than the exterior for some time. The resulting moisture content gradient results in differential shrinkage, with the outer surface of the concrete shrinking at a faster rate than the inner portions. This interior region provides restraint to the free shrinkage that would take place if the entirety of the concrete specimen was at the same water content. Similarly, the interior of a wetted specimen of finite size may remain dry for some time, as the wetting front advances into the specimen. This interior dry region causes a restraint of the free expansion that would take place if the specimen was wetted in its entirety simultaneously. Thus, only values of unrestrained shrinkage or swelling strain are intrinsic to the material itself, other values are necessarily dependent on the test specimen geometry. Reported shrinkage and swelling strain values should therefore be taken from specimens of negligible dimensions, or as ultimate values (that is, at long enough times such that the interior of the test specimen has reached moisture equilibrium with the exterior).

Neville reports ultimate shrinkage strain values for various concretes of between 200 and 1200 microstrain, based on Reference 8. If those shrinkage strains are multiplied by the 1/3 factor recommended by Neville, the resulting swelling strains are between 67 and 400 microstrain.

ANALYTICAL APPROACH

The purpose of this study is to analyze the effect that swelling due to coring water will have on the in-place stress calculations of the core drilling method. The two parameters investigated were depth of water penetration t^sub w^ and magnitude of swelling strain a^sub w^. According to Eq. (11), t^sub w^ depends on three factors, the sorptivity of the specimen S, the time of water exposure t, and the porosity f. In fact, none of these parameters, S, t, f (from which t^sub w^ is derived), nor a^sub w^ is known for a particular test a priori, although t may be measured as the test is performed, and there are standardized tests that may be used to measure S in place. For the current work, values consistent with the literature and with coring practice have been used to present a baseline case.

When coring a hole, the specimen will be wetted primarily at two locations, namely, the top surface of the specimen, where the drilling water is introduced and around the circumference of the hole as the core is drilled. For this study, the assumed water exposure is divided into two portions as shown in Fig. 2. Portion A is the material around the circumference of the core hole, through the complete depth of the specimen, and Portion B, the material of only the top surface of the specimen. In this study, the top surface and the bottom surface refer to the initial drilling surface and the opposite surface, respectively.

During the coring operation, the material around the inner surface of the core hole is exposed to water only after the drill has reached that depth. Therefore, the profile of the water penetration through the surface for Portion A is likely not a constant linear function, as shown in Fig. 2, but could more accurately be represented by either a linear variation from top to bottom or by some polynomial function of higher order. Two key factors argue for the simplest approximation as shown in Fig. 2. First, it is known that the influence of interior loading or stress on the surface displacements decreases with increasing depth into the specimen,5 with a practical limit being that behavior at a depth below a distance of approximately a core hole diameter is not detectable at the surface. Thus, it is of minimal benefit to approximate the profile with higher order functions. Secondly, the profile is dependent on time of exposure and sorptivity of the specimen as noted previously. Only estimates of these quantities are used herein, making an exact, accurate representation of the wetted profile unwarranted.

The results from wetting Portion A and Portion B are superposed to generate the complete estimation of behavior due to water exposure. The overlap of the two portions is neglected, as it has been shown15 that this has a negligible impact on the results presented herein. Note that the behavior from each portion is axisymmetric about the core hole center, as the model and associated loads for each case comprise an axisymmetric system. The displacements of interest are those resulting from the difference between a dry uncored specimen and a wet cored specimen; these are the displacements modeled herein.

It is important to note that one of the assumptions in the derivation of the sorptivity parameter is violated during this approach, namely that the water absorption is one-dimensional. For example, for the water absorbed in Portion B, although the primary direction of water movement is down into the specimen, the wetted front will also advance radially outward from the extreme edge of the Portion B wetted area shown. It is believed that this difference is small and any effects it may produce are neglected herein.

The finite element (FE) method was employed to estimate surface displacements due to water-induced swelling. The water-induced swelling expansion was modeled statically by analogy in an FE program as swelling due to thermal effects.

After completion of a mesh refinement/convergence study, baseline cases for Portions A and B, with appropriate values for t^sub w^ and a^sub w^, were analyzed to determine the surface displacements caused by the swelling behavior.

As a baseline for this study, a value for sorptivity of S = 0.1 mm/[radical]min (0.004 in./[radical]min) was assumed. The exposure time t for the baseline case was assumed to be 60 minutes, which, in conjunction with the assumed sorptivity, yields a depth of water penetration t^sub w^ of 6 mm (0.236 in.), according to Eq. (11), for an assumed porosity of f = 0.1225. The swelling strain for the baseline case was assigned as 167 ? 10^sup -6^.

Three dimensional, eight-node trilinear displacement and temperature solid elements were used to create the Portion A and B models, as shown schematically in Fig. 3. The meshes for the two models are shown in Fig. 4. The center hole region was actually meshed with similar elements with negligible material and thermal properties and is not shown. The boundary conditions of the Portion A model were full symmetry on Face A, Face B, and Face C, so that one half the thickness of a slab specimen is represented. The Portion B model was similar, except that the full thickness of the slab specimen was modeled because the behavior in this case is non-symmetric about the midline through the thickness. The overall radius of the models R was chosen to ensure that edge effects did not influence the displacements near the core hole.

Equations (3) to (5) do not account for any behavior in the out-of-plane direction, and thus only the in-plane displacements from the finite element models are reported in this paper. When core drilling, the relieved displacements (due to stress relief rather than moisture uptake) attenuate rapidly with distance from the edge of the core hole. Thus, any displacement measurement during a core drilling method test for in-place stress will likely be performed in the surface region that is within approximately a core hole diameter or less from the edge of the core hole. Thus, moisture displacements will not be reported herein past a distance of 3a from the core hole center. The baseline model parameters are as follows: a = 75 mm (2.953 in.), t^sub s^ = 150 mm (5.906 in.), S = 0.1 mm/[radical]min (0.004 in./[radical]min), t = 60 minutes, a^sub w^ = 167? 10^sup -6^, r^sub w^ (Portion B) = 150 mm (5.906 in.), t^sub w^ = 6 mm (0.236 in.), E = 28,270 MPa (4100 ksi), ? = 0.20, R = 750 mm (29.528 in.), and f = 0.1225.

Figure 5(a) shows plots of the in-plane radial displacement versus the measurement radius for the baseline models. In the Portion A model, a strong peak is depicted in displacement that occurs at a measurement radius m, of approximately 82 mm (3.228 in.). This coincides closely to the value of the wetted radius r^sub w^ for this model. Note that for Portion A, r^sub w^ is simply the core hole radius a, plus the wetted thickness t^sub w^, and in this case is equal to 81 mm (3.189 in). For Portion B, the wetted radius must be chosen to simulate the expanse of surface area subject to wetting during core drilling. For the baseline Portion B case, this expanse was defined such that r^sub w^ = 2a = 150 mm (5.906 in.). The validity of this assumption was investigated.15 Unlike Portion A, where the displacements through the thickness of the modeled specimen are similar, the water-induced swelling of the top face causes bending of the specimen, and displacements that vary through the depth of the model. A plot showing the variation through the depth of the specimen at various radii is shown as Fig. 5(b). Overall, the top surface expands and the bottom surface contracts slightly. In particular, the wetted region expands in all directions, primarily radially outward, but also upward and radially inward (especially in the region closest to the core hole; for example, r = 75 to 100 mm [2.953 to 3.937 in.]).

The actual stresses in the concrete created by the moisture induced restrained swelling are small and are not shown herein, however, the moisture displacements are significant. Equations (3) to (5) were applied to the moisture displacements, as shown in Fig. 5(a), to yield the apparent in-place stress readings in the core drilling method that result entirely from swelling caused by moisture uptake. These calculated stresses are termed apparent stresses in this paper, and it is emphasized that they are not related to the in-place stress in the concrete at the time of the test. When evaluated within the equations, the moisture displacement fields generate apparent in-place stresses that appear primarily as hydrostatic tension, that is, s^sub x^ = s^sub y^, t^sub xy^ = 0, although on the bottom face of the Portion B model, the induced bending causes hydrostatic compression. This finding is significant and serves to explain some of the anomalous results of Reference 4, as shown in the subsequent section. Further, only one quantity needs to be tracked, namely the magnitude of the apparent hydrostatic tension stress. The apparent stress for each baseline model is plotted versus the measurement radius in Fig. 6.

As mentioned previously, relieved displacements (due to stress relief, not moisture uptake) attenuate rapidly with distance from the core hole. Thus, for a core hole radius a of 75 mm (2.953 in.), a measurement radius m considered might be 100 mm (3.937 in.), so that the magnitude of displacements can be captured by available measurement techniques. At m = 100 mm (3.937 in.), the baseline case apparent stress values are as follows: Portion A stress = 1.06 MPa (0.154 ksi), Portion B top face stress = -0.01 MPa (-0.001 ksi), Portion B bottom face stress = -0.28 MPa (-0.041 ksi), Portion B average stress = -0.15 MPa (-0.022 ksi), superposed top face stress = 1.05 MPa (0.152 ksi), superposed bottom face stress = 0.92 MPa (0.133 ksi), superposed average stress = 0.78 MPa (0.113 ksi).

A total of 54 models were created in which t^sub w^, a^sub w^, or both were varied from the baseline models. The magnitudes of the modified quantities were chosen to bound a realistic range of these two parameters. The range of t^sub w^ considered was from 2 to 25 mm (0.079 to 0.984 in.), corresponding to a sorptivity range of S = 0.03 to 0.40 mm/[radical]min (0.001 to 0.016 in./[radical]min) at an exposure time of 60 minutes, or S = 0.08 to 0.97 mm/[radical]min (0.003 to 0.038 in./[radical]min) at an exposure time of 10 minutes, for example (with f = 0.1225). The range of a^sub w^ considered was 167E-7 to 100E-5. A scatter-plot summary of the cases investigated is shown as Fig. 7, the corresponding data is available in Reference 15.

Similar to the baseline cases, the displacements from all the cases considered were converted to apparent stresses using Eq. (3) to (5). For the Portion A cases, the shape of the stress error versus measurement radius curves for all cases are quite similar, in each case, starting at an intermediate value of error at the core hole radius a, rising to some maximum value of error at an intermediate radius, and then smoothly diminishing from the peak value as the measurement radius increases further. This similarity allows each Portion A curve to be approximated as a combination of linear segments between defined key points, as shown in Fig. 8. In this manner, the apparent stresses for the Portion A models may be defined for any measurement radius via linear interpolation, provided the key point values are known.

With multiple linear regression techniques, statistical models were generated that describe each of the key points (the dependent variables) in terms of two independent variables, t^sub w^ and a^sub w^. The results of this procedure are a series of regression coefficients that denote the dependence of the output variable on each of the two input variables. Quadratic dependence on each of the dependent variables was considered, as was cross-dependence. Only those predictor terms that have statistical significance were retained.

The linear regression procedure was performed, yielding the regression equations

A^sub 75^ = 0.00138a^sub w^ + 0.000678a^sub w^t^sub w^ - 1.620E - 5a^sub w^t^sup 2^^sub w^ (12)

A^sub 100^ = 0.00141a^sub w^t^sub w^ - 1.775E - 5a^sub w^t^sup 2^^sub w^ - 0.00109a^sub w^ (13)

A^sub 125^ = 0.000750a^sub w^t^sub w^ - 7.062E - 6a^sub w^t^sup 2^^sub w^ (14)

A^sub MAX^ = 0.00119a^sub w^t^sub w^ - 8.445E - 6a^sub w^t^sup 2^^sub w^ + 0.00126a^sub w^ (15)

r^sub MAX^ = 74.25 + 1.402t^sub w^ (16)

where A^sub 75^, A^sub 100^, and A^sub 125^ are the apparent stresses at 75, 100, and 125 mm (2.953, 3.937, and 4.921 in.) and A^sub MAX^ and r^sub MAX^ are the apparent stress and radius at the point of maximum apparent stress. Note that a^sub w^ is expressed in microstrain, t^sub w^ in mm such that the units for the resulting apparent stresses are in MPa. To convert the results, note that 1 MPa is equal to 6.895 ksi.

Due to the number of key points required to fully define the apparent stress versus measurement radius curves on the top and bottom surface for the Portion B models (for example, refer to Fig. 6), only the apparent stresses on each surface of the slab specimen at m = 100 mm (3.937 in.) were deemed key points, for reasons explained in the next section. Following the same regression procedure, the following equations were obtained

... (17)

... (18)

where B^sub 100top^ and B^sub 100bottom^ are the apparent stresses in the Portion B models at a measurement radius of 100 mm (3.937 in.) on the top and bottom surface respectively, and the input units and conversion procedures are the same as for Eq. (12) to (16).

In addition to t^sub w^ and a^sub w^, other parameters that can potentially affect the moisture displacement behavior were investigated. Among them were object plan dimension R, the modulus of elasticity of the concrete E^sub c^, the assumed wetted radius r^sub w^, and the thickness of specimen t^sub s^. Provided R > 4a, the plan dimensions of the object do not unduly influence the results presented herein.15 The moisture displacements are negligibly effected by the concrete modulus; however, an examination of Eq. (3) to (5) reveals that this means that the apparent stresses scale directly with the concrete modulus. Thus, the apparent stress for concretes of any modulus should be calculated by multiplying results related herein by the ratio of the tested concrete modulus to the baseline modulus.

Models were created identical to the baseline Portion B model excepting that the thickness of the specimen ts was variable. The apparent stresses vary as the inverse of the specimen thickness. For example, Fig. 9 shows the values for B^sub 100top^ and B^sub 100bottom^ plotted versus the specimen thickness. The equations of the dashed lines in the figure are

... (19)

... (20)

where t^sub s^ is expressed in mm, and the results are in MPa. To convert results after calculation, note that 1 MPa is equal to 6.895 ksi.

The poor fit near t^sub s^ = 75 to 150 mm (2.953 to 5.906 in.) for the curve representing the bottom surface apparent stresses is likely due to the fact that with thinner specimens, the swelling behavior on the top face strongly influences the bottom face behavior, due to the proximity of the two faces in thinner specimens. It is recommended in this region (t^sub s^ = 75 to 150 mm [2.953 to 5.906 in.]) to use

B^sub 100bottom^ (t^sub s^) = -0.26 (21)

and to use Eq. (20) for thicker specimens.

The thickness investigation was based on the baseline Portion B case (that is, a^sub w^ = 167 ? 10^sup -6^, t^sub w^ = 6 mm [0.236 in.]). Although unverified, the general inverse t^sub s^ behavior noted should hold for other cases of a^sub w^ or t^sub w^, although the constants noted in Eq. (19) to (21) would change.

Although Eq. (19) to (21) are provided, it appears that for specimens with t^sub s^ > 300 mm (11.811 in.), it may be assumed that the thickness of the specimen has no influence on the apparent stresses, with little loss in accuracy. Considering the accuracy inherent in predictions for parameters such as sorptivity and swelling strain, it may be possible to neglect the thickness dependence altogether for specimens normally encountered in practice.

It is possible to superpose the apparent stress results of the baseline Portion A and B models to generate the complete apparent stress state due to the total moisture displacement field because the behavior is assumed to be linear elastic. Figure 10 shows the apparent stress versus measurement radius on the top and bottom faces for the superposed baseline case. The average of the top and bottom faces is also shown and is used in the next section. It is noted that the apparent stresses at 100 mm (3.937 in.) follow directly from

AB^sub 100top^ = A^sub 100^ + B^sub 100top^ (22)

AB^sub 100bottom^ = A^sub 100^ + B^sub 100bottom^ (23)

... (24)

as expected. Note that if adjustment is to be made based on specimen thickness ts (following Eq. (19) to (21)), it should be performed prior to substitution of B^sub 100top^ and B^sub 100bottom^ into Eq. (22) to (24).

At m = 100 mm (3.937 in.), values of apparent stress for cases with t^sub w^ and a^sub w^ other than as for the baseline case may be calculated by using the regression equations (Eq. (13), (17), and (18)). The values calculated via regression can be substituted into Eq. (22) to (24) noted previously to yield the appropriate apparent stresses.

APPLICATION TO EXPERIMENTAL RESULTS

Introduction and background

Buchner4 presents the results of a series of tests using a method similar to the core drilling method that measured stress in a number of concrete slabs. Although an error in applied stress versus measured stress of approximately ?10% was reported as being potentially achievable, for the nine slabs tested with a core hole radius of 75 mm (2.953 in.) (some others were tested with a = 37.5 mm [1.476 in.]), the average error is considerably higher, especially at measurement times immediately following the coring of the slabs. The approach outlined previously to correct for moisture induced swelling was applied to the data from these nine slabs to evaluate the influence of this correction on the predicted stresses.

The slabs tested by Buchner measured approximately 1 x 1 x 0.1 m (39.37 x 39.37 x 3.937 in.). The slabs were demolded approximately 20 hours after casting and allowed to cure under plastic for 1.5 to 2 days before being moved to a storage room and stored in an upright position that allowed drying from both faces. The slab dimensions and age at testing are contained in Table 1; the water-cement ratio (w/c) of the mixture was 0.4. Although Reference 4 is slightly ambiguous on this point, the shrinkage strain of the tested concrete was estimated previously by Buchner to be 520 ? 10^sup -6^, which, as noted previously, corresponds to a swelling strain a^sub w^ of approximately 173 ? 10^sup -6^.

Loading of the slabs was accomplished in an upright position within a steel testing frame that consisted primarily of a braced cross-beam supported above a concrete reaction floor. A series of small 199.3 kN (20 ton) capacity hydraulic jacks suspended from the cross-beam were used to load the slabs. To ensure load uniformity, a thick steel load redistribution plate was placed between the slab and the jacks, and plastic padding was used to level the edges of the slabs. Biaxial loading of a slab was accomplished through the use of a self stressing frame consisting of two pairs of threaded rods connected to two 498.2 kN (50 ton) jacks on one side of the slab and a steel load distribution beam on the opposite side of the slab. A pivoting system was incorporated to ensure that load was applied only in the plane of the slabs.

The slabs were wet cored with a 150 mm (5.906 in.) coring bit (a = 75 mm [2.953 in.]) and instrumented around the hole with radial arrays of vibrating wire and demountable mechanical strain (DMS) gauges. An orthogonal grid of DMS targets with coverage of the entire slab was also used, in addition, deformation readings on the core material itself were performed. Although Reference 4 details the results from all of these numerous measurement devices, only the results from the demountable mechanical strain gauges arrayed in a measurement circle with radius m = 100 mm (3.937 in.) are reviewed herein.

Buchner calculates in-place principal stresses from the strains derived from measuring across the hole at the DMS target locations. Readings were taken immediately after coring, and repeated for several subsequent hours. The results reviewed herein are the average of the reading from immediately after coring and the reading taken 1 to 2 hours after coring. These readings correspond to a time of water exposure t of approximately 30 to 60 minutes, although the water source in this case is not a continuous reservoir as is typically assumed in the sorptivity derivations presented earlier. Furthermore, data reported at these early times should minimize the influence of other time-dependent phenomena, such as creep. In a different, preliminary slab test, Buchner detailed stress results on both faces of a slab (top and bottom), and reported,

"...tensile strains created by water absorption on the front face, caused a warping effect which resulted in greater compressive strains measured on the back face. This implied that a bending process was induced due to the coring water."

Each stress reported by Buchner is the average of principal stresses calculated on the front and back faces of the slabs.

Columns (1) through (11) of Table 1 summarize the important experimental parameters for each of the nine slabs. The SRSS error column is the square root of the sum of the squared values for the errors in s^sub max^ and s^sub min^. Where the applied s^sub max^ stress was equal to zero, the relative difference in the measured s^sub max^ value is referenced to the applied s^sub min^ value.

An examination of the measured data in Table 1 shows that for every slab, the calculated stresses appear to differ from the applied stresses primarily by a hydrostatic tension stress. As an example, Fig. 11 shows a Mohr's circle representation of the applied and measured stresses of Slab II. The diameter of each circle is approximately the same, so they differ only by a hydrostatic stress. The calculation of the adjusted stress Mohr's circles in the figure is described subsequently. From this observation, and the quote noted previously, it is reasonable to conclude that coring water significantly affected the Buchner results.

Correction for wetting

To correct the Buchner results for swelling strains, the complete superposed Portion A and B baseline case results calculated herein may be removed from the measured stresses. Although sorptivity, time of water exposure, porosity, and swelling strain were not explicitly reported by Buchner, some estimates are made after the fact. As noted previously, a^sub w^ was approximately 173 ? 10^sup -6^ for the Buchner study, similar to the 167 ? 10^sup -6^ used for the baseline case herein. Furthermore, for the data summarized, t is approximately 30 to 60 minutes, corresponding to a sorptivity value of S = 0.095 to 0.134 mm/[radical]min (0.004 to 0.005 in./[radical]min) if the baseline case of t^sub w^ = 6 mm (0.236 in.) is applied (with f = 0.1225). These values are well within the bounds for sorptivity and swelling strain noted previously.

Columns (12) to (17) of Table 1 show the effects of removing the baseline case apparent hydrostatic stress from the Buchner data. For each case, the baseline Portion B apparent stress value been translated from the baseline slab thickness (t^sub s^ = 150 mm [5.906 in.]) to the Buchner slab thickness (t^sub s^ = 100 mm [3.937 in.]) using Eq. (19) to (21). After the Portion A and B baseline results are superposed, the resultant is scaled by the ratio of the individual Buchner slab elastic modulus divided by the baseline modulus (E = 28,270 MPa [4100 ksi]). The apparent stress removed is the average of the values from the top and bottom faces. The removal of these apparent stresses reduces the average RSS error from 47 to 14%, a significant improvement.

Clearly, if more were known regarding the properties of the concrete that was tested, the appropriate values for aw and t^sub w^ for each slab could be used to generate the correct moisture induced hydrostatic apparent stress for each slab. If the in-place stress for each slab was corrected individually in this manner, it is possible that the average RSS error would be further reduced. Regardless, even with no other knowledge, the correction with the baseline case apparent stress results reduced the errors by more than a factor of 3. Furthermore, the apparent stresses generated by the analytical procedure follow the trends noted in Reference 4 regarding bending in the slabs introduced as a result of the coring water. A clear bending pattern is present in the Portion B results.

CONCLUSIONS

A method to calculate apparent stresses due to coring water-induced swelling has been presented. To increase the accuracy of the core drilling method technique, these apparent stresses should be removed from the in-place stresses so derived.

The following conclusions are made:

1. It was found that the apparent stresses are primarily tension stresses, and furthermore, that they are hydrostatic in nature, that is, s^sub x^ = s^sub y^ and t^sub xy^ = 0. In addition, the coring water causes apparent stresses that appear as bending through the thickness of a plate specimen;

2. For the baseline case (t^sub w^ = 6 mm [0.236 in.]), a^sub w^ = 167 ? 10^sup -6^), the apparent stresses at m = 100 mm (3.937 in.) are as follows: AB^sub 100top^ = 1.05 MPa (0.152 ksi), AB^sub 100bottom^ = 0.78 MPa (0.113 ksi), and AB^sub 100avg^ = 0.92 MPa (0.133 ksi). Apparent stresses for other values of t^sub w^ and a^sub w^ may be calculated via Eq. (12) to (16) and Eq. (17) and (18), along with Eq. (19) to (21);

3. If approximations are warranted, typical values for the moisture movement and swelling parameters (such as those from the reference literature) may be used. Methods for measuring sorptivity both in the laboratory and in-place, respectively, are available if more accurate values of S and hence t^sub w^ are desired; and

4. The approach described herein was used to show that errors in calculated relative in-place stresses in an independent study of concrete slabs are reduced from 47 to 14% for the baseline case.

ACKNOWLDEGMENTS

This research was funded by the Pennsylvania Infrastructure Technology Alliance. Additional support was provided by the Precast/Prestressed Concrete Institute, the Center for Advanced Technology for Large Structural Systems, and by the Department of Civil and Environmental Engineering at Lehigh University. Their support is gratefully acknowledged.