{"id":109,"date":"2021-03-27T17:46:30","date_gmt":"2021-03-27T17:46:30","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/chapter\/solution-exercise-2\/"},"modified":"2021-04-05T00:57:07","modified_gmt":"2021-04-05T00:57:07","slug":"solution-exercise-2","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/chapter\/solution-exercise-2\/","title":{"raw":"Solution Exercise 2","rendered":"Solution Exercise 2"},"content":{"raw":"
\r\n

1) Confined response <\/em><\/p>\r\n

Assume the hydraulic conductivity of the till is so much lower than that of the fractured bedrock that horizontal flow from the till into the pit is negligible, but vertical leakage downward into the fractured bedrock keeps the fractured bedrock fully saturated, thus the fractured bedrock responds as a confined unit. In this case, the time-varying inflow rate Q(t) can be approximated by the equation:<\/p>\r\n

Q(t) = (4\u03c0<\/em>Kbs<\/em>w<\/em><\/sub>) \/ (2.3 log (2.25Kbt \/ r<\/em>p<\/em><\/sub>2<\/sup>S))<\/em><\/p>\r\n

where:<\/p>\r\n

K<\/em> is the hydraulic conductivity of the fractured bedrock horizon (5x10-<\/sup>6<\/sup> m\/s)<\/p>\r\n

b<\/em> is the thickness of the fractured bedrock horizon (30 m)<\/p>\r\n

S<\/em>w<\/em><\/sub> is the design drawdown at the pit face (30 m - 5 m) = 25 m<\/p>\r\n

r<\/em>p<\/em><\/sub> is the radius of the open pit (200 m)<\/p>\r\n

S<\/em> is the specific storage (1x10-<\/sup>5<\/sup> m-<\/sup>1<\/sup>)<\/p>\r\n

After a period of 3 years, the calculated inflow is approximately 360 m<\/strong>3<\/sup>\/d.<\/strong><\/p>\r\n

2) Unconfined response<\/em><\/p>\r\n

For the case where the water table is near the top of the fractured bedrock, the pores of the fractured bedrock will drain so it responds as an unconfined unit, with Q(t)<\/em> approximated by:<\/p>\r\n

Q(t) = (4<\/em>\u03c0<\/em>Kbs<\/em>w<\/em><\/sub>) \/ (2.3 log (2.25Kbt \/ r<\/em>p<\/em><\/sub>2<\/sup>S<\/em>y<\/em><\/sub>))<\/em><\/p>\r\n

S<\/em>y<\/em><\/sub> is the specific yield (0.03).<\/p>\r\n

After a period of 3 years, the calculated inflow is approximately 1240 m<\/strong>3<\/sup>\/d.<\/strong><\/p>\r\n

The predicted inflow is higher for the case where the fractured bedrock acts as an unconfined aquifer because of the greater volume of water released from storage for a unit decline in hydraulic head when the fractured bedrock unit dewater, in comparison to the case where water is released only from elastic storage.<\/p>\r\n

This comparison highlights the fundamental importance of the conceptual model used to characterize the hydrogeologic system, even when using simplified analytical models for order-of-magnitude estimates.<\/p>\r\n

Both calculations assume a negligible inflow to the open pit from the underlying low-permeability bedrock. This is a reasonable approximation given a hydraulic conductivity value of 10-9<\/sup> m\/s. If there were a permeable fracture zone within the deeper bedrock that intersected the pit flow, then higher flows could be anticipated if that fracture zone was itself connected to a more permeable hydrogeologic unit.<\/p>\r\n

Return to Exercise 2<\/span><\/a><\/p>\r\n\r\n<\/div>","rendered":"

\n

1) Confined response <\/em><\/p>\n

Assume the hydraulic conductivity of the till is so much lower than that of the fractured bedrock that horizontal flow from the till into the pit is negligible, but vertical leakage downward into the fractured bedrock keeps the fractured bedrock fully saturated, thus the fractured bedrock responds as a confined unit. In this case, the time-varying inflow rate Q(t) can be approximated by the equation:<\/p>\n

Q(t) = (4\u03c0<\/em>Kbs<\/em>w<\/em><\/sub>) \/ (2.3 log (2.25Kbt \/ r<\/em>p<\/em><\/sub>2<\/sup>S))<\/em><\/p>\n

where:<\/p>\n

K<\/em> is the hydraulic conductivity of the fractured bedrock horizon (5×10–<\/sup>6<\/sup> m\/s)<\/p>\n

b<\/em> is the thickness of the fractured bedrock horizon (30 m)<\/p>\n

S<\/em>w<\/em><\/sub> is the design drawdown at the pit face (30 m – 5 m) = 25 m<\/p>\n

r<\/em>p<\/em><\/sub> is the radius of the open pit (200 m)<\/p>\n

S<\/em> is the specific storage (1×10–<\/sup>5<\/sup> m–<\/sup>1<\/sup>)<\/p>\n

After a period of 3 years, the calculated inflow is approximately 360 m<\/strong>3<\/sup>\/d.<\/strong><\/p>\n

2) Unconfined response<\/em><\/p>\n

For the case where the water table is near the top of the fractured bedrock, the pores of the fractured bedrock will drain so it responds as an unconfined unit, with Q(t)<\/em> approximated by:<\/p>\n

Q(t) = (4<\/em>\u03c0<\/em>Kbs<\/em>w<\/em><\/sub>) \/ (2.3 log (2.25Kbt \/ r<\/em>p<\/em><\/sub>2<\/sup>S<\/em>y<\/em><\/sub>))<\/em><\/p>\n

S<\/em>y<\/em><\/sub> is the specific yield (0.03).<\/p>\n

After a period of 3 years, the calculated inflow is approximately 1240 m<\/strong>3<\/sup>\/d.<\/strong><\/p>\n

The predicted inflow is higher for the case where the fractured bedrock acts as an unconfined aquifer because of the greater volume of water released from storage for a unit decline in hydraulic head when the fractured bedrock unit dewater, in comparison to the case where water is released only from elastic storage.<\/p>\n

This comparison highlights the fundamental importance of the conceptual model used to characterize the hydrogeologic system, even when using simplified analytical models for order-of-magnitude estimates.<\/p>\n

Both calculations assume a negligible inflow to the open pit from the underlying low-permeability bedrock. This is a reasonable approximation given a hydraulic conductivity value of 10-9<\/sup> m\/s. If there were a permeable fracture zone within the deeper bedrock that intersected the pit flow, then higher flows could be anticipated if that fracture zone was itself connected to a more permeable hydrogeologic unit.<\/p>\n

Return to Exercise 2<\/span><\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":39,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-109","chapter","type-chapter","status-publish","hentry"],"part":246,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapters\/109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":9,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapters\/109\/revisions"}],"predecessor-version":[{"id":360,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapters\/109\/revisions\/360"}],"part":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/parts\/246"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapters\/109\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/wp\/v2\/media?parent=109"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/pressbooks\/v2\/chapter-type?post=109"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/wp\/v2\/contributor?post=109"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeology-and-mineral-resource-development\/wp-json\/wp\/v2\/license?post=109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}